UNIVERSE WITHOUT SPACE
AND TIME

Universe
without Space and Time

An Essay on Principles
for Relational Cosmology Drawn from Catholic Tradition and Empirical Science

Rev. Victor P. Warkulwiz,
M.S.S., Ph.D.

Albertus Magnus Apostolate for Religion and
Science

Missionary Priests of the Blessed
Sacrament

Bensalem, PA

Copyright © 2013 by Missionary Priests
of the Blessed Sacrament

ISBN: 978-0-9888603-2-2

Cover: The triangular logo represents relational
cosmology. It is inspired by the doctrine of the Most Holy Trinity. The
triangle has long been the symbol of the Trinity. Each vertex represents a
Divine Person and the lines help express their relations. These relations are
what constitute the distinction between the Persons. They cannot be
distinguished by any attribute because each Divine Person possesses the one
unique infinite Divine Nature completely to Himself. Whatever distinction there
is must be in their relations alone. Analogously, in relational cosmology each
celestial body in the universe is not distinguished from the others by their
locations on an absolute space-time grid. Rather, each one possesses the one
unique universal plenum completely to itself, and it can only be distinguished
from others by their relations with it on its own space-time grid. And, like in
the Trinity, these relations are ultimately a mystery.

Table of Contents

About
the Book.. 7

Introduction.. 8

Chapter
ONE: Medieval and Enlightenment Notions about Place, Space and Time.. 10

Medieval Biblical Theology and
Enlightenment Ideology. 10

Enlightenment Ideology and
Natural Truth. 12

Medieval Notions of Place and
Void. 14

Enlightenment Notion of Space. 26

Medieval and Enlightenment
Notions of Time. 40

Chapter
TWO: Sacred Scripture and the Earth as the Center of the Cosmos  45

The Creation of Heaven and
Earth. 45

The Formation of Heaven and
Earth. 50

The Earth as the Center of
Rest 59

The Notion of Absolute Rest:
Historical Summary. 62

Medieval Earth-Centered
Cosmology and its Decline. 63

Chapter
THREE: Empirical Science and the Earth as the Center of the Cosmos  66

The Logic of Absolute Motion. 66

The Physics of Local Motion. 67

Astronomical Phenomena
Pertaining to the Stability of the Earth  68

Optical Experiments
Pertaining to the Stability of the Earth. 71

Comments on the Nature and
Motion of Light 75

Geometrical and Physical
Centricity of Earth. 76

Chapter
FOUR: The Logic of Newtonian Physics and Relativity   79

Newton’s Laws of Motion and
Inertial Frames. 79

Electrodynamics and
Einstein’s Postulates for Special Relativity  83

Kinematical Contradictions of
Special Relativity. 91

Special Relativity without
Contradictions. 92

General Relativity and
Absolute Space. 100

CHAPTER
FIVE: THE LOGIC OF RELATIONAL PHYSICS  107

Relational Mechanics. 107

Absolute and Relational
Spaces United. 115

Relational Optics. 120

Instantaneous Action at a
Distance, Cause Propagation, and Communication  129

Extension, Timekeeping and
Mass. 149

Chapter
SIX: Conclusion—Principles for Relational Cosmology   157

Appendix
A: Spectroscopic Binaries. 171

Appendix
B: Observations Pertaining to the Relative Rotation of the Earth and the Stars. 172

Bibliography.. 173

About
the Author.. 180

About the Book

This essay is entitled Universe
without Space and Time because it proposes a cosmology that discards the
notion that space and time are independent entities, either in Newton’s sense
of absolute space and time or in Einstein’s sense of a self-subsistent
space-time manifold. Instead, it treats space and time as relational quantities
that are wholly dependent on matter for their meaning. It develops the
scholastic way of thinking about space and time, which is the fruit of
meditation on the biblical account of creation, and results in a way of looking
at the cosmos that is refreshingly different from that of modern cosmology. It
is an essay on principles, which means that it is not a full-blown cosmology
but starting points for a Catholic biblically-inspired cosmology. The
principles are drawn from Sacred Scripture as interpreted in Catholic Tradition
(as passed on by the Fathers, Doctors and Magisterium
of the Church) and from the observations of empirical science. It may be that
more than one consistent cosmology can emerge from the principles because they
may not be powerful enough or complete enough to produce a unique cosmology

The content of
the essay is conceptual and non-mathematical. It is directed to the
scientifically literate reader, both professional and lay. Although written
from a Catholic perspective, the book is intended to appeal to believers of all
faiths that hold Genesis to be the inerrant Word of God. Even readers who do
not agree with the theme of the book will find much in it that enhances their
understanding of the natural world.

Introduction

This essay is a sequel to my
previous work The Doctrines of Genesis 1-11: A Compendium and Defense of
Traditional Catholic Theology on Origins. I call this work an “essay”
because it presents a personal point of view that is not to be interpreted as
religious or scientific dogma. The principles I set forth are drawn from Sacred
Scripture as interpreted in Catholic Tradition (as passed on by the Fathers,
Doctors and Magisterium of the Church) and from the
observations of empirical science. I appeal to empirical science rather than
theoretical science because the latter is often based more on ideas than facts.

I had no
intention whatsoever of formulating a new cosmology, but in doing research for The
Doctrines of Genesis 1–11 a new cosmological picture began to form in my
mind. I also discovered that the cosmological questions asked by the ancient
and medieval scholars were more pertinent to understanding the cosmos than
those asked by modern scientists. Since the seeds of my thought are in The
Doctrines of Genesis 1–11, I have borrowed liberally from that work, in
some cases whole passages verbatim.

I’ve always
found modern books on space and time boring because the ideas are drawn from
impoverished and godless doctrines of the Enlightenment. Modern science, which
employs those doctrines, is out of its depth when it pontificates on the nature
of space and time because the true nature of space and time lies outside the
set of ideas that confines it.

I hope the
reader will find this work less boring than I have found those works. I made
every effort to stick to the truths of divine revelation and the empirical
facts, both of which work together to give us the most complete and accurate
picture of the cosmos that is possible in this life. And such a picture is not
boring but awesome and beautiful because it is the work of God and is
recognized as such.

I entitled this
essay Universe without Space and Time because it proposes a cosmology
that discards the notion that space and time are independent entities, either
in Newton’s sense of absolute space and time or in Einstein’s sense of a
self-subsistent space-time manifold. Instead it treats space and time as
relational quantities that are wholly dependent on matter for their meaning.
What all this means should become clearer as the reader proceeds through the essay.
Suffice it to say now that it develops the scholastic way of thinking about
space and time, which is the fruit of meditation on the biblical account of
creation.

In the subtitle
I say that it is an essay on “principles.” By this I mean that I am not
offering a full-blown cosmology but only starting points for a Catholic
biblically-inspired cosmology. It may be that more than one consistent
cosmology can emerge from these principles. The principles may not be powerful
or complete enough to produce a unique cosmology.

In the first
chapter I discuss medieval notions of place and time and the enlightenment
notions of absolute space and time. The former are based on divine revelation;
the latter are based on human ideas and ignore divine revelation. In the second
and third chapters I discuss the biblical notion of the earth as the center of
rest in the universe and how this is misunderstood. In the fourth chapter I
discuss the logic of Newtonian and relativistic physics and their common errors
that lead to a false picture of the cosmos. In the fifth chapter I discuss
relational physics, which treats space and time as epiphenomena (or accidents)
of matter and is consistent with traditional Catholic doctrine. Finally, in the
conclusion I collect and summarize the principles that have been put forth.

Rev. Victor P. Warkulwiz, M.S.S.

Chapter ONE: Medieval and Enlightenment
Notions about Place, Space and Time

Medieval Biblical Theology
and Enlightenment Ideology

The High Middle Ages (12th–13th
centuries) was a period of great intellectual activity in Europe. Under the
sponsorship of the Church, Catholic scholars pursued studies in a wide variety
of subjects that included both the spiritual and physical aspects of reality.
One field of interest was natural philosophy, which was concerned with
knowledge about the material world. The medieval scholar observed the world
with his limited technical means of observation. He interpreted his
observations in light of the biblical record, using the Fathers of the Church as
trustworthy exegetical guides. Thus, his foundation for the study of creation
was biblical theology. He also employed the insights of Greek authors, such as
Plato and Aristotle, Arabic authors, such as Avicenna and Averroes, and Jewish
authors, such as Philo and Maimonides. The beginnings of experimental science
are found in the work of Robert Grosseteste and Roger
Bacon. The reasoning of medieval scholars was guided by divine revelation as
proclaimed in Sacred Scripture, Sacred Tradition, and the official decrees of
the Church. The doctrines of the faith disciplined reason and prevented it from
going wild. Because of the widespread and wholehearted acceptance of the
Catholic faith by the European people of that era, the High Middle Ages has
come to be called the Age of Faith

The
Enlightenment (17th–19th centuries) was a period of wholesale rejection of
medieval scholasticism and traditional authority by many of the influential
intellectuals of Europe. It was characterized by scientific, philosophical,
religious and rational attitudes that departed significantly from those of the
Christian Middle Ages. The major figures (literary men, scientists and
philosophers) of the Enlightenment were united in their belief in the supremacy
of reason. In France, their verbal and written attacks on the government and
the Church impelled the physically violent attacks of the French Revolution. In
England the Enlightenment took the form of a cold scientific intellectualism,
which produced some advances in scientific methods but also introduced
seriously flawed scientific notions such as biological transformism
and uniformitarian geology. Because of the divinization of the human mind by so
many of the intellectuals of the era, the Enlightenment has come to be called
the Age of Reason.

Enlightenment
ideology is a way of thinking that was conceived in the humanism of the
Renaissance (14th–17th centuries), born in the rationalism of Enlightenment,
came of age in the atheism of the Modern Era (19th–20th centuries), and has
reached adulthood in the neo-paganism of the Postmodern Era (21st century). It
is the attitude of mind inherited by modern scientists, including the many
Christian ones who compartmentalize it in their scientific work. Enlightenment
ideology is

1. ideological
because it places total confidence in its own set of human ideas and none in
divinely or humanly established authority;

2. rationalistic
because it holds that human reason is the supreme arbiter of truth;

3. naturalistic
because it holds that the world alone can tell us everything there is to
know about it;

4. materialistic because it
asserts that all manifestations of the supernatural (such as miracles and
design in nature) are explainable by physical causes, even if those causes
cannot be identified;

5. scientistic
because it places exaggerated trust in efficacy of the methods of natural
science, and it condescendingly applies those methods to other fields of
knowledge.

Enlightenment
ideology pilots modern science. The study of nature today is guided exclusively
by observation, experiment, and ideologically-governed reason. Divine
revelation is excluded as a source of knowledge; human ideas replace divine
revelation. Observation and experiment have been enhanced by modern technical
innovations, but those are products of discovery and tinkering, not of
enlightenment ideology.

Enlightenment Ideology and
Natural Truth

Enlightenment ideology succeeds
admirably in inventing methods for squeezing facts out of nature. But it fails
miserably in the interpretation of those facts. It succeeds in the former
because it meticulously conforms itself to naturally revealed truth. It fails
in the latter because it resolutely refuses to be informed with divinely
revealed truth.

Enlightenment
ideology, by not allowing itself to be guided by divine revelation, has sent
science off in the wrong direction in a number of areas. By rejecting the
creation account in Genesis 1 it has given a false cosmology and a false
biology. Genesis 1 clearly teaches that the universe was created and formed
over a period of six days; living creatures were created instantly, each with a
complete fixed living nature. That picture is direct opposition to that given
to us by big bang cosmology and evolutionary biology, which tell us that the
celestial creatures were formed over billions of years and that the living
creatures continually transform into creatures with more and more complex
natures. Unbiased observation of the natural world clearly supports the
biblical picture. This is shown in many places.

The rejection of
the account of the creation of man in Genesis 2 by enlightenment ideology has
led to false anthropology, false psychology and false sociology. Genesis 2
clearly teaches that the first man and woman were specially created by God, who
gave them a nature that was both material and spiritual. This gave them a
nature that was different in kind and not only degree from all the other
members of the animal kingdom. This difference is made manifest in the
intellectual and volitional life of the human being. God made the first man and
woman persons, like Himself. In their intellectual and volitional life and
personhood, God made the first couple images of Himself.
But modern “enlightened” anthropology denies this. It sees the human being,
either wholly or in its material component, as having “evolved” from lower
forms of life through an innumerable (and unobserved) succession of
intermediate forms. It sees the spiritual element in man (the soul) either as
an illusion or as an epiphenomenon of matter, having gradually emerged from it.
This view has led to a purely animalistic human psychology, which views human
personhood as little more than a succession of conscious states. This aberrant
psychology manifests itself in erroneous sociological notions. For example, in
totalitarian states, inspired by evolutionary biology, people have been
deprived of their rights as persons and treated solely as servants to the
community, like a bees in a hive. Also evolutionary biology inspired the notion
that animals have rights, just like human beings. Some extreme activists even
see animals as having a priority in rights over humans simply because they were
here first. These and other bizarre notions are the spawn of evolutionary
biology.

The rejection of
the biblically-attested fact that the world was completely destroyed by a
universal flood as related in Genesis 6-8 has given rise to a false geology,
namely uniformitarian geology. Uniformitarian geology insists that the features
on the earth were produced by slow processes acting over millions of years and
not by a worldwide catastrophe like the great flood. The geological data,
however, provide strong evidence in favor of a worldwide catastrophe.

By rejecting the
primal history of the human species as related in Genesis 9-11, enlightenment
ideology has misled archaeology, preventing it from giving proper
interpretations to its data. And by rejecting the account of the origin of
languages given in Genesis 11, enlightenment ideology has further misguided
cultural anthropology.

By presuming
that the earth moves absolutely in space around the sun, in conflict with
Sacred Scripture, astronomers pretend to measure distances to celestial
objects. Since they cannot demonstrate that the earth moves absolutely, their
results are inconclusive. Yet they present their distances as if they were
unquestionable facts.

Finally, by not
drawing the proper inferences from the creation account in Genesis 1, modern
physics has given us false notions about the nature of space (or void) and
time. Medieval thinkers, like St. Thomas Aquinas, guided by the scriptural
record, formed correct notions about space and time but did not develop them.
The present work is a beginning of such a development in the light of current
knowledge.

Medieval Notions of Place and
Void

Medieval scholars did not employ the concept of free space
that we have inherited from the Enlightenment, even though it had been
conceived in antiquity by the Greek atomists. So to understand how they
thought, we must do our best to set aside our concept of free space. This is
very difficult indeed because it is so deeply ingrained in our minds and
imagination. We can hardly believe that there can be any other way to conceive
the universe than as being imbedded in an independently-existing
three-dimensional void.

To condition yourself for a change in perception do the following thought
experiment: Image yourself being present on the first day of Creation. The
material universe consists of the earth alone, which is completely covered with
water. God equips you with scuba gear and a few devices and places you beneath
the surface of the water. This is where you come to consciousness. You start to
test your environment by letting go of a few hollow rubber balls that God gave
you. You find that they float up to a certain point and go no further. Thus you
deduce that where they stopped is the boundary of the universe in which you
were placed. At this point you can’t imagine anything being beyond there
because nothing you have experienced so far suggests that there is. You name
the region where the balls stopped the “surface” of the water. It is the
boundary that defines the “place” where you live.

*

The concept of place
held much significance for medieval scholars. Their conceptions of place were
built on that of Aristotle. Aristotle struggles with the notion of place
in Book IV of his Physics. He concludes by defining it as follows: Place
is “the innermost motionless boundary of what contains” [1, p. 278]. So in our
thought experiment so far, the complete surface of the water contains the place
of the earth; but that surface itself does not have a place because nothing
contains it.

Aristotle goes
on to say that only movable bodies have a place. The term “movable” has no
meaning on the first day of Creation because then only the earth existed. At
least two bodies must exist for the word motion to have meaning. So the
question of whether or not the earth moves will be moot until the fourth day of
Creation, when the heavenly bodies are created. Sacred Scripture tells us that
God made the earth the standard of rest in the universe, but this does not mean
that the earth is incapable of being moved. We can feel free to apply Aristotle’s
definition of place to it, even on Day One.

For a summary of
Aristotle’s views on space and place see [2].

Pierre Duhem gives a comprehensive survey of medieval notions
about place in chapters 4–6 of [3]. Duhem points out that
there was ample development of the theory of place at the University of Paris
in the middle of the thirteenth century. Especially interesting are the views
of St. Thomas Aquinas. In a discussion of the motions of the heavens around the
earth, in his Expositio super libros De Caelo et Mundo, he makes the
observation that the center of rotation must exist in a corporeal body. St.
Thomas said:

There has to be
something remaining immobile at the center of a body moving circularly. It is
evident that any circular movement occurs around a fixed center. And it needs
to be that this center is located in a fixed body, for what we call the center
is not something subsisting in itself. It is an accident belonging to something
corporeal; this center can only be the center of a body. [3, p. 153]

Aquinas goes on
to say that the rotations of the heavens would be a meaningless notion if the
earth did not exist:

This fixed body must
be part of the world … but it cannot be part of the mobile orb, meaning the
celestial body.… That which is at the center is eternally immobile, as heaven
moves eternally.… And that which is naturally immobile at the center is the
earth.… Therefore, if heaven revolves eternally, the earth has to exist. [3, p.
153]

Aquinas sees the
notion of place as intimately connected with the motion of corporeal bodies. In
his In libros Physicorum Aristotelis he
states:

Place would not be
investigated if it were not for movement; movement calls attention to place
because bodies succeed each other in one place. Hence although a body does not
of necessity have a place, nevertheless, a body moved with respect to place
does have a place of necessity. Therefore, it is necessary to assign a place to
a body moved in place insofar as one considers in that movement a succession of
various bodies in the same place. Thus in things moved in a straight line, it
is clear that two bodies succeed each other in place with respect to the whole.
For the whole of one body leaves the whole place and into that whole place another
body enters. Hence it is necessary that a body moved in a straight line is in
place with respect to its whole self. [3, p. 154]

Aquinas accepted
the geocentric cosmology of Aristotle and Ptolemy, as did apparently all of his
contemporaries. Thus the movements that he was primarily interested in were the
circular movements of the heavens. The heavens were thought to move around the
earth like spherical shells. The ultimate or final celestial sphere was thought
by some to have a place; others reasoned it had no place because it did not and
could not exhibit local movement but only circular movement. Aquinas, further
on in In libros Physicorum Aristotelis, gives his view:

Therefore in
circular movement attention is directed to the succession in the same place,
not of whole bodies, but of parts of the same body. Hence for a body moved in a
circle, a place with respect to the whole is not due of necessity, but only in
respect of the parts.… Moreover it is much more suitable to say that the
ultimate sphere is in place because of its own intrinsic parts than because of
the center which is altogether outside of its substance; and this is more
consonant with the teaching of Aristotle. [3, p. 154]

A paradox that
vexed the medieval scholars was the notion that, according to Aristotle, place
was at once both movable and immovable. It seemed moveable because it was
somehow attached to the body in motion. It seemed immovable because another
body moved into it after a first body left it. Aquinas resolved the paradox by considering
that place has two senses, one referring to the body itself and the other
referring to ambient bodies. The first means that for a place to exist there
must be a body to be in place; that is, there is no such thing as absolute
place, place without a physical body. The second means that a body has a
relationship to other bodies that is called place. In De natura loci, which is attributed to St. Thomas, the author
explains that the “set of celestial bodies” is the reference base for
identifying an immobile place:

That is the way in
which we ought to understand that the extreme parts of natural bodies form the
place of other bodies; they form it in virtue of the relative position, the
order, and location that they present with respect to the set of celestial
bodies. The latter is the natural container, the principle of conservation and
all location. [3, p. 156]

Thus if two
bodies, at different times, possessed the same relationships with the “set of
celestial bodies,” they can be said to have been in the same place. In De natura loci St. Thomas elaborates a bit more on the
place of the ultimate sphere. He says that the ultimate sphere is in a place accidentally
because its parts are in place, albeit potentially and not actually. A thing is
in a place accidentally by being attached somehow to something that is in a
place.

As Thomistic doctrine was developed by later medieval masters,
it became clear that to be able to identify an immobile place, the reference
base itself must be immobile. Thus the universe must be bounded by an immobile
spherical surface. According to Duhem [3, pp. 169,
178], the “natural conclusion of the Peripatetic theory of place” is “the
hypothesis of a necessarily immobile empyrean sphere.” Theologians had no
difficulty with that concept. Some of them even thought that Sacred Scripture
affirmed the existence of such a sphere. St. Bonaventure in commentary on Peter
Lombard’s Sentences spoke of an immobile orb “which contains and is not
contained” [3, 174]. This notion was taken up later by Copernicus. But he did
not take the empyrean sphere as the immobile reference for movements of the
celestial bodies. Rather he took the sphere of the fixed stars.

In his Writings
on the “Sentences” of Peter Lombard Aquinas sets forth his view that what
is called place or space is defined by the objects in it and was created with
the world. He makes the further observation that what we call void is not a
simple negation but a privation and is neither self-existent
nor created; more will be said later about the notion of void:

[I]t ought to be
said that before the creation of the world there was no void, as there is none
after, because the void is not a simple negation but a privation. Hence, in
order that there be a void, as those who suppose that
there is one would say, there must be a place or real dimensions, neither of
which did exist before the world. [4, p. 97]

In his Summa Theologica Aquinas reaffirms his view that place or
space was created in the beginning:

Whereas we hold that
there was no place or space before the world was. [5, Part I, Q. 46, A. 1,
Reply Obj. 4]

*

Let us return now to our thought
experiment. Imagine that God has also provided you with a rod. You go close to
the surface of your world and poke at it with the end of your rod. To your
amazement you find that the rod shortens. You then pull the rod back toward you
and find that it has returned to its full length. Your first deduction might be
that the rod shrinks as it makes contact with the surface. You then find that
God has provided you with another rod, one that is not uniformly thick. It
tapers down to a point. You now probe at the surface of the water with the
point of that rod and find that the rod doesn’t shrink. Rather, the pointed end
simply disappears. You then pull that rod back toward you and find that the
pointed end reappears. You are amazed.

*

In 1277 a council of the doctors
of the Sorbonne, which took place under the presidency of the bishop of Paris,
Etienne Tempier, condemned the notion that God is
unable to move the whole universe in rectilinear motion because the universe
would then leave behind a void. It was the denial of God’s power that was
condemned, not the reason given for denying that power. Actually, Aristotelians
and Thomists would not have given the reason stated
by the council. They would say that motion of the whole universe is a
meaningless one because outside the universe there is no place or void in which
to move and no reference basis against which motion can be identified. Others
would say that God could create a void in which the universe could move. The
end result of the condemnation, according to Duhem,
was that “the theologians of the Sorbonne traced out a path to the system of
Copernicus” [3, 197].

This leads us to
the question of the nature of void. Is it something real? If so, was it created
or does it coexist alongside God? In Book IV of his Physics, Aristotle
defines void as “place bereft of body” [1, p. 270]. He argued that there is no
void outside a body, no void occupied by a body, and no void in a body; that
is, there is no void at all [1, pp. 280-289]. When a body moves it takes
occupancy of a place previously occupied by another body. St. Thomas used the
conceptual framework of Aristotle but applied his own insights. Apparently he
believed in the reality of void because we heard above from him that the void
is not a simple negation but a privation. A privation is the absence of
something from where it naturally should or could be. For example, the lack of
the power of sight is a privation in a human person or a dog because sight
belongs to the nature of those creatures. But the lack of power of sight in a
tree is a negation because the power of sight does not belong to the nature of
a tree. So it would seem then that, according to Aquinas, a void is the absence
of a corporeal body from where one could be; that is, it is an empty place.
Void is not a negation; that is, it is not simply nothingness. Thus Thomas ties
in the nature of void with matter.

In his rejection
of the possibility of a void Aristotle, according to some interpreters, argued
that if there were motion in a void, a corporeal body would move
instantaneously because there would be nothing to resist its motion. (Only a
plenum would be able to offer resistance so that it would take a period of time
for a body to travel from one place to another.) And since instantaneous motion
was considered impossible, it followed that a void is also impossible.

Aquinas,
contrary to that interpretation of Aristotle, defended the possibility of
natural motion in a void (see [1, pp. 378–380] and [6, pp. 134–142]). He held
that, in addition to the resistance of a material medium in which a body moves,
there is also a inclination in a body to resist motion
contrary to its natural motion (violent motion) and an internal inertia of
bodies that resisted being moved from one natural place to another. (Medieval
scholars followed Aristotle in believing that the elements of fire, air, earth
and water, had a natural inclination to move towards places in the universe
reserved for those elements. Such motion is called natural motion. The natural
motion of the fifth element, quintessence, of which the celestial bodies were
supposed to be composed, was uniform circular motion about the earth.) So even
in the absence of a material medium it would take a period of time for a body
to move from one place to another because a body would provide its own
resistance. Natural motion had a “natural velocity.” More than three centuries
later, Galileo, in opposition to the prevailing opinion, would follow Aquinas
in upholding the possibility of motion in a void.

Pierre Duhem credits Aquinas with being the first to introduce the
notion of mass into physics [3, pp. 379-380]. This comes about in Aquinas’ discussions
on falling bodies. Aquinas insisted that nature is not the efficient cause in
the free fall of corporeal bodies; that is, the nature of a body is not the
cause of its falling in the way that the nature of an animal is the cause of
its movements. Rather, nature is an “active principle” in such free fall; that
is, it is the nature of a corporeal body that makes it possible for it to fall.
What is it in the nature of a corporeal body that makes it possible to
fall?  Aquinas answers that question in a lecture in his commentary on
Aristotle’s Physics:

When
the form, which the generator imparts, is removed from heavy and light things,
a body with magnitude remains only in the understanding. But a body has
resistance to a mover because it has magnitude and exists in an opposite site
{opposite to where the movement would lead it}. No other resistance of
celestial bodies to their movers can be understood. [3, p. 378]

Thus Aquinas
abstracts from a material body the notion of “magnitude,” what we today call “mass.”
Duhem sees this as a revolutionary accomplishment
that Aquinas managed by distinguishing in thought, “on the one hand, a form,
the motor force or gravity, and, on the other hand, prime matter given
determined dimensions, not prime matter bare and simple, but a quantified body
occupying a certain location and resisting the force attempting to bring it
elsewhere” [3, p. 379]. Duhem extols the magnitude of
this achievement of St. Thomas. Referring to the passage above he states:

Thomas’s assertion,
which we have just quoted, is extremely brief: let us not allow its brevity to
make us misunderstand its importance. For the first time we have seen human reason distinguish two elements in a heavy body: the motive
force, that is, in modern terms, the weight; and the moved thing, the corpus
quantum, or as we say today, the mass. For the first time we have seen the
notion of mass being introduced in mechanics, and being introduced as
equivalent to what remains in a body when one has suppressed all forms in order
to leave only the prime matter quantified by its determined dimensions. St.
Thomas Aquinas’s analysis, completing Ibn Bajja’s, came to distinguish three notions in a falling
body: the weight, the mass, and the resistance of the medium, about which physics
will reason during the modern era. [3, p. 379]

In the same
lecture cited above, Aquinas magically arrives at the notion of accelerated
fall:

The Commentator
replies that the natural movement of light and heavy things requires this
impediment from the medium so that there might be a resistance of the mobile
body to the mover, at least from the medium. But it is better to say that all
natural movement begins from a nonnatural place and
tends to a natural place. Hence, until it reaches the natural place, it is not
unsuitable if something unnatural to it is joined to it. For it gradually
recedes from what is against its nature, and tends to what agrees with its
nature. And because of this natural movement it is accelerated at the end. [3,
p. 380]

The profundity
of St. Thomas’ cosmological insights will become more apparent as we proceed
through this essay.

*

Let us return once again to our
thought experiment. You try to explain your observations with the rods. Your experience
with the tapered rod made it clear that the rods did not shrink. Either the
ends of the rods were annihilated and recreated or there was something beyond
the surface of the water that “absorbed” them. You dismiss the first
alternative because you know that God gives his creatures persistence; He holds
them in existence; He doesn’t toss them in and out of existence. Then something
must have “absorbed” the ends of the rods without destroying them. You call
that something “void.” You do not know what it is or if it is material; but you
now know that it is part of your world. The void provided a place for the ends
of the rods.

You next
test to see if the void is made of matter. You do this by attaching one of the
rubber balls to the end of one of the rods. You then push the rubber ball into
the void and move it laterally with the rod to see whether the void offers any
continual resistance to lateral motion of the ball, which you can sense through
the rod. You find out that it doesn’t, so you are convinced that the void is
not material.

You then reason
that a rod is a material object with dimensionality. When one protruded through
the surface of the water, it lent its dimensionality to the void it pierced.
Before that the void was dimensionless nothingness, that is, it was no-thing;
it was neither substance nor accident. Then you reason further. If the rod lent
its three-dimensionality to the void then the whole earth must lend its
three-dimensionality to the void, presuming that the earth is finite in size.
That is a reasonable presumption because if the earth was infinite in size
there would be no surface to its water. You then come to the final conclusion
that the void is somehow part of the earth. You come to see that the void is a
shadowlike extension of the earth’s existence because it provides other places
in which the things of the earth can exist.

Enlightenment Notion of Space

The greatest change in
cosmological thinking during the Enlightenment was the replacement of the
concepts of place and void by the concept of immobile absolute empty space.

According to Max
Jammer, the first major contribution to the concept of such a space was made in
the sixth century a.d. by the
philosopher Philoponus, also called John the
Grammarian. Philoponus stated:

Space is not the
limiting surface of the surrounding body … it is a certain interval, measurable
in three dimensions, incorporeal in its very nature and different from the body
contained in it; it is pure dimensionality void of all corporeality; indeed, as
far as matter is concerned, space and void are identical. [2, p. 56]

At first sight
John seems to be simply formulating the belief of the Greek atomists, who
preceded him, in contrast to the belief of Aristotle. The first century b.c. Greco-Roman poet Tius Lucretius Carus enshrined
the philosophy of the Greek atomists in Latin verse in his poem On the
Nature of Things [7]. In that poem he emphatically says that nothing exists
but atoms and void.

John the
Grammarian’s position, however, appears to differ somewhat from that of the
Greek atomists. Jammer explains Philoponus’
identification of space and void:

However this
identification of space and void does not assume the existence of a void as
such “in actu.” The void, although a logical
necessity, is always coexistent with matter. Void and body are two inseparable
correlates, each of them requiring the existence of the other. As soon as one
body leaves a certain part of space, another body “replaces” the first. A
certain region of space can receive different bodies in succession without
taking part in the motion of the occupying matter. Philoponus’
phoronomy is completely analogous, as Duhem points out, to Aristotle’s doctrine of substance and
form, where one form is succeeded by another continuously, so that substance is
never void of form. Just as matter successively receives one form after
another, so a section of space may be occupied by one body after another, space
itself remaining immobile. [2, p. 56]

Also, John’s
space does not have a favored direction, as does that of the Greek atomists.
Lucretius speaks of atoms continually falling downward in infinite space. For Philoponus “down” is the direction toward the earth, which
material bodies have an inherent tendency to reach; “down” is not a property of
space itself.

It wasn’t until
the seventeenth century, more than a millennium after John the Grammarian
proposed his notion of absolute space, that Isaac Newton gave the concept of
absolute space a long-enduring place of honor in physics. Newton presented his
conceptual scheme of space, time, matter and motion in his Philosophiae
naturalis principia mathematica
(1687), known simply as the Principia. In the beginning of the Principia
Newton made clear his meaning of “absolute space” by comparing it with what he
called “relative space”:

Absolute space in
its own nature, without relation to anything external, remains always similar
and immovable. Relative space is some movable dimension or measure of the
absolute space; which our senses determine by its position to bodies; and which
is commonly taken for immovable space; such is the dimension of a
subterraneous, an aerial, or celestial space,
determined by its position in respect to the earth. Absolute and relative
spaces are the same in figure and magnitude; but they do not remain always
numerically the same. For if the earth, for instance, moves, a space of our
air, which relatively and in respect of the earth remains always the same, will
at one time be one part of the absolute space into which the air passes; at
another time it will be another part of the same, and so, absolutely
understood, it will be continually changed. [2, pp. 99–100]

A little further
on in the Principia Newton substitutes “sensible measures” for the parts
of absolute space because absolute space itself is insensible and its parts
indistinguishable:

But because the
parts of space cannot be seen, or distinguished from one another by our senses,
therefore in their stead we use sensible measures of them. For from the positions
and distances of things from any body as considered
immovable, we define all places; and then with respect to such places, we
estimate all motions, considering bodies transferred from some of those places
to others. And so, instead of absolute places and motions, we use relative
ones; and that without any inconvenience in common affairs. [2, p. 100]

Newton professed
to eschew metaphysical reasoning in natural science. He said: “We are to admit
no more causes of natural things than such are both true and sufficient to
explain their appearances” [2, p. 101]. But he seeks to justify his
introduction of absolute space with the famous statement: “But in philosophical
disquisitions, we ought to abstract from our senses” [2, p. 101]. His notion of
absolute space is purely metaphysical because absolute space is perceived only
by the mind and not by the senses. The only things that we observe are relative
places and motions measured against an arbitrary standard of rest. We may
rightly ask whether absolute space is really a necessary abstraction or whether
it is an invention, a “free creation of the human mind,” to use the words of
Albert Einstein. Absolute space is not necessary for the validity of Newton’s
three laws of motion and his law of gravity. Although he formulated them with
absolute space in mind, they have only been experimentally verified in relative
spaces, with the earth or some other celestial body as the standard of rest.
Newton recognized that his laws were valid in a whole class of relative spaces
that we today call “inertial spaces.” In a corollary of the Principia he
says: “The motions of bodies included in a given space are the same among
themselves, whether that space is at rest, or moves uniformly forwards in a
right line without any circular motion” [2, p. 102]. The notions “rest,” “right
line,” and “circular motion” can have an empirical meaning only with respect to
corporeal bodies. In another corollary in the Principia, Newton
acknowledges the necessity for an arbitrary corporeal standard of rest: “That
the centre of this system of the world is immovable. This is acknowledged by
all, while some contend that the earth, others that the sun, is fixed in the
centre” [2, 203]. For Newton the center of the world is the center of mass of the
bodies of the solar system. The center of mass of a system of corporeal bodies
can, in principle, be located inside one of the bodies or inside none of them;
its location depends on their relative masses, sizes, and distances. Still, a
center of mass is a standard of rest that ultimately depends on the existence
of corporeal bodies. To say whether the center of mass of the solar system
moves, we would have to observe whether it moves with respect to the stars. The
notion of the center of mass of the whole universe moving through absolute
space is empirically meaningless.

In modern
physics, coordinate systems freestanding in absolute space are just as
metaphysical as absolute space itself. Such coordinate systems and the absolute
space (or space-time) they structure are fictional, but somehow they have
proved quite useful. However, it will become clearer as we proceed in this book
that too heavy a reliance on them has led physics up a blind alley.

Although Newton
recognized that absolute space did not manifest itself kinematically,
he believed that it did manifest itself dynamically. He believed that inertial
effects, like the resistance of material bodies to a change in their speed and
the concave surface of the water in a rotating bucket of water are caused by
motion relative to absolute space. Thus uniform linear motion and accelerated
motion have different manifestations in absolute space—the one relative, the
other absolute. But Newton’s notion that the center of the world is at rest
allowed uniform linear motion to be referred to that point of rest, so that it
too could be “absolutized.” But uniform linear motion
is then absolute by definition while accelerated motion is absolute by nature.
To distinguish absolute motion from relative motion, Newton introduces the
concept of “force” which is a “cause” that generates “true” motion:

The causes by which
true and relative motions are distinguished one from the other, are the forces
impressed upon bodies to generate motion. True motion is neither generated nor altered,
but by some force impressed upon the body moved; but relative motion may be
generated or altered without any force impressed upon the body. For it is
sufficient only to impress some force on other bodies with which the former is
compared, that by their giving way, that relation may be changed, in which the
relative rest or motion of this other body did consist….  [2, p. 105]

Newton proceeds
to admit the difficulty of distinguishing “true” motions of bodies from
“apparent” motions, but he does not admit the impossibility of doing so:

It is indeed a
matter of great difficulty to discover, and effectually to distinguish, the
true motions of particular bodies from the apparent; because the parts of that
immovable space, in which those motions are performed, do by no means come
under the observation of our senses. Yet the thing is not altogether desperate;
for we have some arguments to guide us, partly from the apparent motions, which
are the differences of the true motions; partly from the forces, which are the
causes and effects of the true motions. [2, p. 105]

Jammer
says that Newton’s forces, as presented above, are “metaphysical entities
conceived anthropomorphically” and not functional entities [2, p. 106]. He says
that Newton’s arguments “from causes” are based on traditional metaphysics.
This is so even though Newton had strongly objected to the use of metaphysical
arguments in natural science. Jammer says that there is a vicious circle in
Newton’s reasoning concerning absolute motion and absolute force. He says that
this can be seen by thinking of a world of moving masses in which no living
organism [self-mover] existed. He says that “in such a world an absolute force
can be determined, according to Newton, solely by the absolute motion of the body
on which this force is exerted” [2, p. 106]. That is, the fact that there is
absolute motion means that there must be a force which means there must be
absolute motion, which means there must be a force, and so on—thus the
circularity.

Newton’s notion of
absolute space was criticized by three notable contemporaries: G. W. Leibniz
and G. Berkeley (summaries of their criticisms are given in [8, pp. 97–106])
and C. Huygens (a summary of his criticism is given in [2, pp. 119–126]), none
of whom accepted his dynamical arguments. Leibniz argued that space and time
are not independent entities but depend on matter and material phenomena to
give them meaning. Berkeley argued that since absolute space in no way affects
the senses, it is useless for distinguishing motions. He argued that all
motion, including rotational motion, requires a corporeal frame of reference:

If we suppose the
other bodies were annihilated and, for example, a globe were to exist alone, no
motion could be conceived in it; so necessary is it that another body should be
given by whose situation the motion should be understood to be determined. The
truth of this opinion will be very clearly seen if we shall have carried out
thoroughly the supposed annihilation of all bodies, our own and that of others,
except that solitary globe.

Then
let two globes be conceived to exist and nothing corporeal besides them. Let
forces then be conceived to be applied in some way; whatever we may understand
by the application of forces, a circular motion of the two globes round a
common centre cannot be conceived by the imagination. Then let us suppose the
sky of fixed stars is created; suddenly from the conception of the approach of
the globes to different parts of that sky the motion will be conceived. [2, p.
109]

However,
Berkley’s argument was kinematical and does not adequately explain dynamic
effects, such as the concave surface on a rotating pail of water. As we shall
see later, the nineteen-century physicist, Ernst Mach, will give an explanation
for that that avoids the notion of absolute space.

Leibniz, succinctly gives his conception of space, which is
opposed to that of Newton, in a letter to S. Clarke, a disciple of Newton:

As for my opinion, I
have said more than once, that I hold space to be something merely relative, as
time is; that I hold it to be an order of coexistences, as time is an order of
successions. For space denotes, in terms of possibility, an order of things
which exist at the same time, considered as existing together; without enquiring
into their manner of existing. And when many things are seen together, one
perceives that order of things among themselves. [8, pp. 97–98]

Leibniz further
compares Newton’s attributing a real identity to absolute space to attributing
a real identity to a genealogical tree. In a genealogical tree the individuals
and their generational relationships are real things, but the tree they inhabit
is only a mental construct. Likewise, corporeal bodies and their spatial and
temporal relationships are real things, but the absolute space they inhabit is
only a mental construct.

The arguments of
Leibniz, like those of Berkeley, were kinematical. Leibniz, despite much
effort, was unable to explain dynamic effects by relativity of motion. Jammer,
however, credits him with coming close to Mach’s solution by attempting to
reduce gravity to centrifugal force. Mach also connected gravity to centrifugal
force but in the opposite way, by reducing centrifugal force to an effect of
gravity.

Jammer credits
the third contemporary critic of Newton’s absolute space, Christian Huygens, as
the first physicist who defended both kinematic and dynamic relativity. His
defense of dynamic relativity, however, was faulty. He explained the effects of
centrifugal forces on a rotating disk as merely an indication of the relative
motion of different parts of the disk. If one took as a reference system one
rotating like the disk, then the motions of the parts of the disk would
disappear. However, he neglected to observe that the pressure caused by the
centrifugal forces and tending to pull the disk apart would still be present
and would have to be explained.

The most
outstanding critic of Newton’s concept of absolute space was the
nineteenth-century physicist Ernst Mach. He was the first person to credibly
defend dynamic relativity. Mach said that absolute space and absolute motion
are “pure things of thought, pure mental constructs,
that cannot be produced in experience” [10, p. 280]. Since there is no absolute
motion, the motion of bodies is determined only in reference to other bodies.
Thus, since there is only one system of the world, “the motions of the universe
are the same whether we adopt the Ptolemaic or the Copernican mode of view.
Both views are, indeed, equally correct; only the latter is more simple and more practical” [10, p. 283–284].
Mach held that inertial effects were not the result of the action of absolute
space on a body; rather they were the combined effect of all the other material
bodies in the universe on the body. Thus, for example, the earth bulges at the
equator not because absolute space “pulls” on it; rather, the mass of cosmic
bodies rotating around it “pulls” on it. And it does not matter if one thinks
of the cosmic bodies as rotating or the earth as rotating. Both views are
equivalent. The inertial effects are produced by the relative rotation
of the earth and the heavens. Mach wrote: “[I]t does not matter if we think of
the earth as turning on its axis, or at rest while the fixed stars revolve
around it…. The law of inertia must be so conceived that
exactly the same thing results from the second supposition as from the first”
[11, p. 10]. This idea, which has come to be known as Mach’s
principle, implies that if there were no cosmic bodies there would be no inertial
effects on the earth, for example, the earth would not bulge at the equator. It
is not possible to test this directly because one cannot simply remove all the
heavenly bodies. But, in principle, it can be confirmed indirectly by looking
for inertial effects caused by the relative motions of terrestrial bodies. But
such effects would be very small and very hard to measure. So far Mach’s
principle has not been verified experimentally. Mach stated his principle in
general terms, but he did not implement it. He said nothing about the nature of
the interaction of material bodies with the rest of the universe. His principle
is a simple concept, but its implementation required the rethinking of some
physical concepts.

Theological
considerations also were important to the seventeenth-century contestants on
the issue of absolute space. Berkeley gave a cogent theological argument
against absolute space. He said that space must be considered as relative “or
else there is something beside God which is eternal, uncreated, infinite,
indivisible, unmutable” [2,
p. 112]. But Newton did not conceive space as coexisting with God. Rather he
identified absolute space as an attribute of God. In the Principia he
makes the statement:

He [God] is not
eternity and infinity, but eternal and infinite; he is not duration or space,
but he endures and is present. He endures forever, and is everywhere present;
and by existing always and everywhere, he constitutes duration and space. [2,
p. 113]

Newton seems to
have thought that God is spatially extended because He is able to move all the
bodies in the universe. He is more able to move the bodies “within his
boundless uniform Sensorium, and thereby to form and reform the Parts of the Universe,
than we by our Will to move the Parts of our own Bodies” [2, p. 113]. Leibniz
argued that Newton’s identification of the omnipresence of absolute space with
the omnipresence of God implied that God is divisible because absolute space is
divisible, a contention that was contested by Clarke. Leibniz interpreted
Newton as conceiving space as an organ that God uses to perceive things.
Therefore, continues Leibniz, it would follow that things do not depend
altogether on God and were not produced by Him. But this argument rests on what
may be a too literal interpretation of the word “sensorium.”
Newton seems to have used the word in an analogous sense.

Leibniz
ridicules the notion that absolute space devoid of material bodies is still not
really empty. This notion was a refuge of Newton supporters who wanted to
retain the concept of place in space void of matter. He asks what it is filled
with. Is it filled with extended spirits or other immaterial substances capable
of extension, contraction and interpenetrability?
Leibniz takes issue with their fantastic theology:

Some have fancied,
that Man in the State of Innocency, had also the Gift
of Penetration; and that he became Solid, Opaque, and Impenetrable by his Fall. Is that not overthrowing our Notions of Things, to
make God have Parts, to make Spirits have Extension? [2, p. 118]

Critics of
Newton also pointed out that while absolute space acts on a material body, the
body does not react on absolute space. This would violate a general physical
principle, which is embodied in Newton’s own third law, that every physical
action is accompanied by a reaction that maintains balance in the universe.

Newton’s
conception of absolute space involved the rejection of the conceptual scheme of
substance and accident. Traditional Catholic philosophy rejects the notion of
absolute space because it is incompatible with the concept of quantity as
understood by the scholastic masters. The prominent sixteenth-century
scholastic theologian Francisco Suarez upheld the total dependence of space on
matter:

[Space is] a
conceptual entity, not, however, formed at will like chimeras, but extracted
from bodies, which by their extension are capable of constituting real spaces (Metaphysical
Disputations 51)

.

Quantity is the
principle of individuation. Among material substances there are many species
and many individuals of the same species. The individuals are not individuated
by nature (as are spiritual creatures) but by matter itself, prime matter
determined by the accident of quantity. Matter so individuated is called signate matter or matter marked by
quantity. Scholastic philosophy holds that absolute space is only a
conceptual entity that is abstracted from signate
matter. Extension is an accident of physical bodies that the mind perceives and
from which the mind constructs absolute space. Extension is a necessary
concomitant to quantity, and every quantity is the quantity of something. But
absolute space is pure extension, which means it is quantity without a subject.
In other words, absolute space is quantified nothingness, which is a
contradiction in terms. It is a contradiction in reality; but it is not,
however, a contradiction in the mind because it is a mental abstraction. It is
an accident without a subject. It is like the shape of a statue without any
material holding that shape; such can exist only in the mind and not in
reality. Further, absolute space is not a privation, as St. Thomas Aquinas
identified void, because privation implies means the absence of something where
it can be. But absolute space is conceived without reference to anything but
itself.

Enlightenment
thinkers conceived of space as an attribute of God or as coexistent with God.
But they do not seem to have considered the idea of space as a creation of God.
If they did, their thinking would have led them to a more realistic vision of
the universe. We saw above that St. Thomas Aquinas clearly taught that space
(void) was created in the beginning of the world along with matter. When God
created the earth as the first material body, He created the three-dimensional
space it occupies. Space, like time, is an epiphenomenon of material creation.
With the creation of the celestial bodies God created void, which separates and
helps distinguish the heavenly bodies from each other and the earth. Void has
no meaning except in reference to the material objects it surrounds. Matter
lends its dimensionality to void. Job 26:7 confirms that the
three-dimensionality of void is extrapolated from three-dimensional matter:

He stretches out
the north over the void, and hangs the earth upon nothing.

Before creation
there was no infinite three-dimensional absolute space into which God injected
matter. The mental image of an empty three-dimensional absolute space existing
before creation is abstracted by our minds from a world filled with matter.
Before creation there was nothing but God. And “nothing” does not mean
“three-dimensional emptiness.” It means “no thing.”

Newton’s concept
of absolute space provided an amazingly successful basis for the explanation of
the observed inertial behavior of material bodies and thus led to the
development of classical mechanics despite the problems concerning its
hypostatization. The successes of classical mechanics overshadowed objections
against absolute space until the development of modern physics in the twentieth
century, when they once again came to the fore. Among scientists who developed
classical mechanics from Newton’s laws, like, for example, Lagrange, Laplace
and Poisson, there was little interest in the reality of absolute space. They
just accepted it as a working hypothesis. The great formulator of classical
electromagnetic theory, James Clerk Maxwell, succinctly presented the paradox
that the notion of absolute space introduced into physics. He said: “All our
knowledge of space and time is essentially relative” [9, p. 12]. But he adds
the following footnote to that statement: “The position seems to be that our
knowledge is relative, but needs definite space and time as a reference for its
coherent expression.” Absolute space is the phantasm of disembodied quantity
that haunts classical mechanics.

Medieval and Enlightenment
Notions of Time

The history of opinions about
time is long and tortuous. In his cosmological dialogue Timaeus
Plato calls time a “moving image of eternity” [12, p. 1167]. In his Physics
Aristotle said that time is the measure of movement and movement is the measure
of time; movement and time define each other [1, p. 294]. The Greek atomists said that time has no separate existence; things in
motion cause time [7, p. 33]. Here we are only concerned with differences in
the conception of time between the scholastic doctors and enlightenment
thinkers.

The scholastic
doctors, following Scripture under the guidance of the Church, rightly believed
that time was created by God in the beginning. The first Christian writer to
write extensively on time and whose views on time carried great weight with the
scholastics was St. Augustine. Augustine explores the subject of time in Book
XI of his Confessions. He declares that it is a difficult subject: “What
then is time? If no one asks me, I know; if I want to explain it to someone who
asks me, I do not know. I can state with confidence, however, that this much I
do know: if nothing passed away there would be no past time; if there was
nothing on its way there would be no future time; and if nothing existed there
would be no present time” [13, pp. 295–296]. Thus he denies the self-existence
of time. In Chapter 5 of Book XI of the City of God Augustine affirmed
his belief that before the creation of the world there was no time: “It is idle
for men to imagine previous ages of God’s inactivity, since there is no time
before the world began” [14, p. 435]. St. Augustine refuted the idea that time
existed before the creation of the world because it makes God live in time and
the creation of the world look like a thought that suddenly occurred to Him,
thus making Him changeable and not eternal. In Chapter 6 of Book XI of the City
of God he affirms his belief that “without motion and change there is no
time” [14, p. 435]. He goes on to reaffirm his belief in the creation of time:
“The world was not created in time but with time” [14, p. 436]. St.
Thomas Aquinas concurs with Augustine saying: “Things are said to be created in
the beginning of time, not as if the beginning of time were a measure of
creation, but because together with time heaven and earth were created” [5,
Part I, Q. 46, A.3, Reply Obj. 1]. Lateran Council IV
and Vatican Council I affirmed the creation of time. They both decreed that God
“from the beginning of time created each creature from nothing…” [15, nos. 428, 1783].

Catholic
philosophy, following Aristotle, Augustine and Aquinas, associates time with
movement. The Catholic Encyclopedia (1914) article on time states: “In
fact, say the Scholastics, we never perceive time apart from movement, and all
our measures of our temporal duration are borrowed from local movement,
particularly the apparent movement of the heavens” [16, article entitled
“Time”].

The thinking of
enlightenment philosophers on time, like their thinking on space, deviated from
that of the scholastic masters. Newton, in the same scholium in his Principia that he presents his
notions of absolute and relative space, also presents his notions of absolute
and relative time. He describes them as follows:

Absolute, true, and
mathematical time, of itself and from its own nature, flows equably without
relation to anything external, and by another name is called ‘duration’;
relative, apparent, and common time is some sensible and external (whether
accurate or unequable) measure of duration by means
of motion, which is commonly used instead of true time, such as an hour, a day,
a month, a year. [17, p. 17]

The notion that
absolute time “flows” is a very peculiar one indeed. If it is intended as a
metaphor, it is a very misleading one. The flow-of-time concept is circular
because the concept flow already includes time, measured time. Does time
flow at x seconds per second? Or perhaps there is a hierarchy of time, that is,
time flows at x seconds per supersecond. But do superseconds also flow, perhaps at y superseconds
per second? But now we are in a vicious circle. Then maybe superseconds
flow at y superseconds per supersupersecond.
We are now in an infinite regress. So where do we go with the notion of the
flow of absolute time?

Newton sees
absolute time as the standard for calibrating relative time, but does not show
how such calibration can be done.

Absolute time, in
astronomy, is distinguished from relative by the equation or correction of the
apparent time. For the natural days are truly unequal, though they are commonly
considered as equal and used for a measure of time; astronomers correct this
inequality that they may measure the celestial motions by a more accurate time.
It may be that there is no such thing as equable motion whereby time may be
accurately measured. All motions may be accelerated and retarded, but the
flowing of actual time is not liable to any change. The duration or
perseverance of the existence of things remains the same, whether the motions
are swift or slow, or none at all; and therefore this duration ought to be
distinguished from what are only sensible measures thereof and from which we
deduce it, by means of the astronomical equation. The necessity of this
equation, for determining the times of a phenomenon, is evinced as well from
the experiments on the pendulum clock as by eclipses of the satellites of
Jupiter. [17, p. 19]

Newton seems to
have said that the very fact of something existing gives rise to absolute time,
even if no change takes place in the existing thing. Its “perseverance” in
existence causes absolute time. But how is time in that way measured, or even
defined? God perseveres in existence, but He is unchanging and does not live in
time but transcends time. The Scholastics understood that, but apparently
Newton did not.

The only way to
set up a measurable standard of time is to use a periodic physical phenomenon.
That physical phenomenon can be compared with another periodic physical
phenomenon to see if their periodicities synchronize. If they do, then the
standard is reinforced. If they don’t, then one of the phenomena is accepted as
the standard and the other is “corrected” to agree with it. In the passage
above Newton said that “it may be that there is no such thing as equable motion
whereby time may be accurately measured.” He would have been more on target if
he removed the words “it may be that.” There is no such thing as “equable
motion” because there is no way to physically define it. It cannot be
physically defined because there is no way to make a comparison with something
as abstract as absolute time. Absolute time, like absolute space, is
disembodied quantity. It exists only in the mind but not in reality.

Newton proposes
that the “astronomical equation,” which is presumably his law of gravitational
attraction, is a means for determining absolute time. Mathematical equations
simply describe physical phenomena. The better an equation describes an
observed phenomenon, the more useful it is. But an equation does not
hypostatize the quantities it employs. So the fact that the notion of absolute
time is used in an equation does not mean that such exists. The notion itself
is just a convenient mental construct that somehow gives answers in agreement
with observations. Physical science employs a number of such constructs, for
example, points and imaginary numbers.

Enlightenment
opinions about time varied from the extreme objective view of Newton to the
extreme subjective view of Immanuel Kant, who saw time as solely a creation of
the human mind. Such opinions often departed widely from the commonsensical
viewpoint of medieval Christendom. The majority of the medieval schoolmen conceived
time as partly objective and partly subjective. Objectively, motion is
something real; it is an object of experience. Subjectively, the mind divides
motion into before and after and perceives time as the measure of movement
according to before and after [18]. Time can be thought of as that which, to a
finite mind, makes present various potentialities in a subject. Leibniz’ view
of time was perhaps the closest to the medieval view since he held time as an
order of successions.

God gave us
natural standards of rest and time. He made the earth the standard of rest. For
time He gave us natural rhythms rather than a single defined standard. The most
basic is the daily rhythm determined by the stars, which gives us day and
night. Following that He gave us the annual rhythm determined by the sun, which
gives us the cycle of seasons.  Finally the monthly rhythm determined by
the moon, which gives us the tides and graduates the seasons.

Chapter TWO: Sacred Scripture and the Earth
as the Center of the Cosmos

The Creation of Heaven and
Earth

The first three verses of Genesis
relate the absolute beginning of the universe:

In the beginning
God created heaven and earth. And the earth was void and empty, and darkness
was upon the face of the deep. And the spirit of God moved over the waters. And
God said: Be light made. And light was made. [Douay-Rheims]

The Septuagint
says that the earth was “invisible and shapeless.”

The Jewish Biblical
Society version translates these three verses as a single sentence that
highlights the state of the universe when light was created:

When God began to
create heaven and earth—the earth being unformed and void, with darkness over
the surface of the deep and a wind from God sweeping over the water—God said,
“Let there be light”; and there was light.

The first
material object created was the earth. Although “heaven” is mentioned
first, it does not necessarily mean that it was the first thing created. The
first verse may simply be an introductory summary, an abstract, of what
follows. But if it does indeed relate the very first act of God during Creation
Week, then the Hebrew word shamayim,
translated “heaven,” in a physical sense could mean the void surrounding the
earth (the heavenly bodies were not created until the fourth day). The void is
not something that exists in itself; for then it would be coeternal with God,
that is, it would have being that did not come from God, who is the source of
all being. Nor is it an attribute of God because that would limit God by making
Him somehow three-dimensional. Nor was the void created alongside matter, with
a separate and independent existence, because then it would be a substance
without matter and form, which is senseless. Rather, the void is connected with
matter, as St. Thomas Aquinas and others correctly observed. So it came into
existence with the earth. Scripture may even have identified it with the earth
in the second verse. Perhaps the earth being “void” means that the void
surrounding the earth was actually part of it. This makes sense because the
void takes its meaning and its dimensionality from the earth. The earth being “empty”
or “unformed” means that the distinctions of the first three days and
the adornments of the second three days had not yet been made.

The word “heaven”
in the first verse might instead mean the matter of which the celestial bodies
were made. St. Augustine, St. Basil, St. Gregory of Nyssa, St Ambrose and other
Fathers believed that the raw material of all corporeal bodies was created at
the very beginning. This is how Augustine expressed it in Genesis Defended
against the Manicheans

:

So then, that
formless material which God made from nothing was first called “heaven and earth”
where it is said: “In the beginning God made heaven and earth,” not
because that is what it already was, but because it was able to be that—the
making of heaven, you see, is described a little later on. It’s as if, when we
examine the seed of a tree, we were to say that the roots are there, and the
trunk and the branches and the fruit and the leaves, not because they are in
fact already there, but because they are going to come from there. That’s how
it says, “In the beginning God made heaven and earth,” as a kind of seed
of heaven and earth, when the material of heaven and earth was still all
unsorted; but because it was quite certain that heaven and earth were going to
come from there, the material itself was already called heaven and earth. [19,
pp. 45–46]

Augustine also
professes that belief in his Confessions (Book XII, no. 15):

[T]hese two things I have mentioned, heaven and earth, were
what you made before all days, in the beginning. “The earth was invisible
and unorganized, and darkness loured over the abyss.”
These words suggest formlessness, so that the truth may gradually lay hold on
the minds of those who are unable to think of an absolute privation of all form
without pushing the idea to nothingness. From this formlessness were to be made
another heaven and the visible, organized earth, and the beauty of fully formed
water, and whatever else would thereafter constitute our world. In the making
of this world a succession of days is mentioned, because the nature of these
things is such that temporal succession is needed in their case to bring about
ordered modifications of motion or form. [13, p. 320]

The formless
matter that Augustine perceived was not what we would call “amorphous matter”,
that is, matter that has a form but a form that is not well-defined. That
notion he explicitly rejected (Book XII, no. 6). Neither did he perceive it as
matter that has a continual succession of such forms. He also rejected the
notion of formless matter as “something midway between form and nothingness”
(Book XII, no. 6).  He goes on to consider the mutability of corporeal
bodies and begins to suspect that the “transition [of a body] from one form to
another involves passing through formlessness, rather than through absolute
non-being.”

It should
be interjected here that in the Confessions Augustine interpreted the “heaven”
of the first day of creation as the spiritual creation, that is, the creation
of the angels (Book XII, nos. 2–16, 23). This is the “heaven of heaven”
of Psalm 113 (115):

The heaven of
heaven is the Lord’s: but the earth he has given to the children of men.
[Douay-Rheims: Ps 113:16]

The earth of the
first day of creation was formless matter, from which apparently both the
“visible, organized” earth and “another” heaven were made (Book XII, no. 16).
The second heaven is the physical “heaven” of the second day of
creation.

Augustine
perceived formless matter as being in a state of quasi-eternity, that is, in a
timeless state:

… the
invisible and unorganized earth, where also there was no succession of time,
for succession implies that one thing is followed by another, and where there
is no form there cannot be any question of one thing, then another. [13, p.
320]

Augustine’s formless
matter comes close to what is called in scholastic philosophy prime matter.
Prime matter is pure potentiality. It has the potential to be any material
thing. However, it exists separately in the mind only. In the world of real
things it is always united to substantial form. In The Literal Meaning of
Genesis Augustine asserts that formless matter is prior to formed matter as
a source but is not prior in time. He said: “God did not first make formless
material and later on form it, on second thoughts as it were, into every kind
of nature; no, he created formed and fashioned material” [19, p. 181]. In this
Augustine differed from other Fathers who believed that unformed (amorphous)
matter was created on the first day and was “formed and fashioned” on the
following five days.

St.
Thomas Aquinas believed that the original condition of matter was an undefined
mixture of elements waiting to be organized. St. Bonaventure’s view was closer
to that of Augustine than to that of Aquinas. He saw the original condition of
matter, to use modern terminology, as pure energy waiting to be transformed.

The view that
all the matter of the universe was created at the very beginning, in the light
of Genesis 1:1-3, 14, could mean that the earth originally contained all the
matter in the universe, from which God made the heavenly bodies on the fourth
day. In that case earth would be the mother of the universe. Or, it could mean
that earth was the first thing formed from the “shapeless matter,” which would
also make it a special place in the universe.

However, it is
not an issue whether God created all the matter in the universe at the very
beginning of Creation Week or if He created the matter along with the forms of
creatures at various times during Creation Week. The important point Genesis
makes is that God made the earth first and built the rest of the universe
around it and for it because earth was to be the home of His masterpiece, man.

There is a
question that causes wonder in some readers of Genesis 1:3. It concerns the
source of the light that God created on the first day. Where did the light come
from if the sun and stars were not yet made? A possible source for the light
could have been chemical and nuclear reactions in the raw matter of earth
itself. But according to modern physics a source really isn’t needed. Light is
not tethered to a source. Once a photon of light leaves its source it is free
and has an existence of its own. So modern physics has no
problem with the idea that God created light without a source. And
neither did St. Thomas Aquinas have a problem with it. He stated:

I answer, then, with
Dionysius (The Divine Names, Book IV), that the light was the sun's
light, formless as yet, being already the solar substance, and possessing
illuminative power in a general way, to which was afterwards added the special
and determinative power required to produce determinate effects. [5, Part I, Q.
67, A. 4, Reply Obj. 2]

Further, it will
be explained in the next article why there is no problem with the fact that God
set up the standard of a natural day independent of the sun, as related in
verses 4–5.

The Formation of Heaven and
Earth

Verses 1:6–10 of Genesis relate
God’s work on the second and third days, during which heaven and earth were
given their forms. Verses 6–8 relate the formation of heaven with the creation
of the firmament on the second day:

And God said: Let
there be a firmament made amidst the waters; and let it divide the waters from
the waters. And God made a firmament, and divided the waters that were under
the firmament from those that were above the firmament. And it was so. And God
called the firmament Heaven. And the evening and morning were the second day. [Douay-Rheims]

The Jewish
Biblical Society version translates the verses using the words “expanse”
and “Sky,” rather than “firmament” and “Heaven.”

God said, “Let
there be an expanse in the midst of the water, that it may separate water from
water.” God made the expanse, and it separated the
water which was below the expanse from the water which was above the expanse.
And it was so. God called the expanse Sky. And there was evening and there was
morning, a second day.

There is no
special word in Hebrew for what we call the world or the universe
or what the Greeks called cosmos. Instead, Genesis uses more concrete
terms like heaven, earth, waters, land and sea.
The Hebrew word shamayim is translated
“heaven,” in the Douay-Rheims version. But it does not mean God’s special abode
except in a metaphorical sense, as St. Thomas Aquinas points out [5, Part I, Q.
68, A. 4]. Rather, it seems that it corresponds to our
word “space,” the abode of the heavenly bodies. It is sometimes translated
“sky,” as in the Jewish Biblical Society version. In verse 1:8 God names the rakia that He called
into being shamayim. The Hebrew word
rakia is traditionally
translated “firmament,” “dome,” or “vault.” This is unfortunate because it
misleads modern readers. It gives the impression that the Hebrews believed that
the earth was surrounded by a solid dome. The Hebrew word emphasizes strength
and fixity, but it does not imply solidity. The most accurate translation is
probably “expanse.” More than one expanse is not excluded by the text. There
may be one expanse below the separated waters and another above, the one above
being the “heaven” mentioned in the first verse.

St. Thomas saw
two interpretations for “firmament.” The first is the “starry
firmament.” “Another possible explanation is to understand by the firmament
that was made on the second day, not that in which the stars are set, but the
part of the atmosphere where the clouds are collected, and which has received
the name ‘firmament’ from the firmness and density of the air” [5, Part I, Q.
68, A. 1].

Genesis locates
water in three places in the universe—above the expanse (1:7; 7:11), on the
earth (1:7, 9), and under the earth (7:11). The waters above the expanse cannot
be reckoned as clouds and vapor such as we have in our atmosphere. Clouds and
vapor can hardly account for the huge mass of water that was separated from the
deep. The text does not say what configuration the waters above the expanse
took; it remains a mystery. Perhaps the moon was once covered by water, or
maybe there were other moons that were composed of water. It may have been that
such moons supplied the water that flowed through the “flood gates of
heaven” (Gn 7:11) contributing to the Great
Flood.

St. Thomas
Aquinas held that the waters are material entities and not spiritual entities,
as some authors asserted; but he was not definite about their material nature:

We must hold, then,
these waters to be material, but their exact nature will be differently defined
according as opinions on the firmament differ. For if by the firmament we
understand the starry heaven, and as being of the nature of the four elements,
for the same reason it may be believed that the waters above the heaven are of
the same nature as the elemental waters. But if by the firmament we understand
the starry heaven, not, however, as being of the nature of the four elements then
the waters above the firmament will not be of the same nature as the elemental
waters, but just as, according to Strabus, one heaven
is called empyrean, that is, fiery, solely on account of its splendor: so this
other heaven will be called aqueous solely on account of its transparence; and
this heaven is above the starry heaven. Again, if the firmament is held to be
of other nature than the elements, it may still be said to divide the waters,
if we understand by water not the element but formless matter. Augustine, in
fact, says that whatever divides bodies from bodies can be said to divide
waters from waters (Genesis Defended Against the
Manicheans, Book I, 5, 7).

If,
however, we understand by the firmament that part of the air in which the clouds
are collected, then the waters above the firmament must rather be the vapors
resolved from the waters which are raised above a part of the atmosphere, and
from which the rain falls. But to say, as some writers alluded to by Augustine,
that waters resolved into vapor may be lifted above the starry heaven, is a
mere absurdity (The Literal Interpretation of Genesis, Book II, Chapter 4). The solid nature of the firmament, the
intervening region of fire, wherein all vapor must be consumed, the tendency in
light and rarefied bodies to drift to one spot beneath the vault of the moon,
as well as the fact that vapors are perceived not to rise even to the tops of
the higher mountains, all go to show the impossibility of this. Nor is it less
absurd to say, in support of this opinion, that bodies may be rarefied
infinitely, since natural bodies cannot be infinitely rarefied or divided, but
up to a certain point only [5, Part I, Q. 68, A. 2.].

It may be that
the water above the firmament was the raw material that God used to create the
heavenly bodies on the fourth day. It may actually have been real water that
God transformed to make the heavenly bodies, just as Christ transformed water
into wine at Cana.

St. Augustine in
Genesis Defended against the Manicheans saw water as possibly being a
name for the formless matter:

He also called the
very same material [formless material] water, over which the Spirit of God was
borne as the will of the craftsman is borne over things to be crafted. The
reason though it is not absurd to call this material “water” is that everything
that is borne on the earth, whether animals or trees or grasses and anything
else of that sort, starts off by being formed and nourished from moisture. [19,
p. 46]

In The
Literal Meaning of Genesis he says essentially the same thing: [Scripture]
“may have wanted to call by the name of ‘water’ the whole basic material of the
bodily creation” [19, p. 172]. Augustine points out in his Unfinished
Literal Commentary on Genesis [19, pp. 120–122] and in The Literal
Meaning of Genesis [19, p. 180] that nowhere in the creation account is it
said that God made the water. Genesis just presumes its existence. This
strengthens the argument that water is simply a name for the formless matter
[or is the formless matter] from which heaven and earth were made.

Verses 1:9–10
relate the formation of the earth on the third day:

God also said:
Let the waters that are under the heaven be gathered together into one place,
and let the dry land appear. And it was done. And God called the dry land
Earth; and the gathering together of the waters he called Seas. And God saw
that it was good. [Douay-Rheims]

In Genesis
Defended against the Manicheans Augustine explains this passage as follows:

But it has already
been said about the earlier verse that the name of waters was given to that
basic material over which the Spirit of God was being borne, from which God was
going to form everything. Now however, when it says, “Let the water which is
under the heavens be collected into one collection,” it
means that that bodily material is being formed into the specific nature and
appearance which these visible waters have. The very collecting together into
one, you see, is the formation of these waters which we can see and touch.
Every form, after all, is compressed into fitting the standard of unity.

As
for its saying, “Let the dry land appear,” what else is it to be
understood as saying, but that that material is to receive the visible form
which this earth has that we can see and touch? So that the earth was earlier
on being called invisible and shapeless [according to the Septuagint] meant
that the basic material was being named as unsorted and dark; and by the water
over which the Spirit of God was being borne, another name was given to this
basic material. Now, however, this water and earth are being formed from that
material which was earlier on called by their names, before it received these
forms which we can now see. [19, p. 50]

In the Unfinished
Commentary on Genesis, Augustine says essentially the same thing, adding
that the formation of the land and sea was in their naming:

“And God called
the dry land earth, and the collection of water he called sea.”  This
matter of names is still with us; not every piece of water is sea or everything
dry is earth. So exactly what water and what dry land was
meant had to be distinguished by names. But we can still not
unreasonably take it that it was God’s naming of them which distinguished and
formed these elements. [19, p. 134]

We must recall
at this point that Augustine believed that everything was created at once,
either in actuality or in potency, with both matter and form. He explains his
position on that issue quite clearly in his Unfinished Literal Commentary on
Genesis:

So then, perhaps it
is said “And there was made evening and there was made morning, one day”
in the sort of way in which one foresees that something can or ought to be
done, and not in the way in which it actually is done in a certain stretch of
time. After all, it was in its essential nature that God’s creative work was
observed in the Holy Spirit by the author who said, “The one who abides
forever created all things simultaneously” (Sir 18:1). But in this book of
Genesis the story of the things made by God most appropriately sets them out as
it were through intervals of time; by this arrangement of the account in an
orderly sequence, the divine plan itself, which cannot be directly and
timelessly contemplated by our weaker intellects, is presented, so to say, as a
spectacle for our very eyes to gaze on. [19, pp. 130–131]

For Augustine
formless matter exists in the mind only and not in actuality. The division of
God’s labors in shaping formless matter over time is a literary device to make the
story of creation understandable.

Augustine’s
viewpoint notwithstanding, the understanding of water as being the formless
matter of Genesis 1 still makes sense if it is assumed that the whole earth had
the form of real pure water and that God transformed some of the water
into land and gathered the rest into the seas.

The primal earth
might also be thought of as being totally murky water, with the elements of the
earth mixed in with it. God then separated the earthy components to form land.
Or, primal earth might have been an amorphous mixture of elements waiting to be
separated and combined into substances, a la St. Thomas Aquinas, being called
water because of its fluid nature. The Hebrew word mayim
translated “water” is also used figuratively for other fluids.

St. Gregory of
Nyssa used an analogy that may be applied here in a more direct way. He held
that God created everything simultaneously; but He created them in a confused
state, that is, indistinctly. Then “the work of nature” distinguished them according
to an order fixed by God. He gives as an analogy a mixture of oil, water and
quicksilver. Mixed together they are indistinguishable. But after a while the
quicksilver sinks to the bottom, the water settles on it, and the oil rises to
the top. The three liquids are distinct substances, but this becomes apparent
only after gravity is allowed to do its work. His analogy can be applied to
verses 9–10 in this way: The original unformed earth was a fluid mixture of
water and other substances. God separated the other substances from the water,
not necessarily by natural means, to form water and dry land.

Verses 1:14–18
relate the creation of the heavenly bodies on the fourth day of Creation:

And God said: Let
there be lights made in the firmament of heaven, to divide the day and the
night, and let them be for signs, and for seasons, and for days and years: To
shine in the firmament of heaven, and to give light upon the earth. And it was
so done. And God made two great lights: a greater light to rule the day; and a
lesser light to rule the night: and the stars. And he set them in the firmament
of heaven to shine upon the earth. And to rule the day and
the night, and to divide the light and the darkness. And God saw that it
was good. [Douay-Rheims]

The heavenly
bodies may have been created completely, matter and form, on the fourth day; or
they may have been made from the raw material created on the first day. Perhaps
God made them from the waters that were raised above the expanse. Or, perhaps
the expanse was a plenum that contained the raw materials for the cosmic
bodies.

It has been a
cause of wonder that day and night were created before the sun and the moon.
Some readers of Genesis can’t understand how there was a first day before the
sun was created and so dismiss the creation account as myth or allegory. But
verse 16 says that God created the sun and the moon to “rule” the day
and the night, not to determine them. This means that the periods of day
and night ontologically precede the sun and moon. The sun and moon were created
to regulate periods of time that had already been determined. St. John
Chrysostom expressed this way: “He created the sun on the fourth day lest you
think that it is the cause of the day” [20, p. 16].

The Earth as the Center of Rest

Genesis 1 makes it clear that God
made the earth first and built the rest of the universe around it. Scripture
elsewhere makes it clear that God also defined the earth to be the standard of
rest in the universe. This is made clear in Psalms 92 (93):

For
He hath established the world which shall not be moved. [Ps
92:1 (Douay-Rheims)]

The Hebrew word kun translated “established” has a variety of
applications, including “ordain,” “appoint.” The Hebrew word tebel translated “world” means the earth and not the
universe.

The stationary
earth standard is confirmed by Psalms 103 (104):

Who hast founded
the earth upon its own bases; it shall not be moved for ever
and ever. [Ps 103:5 (Douay-Rheims)]

It cannot be
said that the earth is absolutely at rest because that means that it would be
at rest with respect to something else that is absolutely at rest. What would
be that something be other than absolute space? But it was shown above that
there is no absolute space. So a standard of rest must be defined; it is not
given by nature. God defined it to be the earth.

Sacred Scripture
applies the stationary earth standard concretely in describing two famous
miraculous events that occurred in the history of Israel. Both attested to the
movement of the sun in the heavens.. The first event
is “Joshua’s long day.” It is recorded in Joshua 10: 12–14:

Then  Josue spoke to the Lord, in the day that he delivered the Amorrhite in the sight of the children of Israel, and he
said before them: Move not, O sun, toward Gabaon, nor
thou, O moon, toward the valley of Ajalon. And the
sun and the moon stood still, till the people revenged themselves of their
enemies. Is not this written in the book of the just? So the sun stood still in
the midst of heaven, and hasted not to go down the space of one day. There was not before nor after so long a day, the Lord obeying the
voice of a man, and fighting for Israel. [Douay-Rheims]

Joshua’s long
day was observed around the world, as indicated in the folklore of various
nations.

The second event
is “Hezekiah’s sign.” It is recorded in Isaiah 38:7–8:

And this shall be
a sign to thee from the Lord, that the Lord will do this word which he hath
spoken: Behold I will bring again the shadow of the lines, by which it is now
gone down in the sun dial of Achaz with the sun, ten
lines backward.  And the sun returned ten lines by the degrees by which it
was gone down. [Douay-Rheims]

This event
involving the backward movement of the sun is also recalled in 4 Kgs (2Kgs) 20:8-11 and 2 Par (2 Chr)
32:24.

In these
depictions Sacred Scripture is doing more than simply describing the events as
they appeared to observers on earth. It is making the profound implication that
the earth is the center of rest in the universe. If there were such a thing as
absolute rest in the universe, and if the sun were at absolute rest with the
earth moving around it (as per the Copernican system), then the Sacred Author
would be deceiving us in these verses, which is unthinkable.

The essential
misunderstanding in the Galileo affair was the mistaken notion that there is a
natural condition of absolute rest. In both the systems of Ptolemy and
Copernicus it was presumed that there is a place of absolute rest. The major
difference between them was the location of that place.

The earth is
said to be at the center of the universe because it is a place in the universe
with special properties, just as geometric centers and centers of mass are
places with special mathematical and physical properties. God created the earth
first, built the rest of the universe around it, defined it as the center of
rest, and made it the home of man, who is a unique union of matter and spirit.
The centrality of earth in the universe might also be expressed geometrically
and/or physically, but it need not be so to be in accord with Scripture and
Tradition.

The Notion of Absolute Rest:
Historical Summary

The medieval schoolmen saw the
universe as a finite, bounded plenum or quasiplenum
with the earth at rest in the center with the heavenly spheres rotating about
it. They had a notion of void but no notion of absolute space in the Newtonian
sense. Their notion of the earth being at rest meant that the heavens were
moved around the earth by some efficient cause distinct from the spheres. And
the earth was not moved with respect to the heavens by any such efficient
cause. Thus they had a notion of absolute rest. This cosmology colored their
interpretation of the Scriptural passages that relate to the stability of the
earth.

Newtonian
physics also has a notion of absolute rest because it has a notion of absolute
space to which all motion is referred. Newton, however, following Copernicus,
set the sun at absolute rest with the earth moving around it, its motion being
caused by its inertia, which was given to it by God in the beginning [see 17,
pp. 47–49].

The modern view,
following Einstein, sees the universe as an unbounded three-dimensional
absolute space with a geometrical structure determined by the masses that
occupy it. The cosmological principle, which states that the universe looks
pretty much the same from wherever in it you view it, makes the notion of rest
relative. Any body in the universe can be defined to
be at rest.

Without
subscribing to Einsteinian cosmology and the
cosmological principle, one can still interpret rest as relative. The passages
in Scripture referring to the stability of the earth can be interpreted to mean
that the earth is at rest because God defined it to be so. He made the earth
the standard of rest in the universe because it was the first body created and
is the home of man. This requires rejection of the notion of absolute space
because that notion contains within it the notions of absolute rest and
absolute motion.

Medieval Earth-Centered
Cosmology and its Decline

Sacred Scripture makes it clear
that man and his home, earth, are the focus of the universe. The centrality of
man was expressed geometrically in the Christian medieval cosmos by having the
earth at rest with the sun and the heavens moving around it, using a model that
came from the Greeks but was in harmony with Scripture. In the medieval cosmos
there was order and hierarchy. God encompassed all and man, His steward, was at
the center. Love was the great mover. The medieval universe had a rational
structure with a purposeful place for everything. Philosopher of science E. A. Burtt nicely summarizes the medieval Christian vision:

For the Middle Ages man was in every sense the center of the
universe. The whole world of nature was believed to be teleologically
subordinate to him and his eternal destiny. Toward this conviction the two
great movements which became united in the medieval synthesis, Greek philosophy
and Judeo-Christian theology, had irresistibly led. The prevailing world-view
of the period was marked by a deep and persistent assurance that man, with his
hopes and ideals, was the all-important, even controlling fact in the universe.
[21, p. 18]

Medieval
Catholic astronomy testified to the deeply-engrained belief that man is the
masterpiece and center of creation. His good is the end of all creation. Nature
exists for his use, to help him attain his end, which is to serve God here on
earth and to spend eternal life with Him in heaven.

Nicholaus Copernicus disturbed that worldview by having the
earth move, and the theological confusion caused by Galileo’s aggressive
advocacy of Copernicus’ cosmology had the sad effect of clouding the truth of
man’s centrality and shattering the medieval vision. This decline was further
advanced by enlightenment ideology, which produced a cosmology with man removed
from the center of creation.

Burtt contrasts the drab view of man in the universe
advanced by Galileo and developed by enlightenment thinkers with the bright
picture of the medievals:

Note, however the
tremendous contrast between this view of man and his place in the universe, and
that of the medieval tradition. The scholastic scientist looked out upon the
world of nature and it appeared to him a quite sociable and human world. It was
finite in extent. It was made to serve his needs. It was clearly and fully
intelligible, being immediately present to the rational powers of his mind; it
was composed fundamentally of, and was intelligible through, those qualities
which were most vivid and intense and his own immediate experience—colour, sound, beauty, joy, heat, cold, fragrance, and its
plasticity to purpose and ideal. Now the world is an infinite and monotonous
mathematical machine.… It was simply an incalculable change in the viewpoint of
the world held by intelligent opinion in Europe. [21, pp. 123-124]

The modern view,
held by many scientists and scholars today, was clearly expressed by Bertrand
Russell in A Free Man’s Worship (Mysticism
and Logic); it is the wretched fruit of enlightenment thinking:

Such, in outline,
but even more purposeless, more void of meaning, is the world which Science
presents for our belief. Amid such a world, if anywhere, our ideals
henceforward must find a home. That man is the product of causes which had no
prevision of the end they were achieving; that his origin, his growth, his
hopes and fears, his loves and his beliefs, are but the outcome of accidental
collocations of atoms; that no fire, no heroism, no intensity of thought and
feeling, can preserve an individual life beyond the grave; that all the labours of the ages, all the devotion, all the
inspirations, all the noonday brightness of human genius, are destined to
extinction in the vast death of the solar system, and that the whole temple of
Man's achievement must inevitably be buried beneath the debris of a universe in
ruins—all these things, if not quite beyond dispute, are yet so nearly certain,
that no philosophy which rejects them can hope to stand. Only within the
scaffolding of these truths, only on the firm foundation of unyielding despair,
can the soul’s habitation henceforth be safely built. [21, p. 23]

Chapter THREE: Empirical Science and the
Earth as the Center of the Cosmos

The Logic of Absolute Motion

In the first chapter it was
explained why scholastic philosophy considers absolute space a contradiction in
reality, although not in the mind. Thus there is no such thing as absolute
space. And since there is no such thing as absolute space, it logically follows
that there is no such thing as local motion in absolute space and no such thing
as a change in local motion in absolute space. That is, there is no uniform
local motion and no accelerated local motion in absolute space. And since there
is no such thing as absolute accelerated motion, there is no such thing as absolute
force. All motion and all forces are relative to physical bodies, as Ernst Mach
correctly argued [10, p.279].

Isaac Newton
realized that the existence of absolute space cannot be demonstrated by uniform
local motion, but he argued that the inertial effects associated with
rotational motion demonstrated it. He gave his famous example of the concave
surface of a rotating pail of water. Modern geophysicists follow Newton in
considering phenomena such as the oblate shape of the earth, the rotation of the
plane of vibration of the Foucault pendulum, and the diminishing of gravity at
the equator as inertial effects associated with the absolute rotation of the
earth.

Mach refuted
Newton’s argument by pointing out that, even in the case of rotational motions,
we have knowledge only of relative places and motions. We observe only the
relative rotational motion between a rotating body and the rest of the
universe. We cannot logically conclude that the inertial effects associated
with rotation would occur without the rest of the universe present, which would
be the case if rotational motion were absolute. According to Mach, rotational
effects can be explained with reference to relative frames. He argued: “The
principles of mechanics can, indeed, be so conceived that even for relative
rotations centrifugal forces arise” [10, p. 284]. A. Assis
implemented this insight in his development of relational mechanics [8].

The Physics of Local Motion

The physical science that deals
with motion in itself, without the consideration of masses and forces, is
called kinematics. Kinematics is concerned solely with the locations,
velocities and accelerations of physical objects that move locally in any way.
These are entities that are subject to measurement, and there must be standards
for their measurement.

Measurements of
distances and angles, on a material object or in a void, ultimately depend on
the use of rigid material rods on rigid material frames of reference. Even
methods that use light to measure distance must be calibrated according to such
a standard. Rigid rods and frames of reference have parts that remain fixed
with respect to each other.

The surface of
the earth provides a basis for rigid frames of reference for terrestrial
measurements and for the calibration of astronomical measurements.

The fixed stars
provide a rigid frame of reference for astronomical measurements. The fixed
stars do not appear to us to move with respect to each other. This is because
1) they actually do not move with respect to each other; or 2) they move with
respect to each other with a motion too slow to perceive; or 3) they are so far
away that, even if they do move with significant speed with respect to each
other, their motion is imperceptible to us.

The measurement
of motion also requires a standard for the measurement of intervals of time.
Since there is no such thing as absolute time (time is an accident, not a
substance) all intervals of time are relative. Time is measured by comparing
physical processes. Intervals of time are measured by comparison with some
physical process presumed to be uniformly periodic. At one physical extreme we
have an astronomical standard (the sidereal day). At the other extreme we have
atomic clocks. In between we have pendulum and other mechanical clocks. If we
compare the uniformity of two clocks and they agree (that is, m cycles on one
always corresponds to n cycles on the other), then we can interchange them as
standards. However, if they do not always agree, then we must assume that one
is the standard and that the other drifts. If we can give a good physical
explanation why the second clock drifts, then we are satisfied. But if not,
then we reverse the process. However, it seems that God gave us astronomical
time as the ultimate standard.

Astronomical Phenomena
Pertaining to the Stability of the Earth

Believers in a mobile earth point
to two well-known astronomical phenomena that they suppose convincingly
demonstrate motion of the earth through absolute space. Those phenomena are
stellar aberration and stellar parallax. Arguments for a moving earth based on
them can easily be shown to be inconclusive.

The phenomenon
of stellar aberration was discovered by James Bradley in 1726. It is the
apparent displacement in the positions of stars attributed to the finite speed
of light and to the transverse motion of the earthbound observer with respect
to the ray of light from a star. The effect requires the slanting of a
telescope at an angle away from the target star to allow light entering the objective
lens to reach the eyepiece. The telescope must be tilted to allow the ray to
travel down the axis of a transversely moving telescope. If the speed of light
were infinite, that would not be necessary. Stellar aberration has long been
used as evidence for motion of the earth through absolute space. Those who
advance it as evidence for absolute motion of the earth assume two things. They
first assume that light propagates like a wave through a medium called the
ether. Second, they assume that the ether is at rest in absolute space.
According to that view, motion of the star through the ether would not cause
the effect; only motion of the earth through the ether would cause it. But, if
the ether moved like a breeze through absolute space, the same effect would be
produced. One could conceive of the earth at rest with the ether moving around
it with the sun. Also, if the light is conceived as a beam of particles, which
is the quantum mechanical view, then the effect is only one of the relative motion of the earth and star.

Albert Einstein,
in his 1905 paper on special relativity entitled “On the Electrodynamics of
Moving Bodies,” treated stellar aberration as a phenomenon caused by relative
motion of the earth and star [22, pp. 55-57]. Einstein calculated the
first-order stellar aberration, which is caused by a “wobble” of the celestial
sphere with respect to earth. The first-order effect is of equal magnitude for
all the stars. Higher order aberration effects are caused by additional motions
of stars with respect to the celestial sphere.

Stellar parallax
is the angular displacement of certain stars against the background of the
fixed stars. It was first observed by Friedrich Wilhelm Bessel in 1838.
Astronomers attribute this to the optical effect called parallax, which is the
apparent displacement of two objects when viewed from two different positions.
This occurs, for example, when one holds a pencil in front of his nose and
views it with one eye and then other. The pencil appears to move relative to
the background. In the case of stellar parallax, the two observations are made
from the earth six months apart. The earth in then pictured as being at two
different ends of its apparent orbit around the sun. It is assumed that earth
moves with respect to the stars and that the sun remains fixed with respect to
the stars. This means that there would be no parallax on the sun, something
that has not been demonstrated. This explanation further assumes that the stars
themselves are fixed in absolute space, something else that has not been
demonstrated. The phenomenon of stellar parallax, therefore, does not
conclusively demonstrate absolute motion of the earth.

E. Whittaker
summarizes nineteenth-century optical astronomy and concludes that optical
methods had been unable to detect the earth’s alleged absolute motion through
space:

Fresnel inferred
from his formula that if observations were made with a telescope filled with
water, the aberration would be unaffected by the presence of the water—a result
which was verified by Airy (*) in 1871. He showed, moreover, that the apparent
positions of terrestrial objects, carried along with the observer, are not
displaced by the earth’s motion; that experiments in refraction and
interference are not influenced by any motion which is common to the source,
apparatus and observer; and that light travels between given points of a moving
material system by the path of least time. These predictions have also been
confirmed by observation: Respighi (*) in 1861, and Hoek
(*) in 1868, experimenting with a telescope filled with water and a terrestrial
source of light, found that no effect was produced on the phenomena of
reflection and refraction by altering the orientation of the apparatus relative
to the direction of the earth’s motion. E. Mascart
(*) in 1872 studied experimentally the question of the effect of motion of the
source or recipient of light in all its bearings, and showed that the light of
the sun and that derived from artificial sources are alike incapable of
revealing by diffraction-phenomena the translatory
motion of the earth. [23, vol. I, pp. 113-114] [An
asterisk indicates that a source is cited by the author.]

Optical Experiments
Pertaining to the Stability of the Earth

The most famous attempt to
measure the alleged motion of the earth through the ether by optical means was
the Michelson-Morley experiment, first performed in 1887. The logic of the
experiment is as follows: two coherent light beams are sent out from a beam
splitter in mutually perpendicular directions, one in
the direction of the earth’s supposed motion and one perpendicular to it. After
traveling equal distances on the apparatus, the two beams are reflected back to
the beam splitter and into an interferometer. Calculations indicated that the
roundtrip “upstream and downstream” and the roundtrip “cross stream” would take
different periods of time, the upstream-downstream trip taking more time. So
they should both arrive back at their origin out of phase and thus cause a
shift in the interference fringes (from that expected for a null result). But
no such fringe shifts were observed, which implied that earth does not move.
But physicists like G. F. Fitzgerald and H. A. Lorentz, who were totally imbued
with the notion of absolute space filled with ether, attempted to explain the
null result of the experiment by making the incredible proposal that the
apparatus “shrunk’ in the direction of the motion just enough to conceal the
earth’s motion. According to J. S. Bell, Lorentz, rather than  rejecting
the notion of the motion of the earth through the ether, “preferred the view
that that there is indeed a state of real rest, defined by the ‘aether’, even though the laws of physics conspire to
prevent us from identifying it experimentally” [24, p. 77].  A. Assis explains the null result of the Michelson-Morley
experiment in terms of relational mechanics. Assis
maintains that the most straightforward explanation of that experiment is that
there is no ether. He says: “Only the relative motion between the light, the
mirrors, the charges in them and the earth are important, no matter what the
velocity of these bodies relative to the ether or to absolute space” [8, p.
145].

Einstein
expressed his belief in the fruitlessness of attempting to measure absolute
motion of the earth. In the introductory paragraph of his 1905 paper on special
relativity Einstein refers to “unsuccessful attempts to discover any motion of
the earth relatively to the ‘light medium,’ which “suggest that the phenomena
of electrodynamics as well as of mechanics possess no properties corresponding
to the idea of absolute rest” [22, p. 37]. The attempts that he alludes to include stellar aberration, stellar parallax and
the Michelson-Morley experiment, all observations that predate publication of
that paper.

Gerardus D. Bouw [25] describes a
geostationary model of the universe that exhibits all observable astronomical
kinematic phenomena, including the phases of Venus, stellar aberration and
stellar parallax. It is a modified version of that of Tycho
Brahe with the planets and the stars moving around the sun, which, in turn,
moves around the earth.

*

Accelerated motion can be
detected by actual physical effects, for example, compression or tension in an
elastic material. However, the effects cannot tell us whether the acceleration
is caused by motion with respect to absolute space or motion with respect to
the rest of the universe.

In 1913 G. Sagnac, following a suggestion by A. Michelson, used light
in an attempt to determine absolute rotational motion. The experiment was
conducted as follows: Four mirrors were arranged in a square centered on the
axis of a turntable so as to reflect a beam of light around the square. A light
source, a beam splitter, and an interferometer were also placed at appropriate
locations on the turntable. Two coherent beams of light were sent out from the
beam splitter in opposite directions around the square back to the beam
splitter and into the interferometer. When the turntable was at rest the beams
arrived at the interferometer in phase with each other and produced a fringe
pattern. When the turntable was rotated, however, shifts in the fringes were
observed, which indicated that the optical lengths of the two paths were
different. (The same observation was made later by different experimenters with
the light source and observer standing off the rotating platform.) This was
taken as a demonstration that the platform was rotating in absolute space [25,
pp. 281–284; 26, pp. 55–58]. However, the same arguments apply for this
experiment as were made above for mechanical effects of acceleration; that is,
we do not know whether the Sagnac effect is caused by
motion with respect to absolute space or motion with respect to the rest of the
universe. It is not possible to test this directly because one cannot simply
remove all the heavenly bodies. H. E. Ives seems to have recognized this,
although he argued against the Sagnac effect as being
an effect of the relative rotation of material bodies. In a 1938 paper that
deals with the Sagnac effect he concludes:

The observer on the
apparatus has just one reference framework by which he can predict whether the Sagnac effect will appear or not; that framework is the
pattern of radiant energy from the stars. If his apparatus rotates with respect
to the stars he will observe a Sagnac effect, if it
does not, then no matter how great a relative rotation it exhibits with respect
to its material surroundings, there will be no Sagnac
effect. [27, p. 44]

The results of
optical experiments like the Sagnac experiment must
be interpreted with great care because we do not have a clear understanding of
the nature of light and its inertial effects. Light has been observed in
various experiments to behave with apparently irreconcilable wave properties
and particle properties. Waves are propagated; particles are projected or
propelled. Any particular experiment must be interpreted according to whether a
wave property or a particle property is being observed. If a wave property such
as interference or diffraction is being observed, then light must be presumed
to be a wave. Since a wave is propagated, it requires a medium. The medium that
propagates light waves is called ether. Assumptions must be made about the
ether, for example, whether it is at rest or moving and in respect to what.
Particle properties of light manifest themselves in experiments that involve
the exchange of energy and momentum between light and matter. Another
consideration is the speed of light. Is it the same for all sources? How does
reflection of light from a moving mirror affect its properties of wavelength,
frequency and speed? Einstein, in his 1905 paper on special theory of
relativity, assumed that the speed of light in a vacuum is always the same for
everybody [22, p. 41]. However, others interpret empirical evidence to the
contrary [8, pp. 139-140]. In his 1905 paper, Einstein interpreted light as a
wave phenomenon and the constancy of the speed of light for all observers as a
kinematical effect. That interpretation generates contradictions. However, in
the next chapter a dynamic interpretation for the constancy of the speed of
light will be given that is free from contradictions. That interpretation
employs particle properties of light.

Comments on the Nature and
Motion of Light

At this point it would be
sensible to consider the general nature and the motion of light itself because
its nature and its means of moving determine the interpretation of optical
observations.

St. Thomas
Aquinas following Aristotle held that light is an accidental form. St.
Bonaventure held that it is a substantial form. It is interesting that neither
held light to be a substance. Being a form, it exists in something else. As an
accidental form, would the underlying “subject” be a material object or the void?
And, as a substantial form, what is the underlying “matter”? St. Bonaventure
believed in the plurality of substantial forms (more than one substantial form
in a substance) and that the same matter underlies both material and spiritual
substances. He believed that light is the common form of all things. The
nineteenth-century view was that light is a disturbance of an ethereal medium
that is propagated. Thus light was considered accidental in nature. The modern
view is that light is substantial. Photons of light possess energy that can be
transformed into matter.

There are three
ways in which light might move: propagation, projection, and propulsion. In the
so-called “wave theory,” light is propagated as a wave, analogous to water and
sound waves; this is the classical electromagnetic view. In the so-called
“ballistic theory,” light is viewed as a projectile that is given motion by its
source and continues to move along by inertia; this is the picture we are
given, rightly or wrongly, by quantum mechanics. A third view, which does not
seem to have been given much attention by physicists, might be called the
“self-propulsion theory.” It is a combination of the modern and classical
views. Light is seen as an independent entity like a photon. But it propels itself
through the ether, analogous to a fish in water or a snake on land. There is a
hint of this in the classical explanation for the propagation of an
electromagnetic wave. In that view a varying electric field produces a varying
magnetic field in its immediate vicinity, which in turn produces a varying
electric field in its immediate vicinity, and so on. In this way light
“wiggles,” “crawls,” “swims,”  “steps” or “walks” through the ether.

Geometrical and Physical
Centricity of Earth

The earth is at the center of the
universe because it is a place in the universe with special properties, just as
geometric centers and centers of mass are places with special properties. The
definition of “center” is not unique; for example, geometers have a number of
different definitions for the “center” of a triangle. The earth is considered
to be at the center of the universe because God created it first, built the
rest of the universe around it, defined it as the standard of rest, and made it
the home of man, who is a unique union of matter and spirit.

The centrality
of earth in the universe might also be expressed geometrically and/or
physically. And, as we shall see, there is evidence that it is; although it
need not be so to be in accord with Scripture. Striking evidence that the earth
is at or near the center of the universe comes from the observation of galaxies
and quasars. (Quasars, from “quasi-stellar objects,” are star-like sources of
light of unknown nature whose red shifts are large. They must be very bright to
be visible at the great distances astronomers assign to them.) In the early
1970s, William Tifft at the Steward Observatory in
Tucson, AZ analyzed red shift data from galaxies in all directions. His
analysis showed that the red shifts are quantized. This can be interpreted to
mean that the galaxies are arranged on concentric spherical shells. The
quantization effect could be clearly observed only if the earth was close to
the center of the shells. [See Russell Humphreys, “Our galaxy is the centre of
the universe, ‘quantized’ redshifts show,” TJ 16(2):95–104
(2002).] Y. P. Varshni studied the red shifts of 384
quasars. Varshni concluded that if the quasar red
shifts are real and distance related then “the Earth is indeed the center of
the Universe. The arrangement of the quasars on certain spherical shells is
only with respect to the Earth. These shells would disappear if viewed from
another galaxy or a quasar. This means that the cosmological principle will
have to go. Also, it implies that a coordinate system fixed to Earth will be a
preferred frame of reference in the Universe. Consequently, both the Special
and the General Theory of Relativity must be abandoned for cosmological
purposes” [Astrophys. Space Sci. 43:3
(1976); 51:121 (1977)].

Other evidence
offered as suggesting that the earth is at or near the center of the universe
comes form the study of ambient microwave radiation.
In 1965 A. A. Penzias and R. W. Wilson discovered that the earth is immersed in
a bath of microwave radiation corresponding to that found inside a box kept at
a temperature of 2.7 Kelvin. This radiation, called cosmic microwave
radiation (CMR), is very isotropic, having intensity variations with
direction no greater than one part in one hundred thousand. Physicist V. F. Weisskopf made this observation concerning the isotropy of
this radiation: “It is remarkable that we are now justified in talking about an
absolute motion, and that we can measure it. The great dream of Michelson and
Morley is realized. They wanted to measure the absolute motion of the earth by
measuring the velocity of light in different directions. According to Einstein,
however, this velocity is always the same. But the 3 K radiation represents a
fixed system of coordinates. It makes sense to say that an observer is at rest
in an absolute sense when the 3 K radiation appears to have the same
frequencies in all directions. Nature has provided an absolute frame of
reference. The deeper significance of this concept is not yet clear” [Am.
Sci. 71, no. 5: 473]. However, observations show that the CMR wavelength
spectrum is not isotropic in wavelength. Its wavelength spectrum is shifted
down in one direction of the sky and shifted up by the same amount in the
opposite direction. This phenomenon is called dipole anisotropy. It is
attributed to the Doppler effect caused by a speed of
about 260 kilometers per second of the earth relative to the radiation. Weisskopf’s enthusiasm is premature. There is not enough
known about CMR to qualify it as an absolute frame of reference. Is it
isotropic, stationary and thermally uniform throughout the whole universe? Or
is it like our oceans, hotter in some places, cooler in others, with streams
flowing through it? Dipole anisotropy suggests such streams when we take the
earth as the center of rest. It seems then that CMR can no more provide a
standard of absolute rest for the universe that can ocean water provide a
standard of rest for the earth.

Chapter FOUR: The Logic of Newtonian Physics
and Relativity

Newton’s Laws of Motion and
Inertial Frames

The science of matter and motion,
called mechanics, was greatly advanced by the work of Isaac Newton. In the Principia
Newton encapsulated the dynamics of material bodies in three laws [17, pp.
25–26]:

first law: Every
body continues in its state of rest or of uniform motion in a right line
unless it is compelled to change that state by a force impressed upon it.

second law: The change of motion is
proportional to the motive force impressed and is made in the direction of the
right line in which that force is impressed.

third law: To every action there is
always opposed an equal reaction; or, the mutual actions of two bodies upon
each other are always equal, and directed to contrary parts.

The first law is
called the law of inertia. It states that a material body, by virtue of its
inertial mass (“quantity of matter”) alone, will not change its state of rest
or uniform linear motion without an outside influence being impressed upon it.

Newton defines
the “quantity of the motion” (momentum) of a material body as the product of it
mass and velocity.  An applied force changes the momentum along the
direction of the force. The second law states that if a force produces a change
in the quantity of motion, then twice that force will produce twice the change,
three times the force three times the change, and so on.

The third law is
called the law of action and reaction. Whenever one material
body “pushes” on another, the second pushes back with an equal force.

Newton did not
give an adequate definition for the inertial mass of a body. He simply defined
it as the product of the volume of a body and its density. Ernst Mach gave a
much better definition by employing the third law. He stated: “All those bodies
are bodies of equal mass, which, mutually acting on each other, produce in each
other equal and opposite accelerations” [10, p. 266]. For example, consider two
masses at the two ends of a constrained compressed spring on a level
frictionless surface. When the constraint is removed, the expanding spring will
cause both masses to accelerate along the surface. If the accelerations are
equal, the masses are equal. This definition would seem to work well on any
rigid material frame of reference in which both masses start out at rest with respect
to each other and with respect to the frame of reference and no external forces
are present that produce a bias. Such a bias would be present, for example, if
one performed the above procedure on an inclined surface rather than a level
one. Then gravity would decrease the acceleration of the mass going uphill and
increase the acceleration on the mass going downhill. In the case of unequal
accelerations, the ratio of the masses is inversely proportional to the ratio
of the magnitudes of the accelerations.

Newton said that
his laws of motion apply in any frame of reference that is at rest in or moves
in uniform linear motion in absolute space. These are called inertial frames.
Today the term inertial frame is used simply to mean a frame in which Newton’s
laws of motion apply directly, without any reference to absolute space. Frames
of reference in which Newton’s laws do not apply directly (such as rotating
rigid platforms) are called non-inertial frames. In such frames Newton’s laws
of motion have to be modified by the introduction of “fictitious forces,” such
as centrifugal and Coriolis forces. According to
Newtonian mechanics, fictitious forces are forces that cannot be traced to
physical interactions with other material bodies; they are the result of nonuniform and/or nonlinear motion of a frame of reference
with respect to absolute space. According to Machian
mechanics, the so-called fictitious forces are actually real forces that are
associated with interactions arising from nonuniform
and/or nonlinear motion of a frame with respect to the rest of the universe. A
specific nature is given to those interactions by Andre Assis
in his Relational Mechanics [8].

Ultimately,
fictitious forces are explainable in terms of Newton’s three laws because they
derive from the inertial properties of matter contained therein. Therefore they
are also called inertial forces. Newtonian mechanics does not give a reason for
these inertial properties of matter; it only states them. Machian
mechanics, on the other hand, attributes the inertial properties of a material
body to the other matter in the universe. In the Machian
view, every material body resists any change in the arrangement of the
universe, and this is a collective phenomenon.

Newton’s
referencing his laws to absolute space introduces a certain ambiguity in his
first law. In that law he refers to motion in a “right” (straight) line. But
what is a straight line? How can a straight line be defined in absolute space?
If it is defined as the trajectory of a mass that has no force impressed on it,
then his law suffers from circularity. And how would “trajectory” be defined in the first place? How does one determine
geometrically whether or not a force is being impressed? In empty absolute
space no coordinate grid can be established because there is no place to anchor
such a grid and no standard for the measure of distance. Therefore the concepts
of trajectory and straight line are meaningless.

Despite this
Newton was immensely successful in using his laws to explain observed
terrestrial and celestial motions. That is because his laws of motion do not
require the notion of absolute space, as Ernst Mach pointed out. Newton’s laws
of motion only require rigid frames of reference in which they work. All the
frames of reference in which his laws of motion have been empirically confirmed
are frames fixed to material objects, which are relative frames not absolute
ones.

Even though
Newton’s mechanics gave the science of physics a great boost, his faulty
metaphysics pointed physics in the wrong direction. Newton’s rejection of the
scholastic view of space and time led the way to the plethora of esoteric and
confused relativity-based cosmologies that we are plagued with today. His
opposition to the scholastic view is clearly presented in the following passage
from his paper De gravitatione (c. 1670),
in which he defends the reality of absolute space:

… we can clearly
conceive extension existing without any subject, as when we may imagine spaces
outside the world or places empty of body, and we believe {extension} to exist
wherever we imagine there are no bodies, and we cannot believe that it would
perish if God should annihilate a body, it follows that {extension} does not
exist as an accident inherent in some subject. And hence it is not an accident.
And much less may it be said to be nothing, since it is rather something, than
an accident, and approaches more nearly to the nature of substance. There is no
idea of nothing, nor has nothing any properties, but we have an exceptionally
clear idea of extension, abstracting the dispositions and properties of a body
so that there remains only the uniform and unlimited stretching out of space in
length, breadth and depth. And, furthermore, many of its properties are
associated with this idea; these I shall enumerate not only to show that it is
something, but what is. [28, p. 618]

The scholastic
argument, given in Chapter 1, is much sounder; it does not confuse abstraction
with reality.

Furthermore,
Newton’s theology of creation was decidedly non-Catholic. He considered void
not as a freely created entity but as a necessary effect of God, existing
eternally along with Him, and, like God, perfectly simple and immutable. God
had no alternative to creating matter in three-dimensional space. (That would
seem to put an unreasonable limitation on God’s power to create. He would not
be free to create a higher-dimensional world, which does not seem to be an
inherently contradictory notion.) Likewise, Newton considered absolute time to
be uncreated. He viewed the eternity of God not as transcending time but as the
enduring existence of God in absolute time. Newton perceived God as distinct
from but effecting and living in infinite space and time. Moreover, he held
that infinite space is the “sensorium” of God, in
which He observes the world. Newton spelled out these views in De gravitatione, the Principia and elsewhere [see
17, pp. 41–67; 28, pp. 617–644].

Electrodynamics and
Einstein’s Postulates for Special Relativity

The notion of absolute space was
to be looked at in a new light in the nineteenth century with the development
of a completely new science, electrodynamics. This science dealt with the
newly-identified electric and magnetic forces, which, although similar in some
ways, were quite different from the familiar gravitational force. At the center
of electrodynamics is a physical entity called electric charge, of which there
are two kinds, positive and negative. If a material body possesses such a
charge, it will exert a repulsive force on other bodies that possess the same
kind of charge and an attractive force on bodies that possess the other kind of
charge. All uncharged material bodes contain equal amounts of positive and
negative electric charge, which cancel out the effects of each other making the
body overall electrically neutral. Uncharged metals carry “free” negative
charge, that is, charge that is free to move within the metal. But that charge
is balanced by an equal amount of “fixed” positive charge, which makes the
metal overall electrically neutral. Charged metals carry either a deficiency or
an excess of negative charge, making them either positively or negatively
charged. The free charge in a metal can move to constitute what is called an
electric current. Because of their ability to conduct an electric current,
metals are called conductors. Materials that do not possess “free” charge, and
therefore cannot conduct an electric current, are called insulators.

There was yet
another kind of material, called lodestone, which possessed a strange property.
Pieces of lodestone were observed to attract or repel other pieces of
lodestone, even with nothing in between them. And it was found that it could
give this property to iron without losing it itself. This property came to be
known as magnetism. Bodies that possess it are called magnets. Magnets were
also observed to produce effects on electrically charged bodies, but those
effects were different from the effects electric charges produced on each
other. Magnets exerted forces on electrically charged bodies, but only on
charged bodies that move relative to the magnet. If was observed that if a
metal wire was moved toward or away from a magnet an electric current would be
induced in the wire. If instead the magnet was moved in the same way relative
to the wire an identical current would be induced. Thus the induced current was
observed to depend only on the relative motion between the wire and the magnet.

A key figure in
the development of the science of electrodynamics was Michael Faraday, who
performed experiments with charged bodies, wires and
magnets. In his attempt to understand what he observed he invented the concept
of a field, which was mathematically developed by James Clerk Maxwell. The
concept of a field eliminated the need to talk about action-at-a-distance. That
is, one no longer had to think of charged bodies and magnets as exerting their
effects instantly across empty space. Instead, they produce fields of force in
the space around them, which in turn exert their effects by immediate contact.
So there developed two approaches to electrodynamics, the action-at-a-distance
approach, which was developed by Wilhelm Weber, and the field approach of
Faraday and Maxwell. The latter won out in the minds of physicists, but not
without the introduction of new perplexities that replaced those of
action-at-a-distance.

The great
achievement of the field approach to electrodynamics was the discovery that
disturbances in an electromagnetic field are propagated as waves that travel at
the same speed as light. Thus light came to be identified as an electromagnetic
phenomenon. The perplexities introduced were associated with the notion of the luminiferous ether, the mysterious medium required for the
propagation of electromagnetic disturbances. Is it identical to absolute space
or distinct from it? If distinct, of what is it composed? Does it have a solid
or fluid nature? Does it exist in absolute space; and, if so, is it at rest or
does it move in the manner of an ocean current or perhaps multiple ocean
currents? Does it travel with the source of the fields it propagates? Does it
resist the motion of material bodies through it, thus giving rise to the
phenomenon of inertia? Nineteenth century physicists tended to think of the
ether, whatever they perceived its substantial nature to be, as being at rest
in absolute space and as pervading all of space. H. A. Lorentz was the great
champion of the ether notion. Albert Einstein was its great opponent.

The notion of
ether also raises interesting questions for the scholastic philosopher. If the
ether exists, is it a substance or an accident? If it is a substance, is it
material or immaterial? If it is a substance, then arguments that deny the
existence of absolute space, which is nothingness, would not apply to the
ether, which is a created something. If the ether is a substance that pervades
the whole universe, then the universe is a plenum and there is no void. If the
ether is an accident, then in what subject does it exist? Is the ether a
potency and, if so, to what? If it is a potency, what
is its relation to pure potency, that is, prime matter? Is the ether an
incomplete substance, analogous to a disembodied human soul, and, if so, what
completes it? Consideration of such questions could lead to a better
understanding of electromagnetic phenomena.

Einstein
presents the ethereal point of view at the beginning of his 1905 paper on
special relativity [22, pp. 37–38]. He gives the Lorentzian
explanation for the induced current in a conducting wire moving with respect to
a magnet. According to the Lorentzian interpretation
of Maxwell’s field theory, the same current can be produced in the wire for two
different reasons, depending on motion with respect to the ether. If the wire
moves with respect to the ether, then the current is induced simply by the
motion through the magnetic field. If the magnet moves, the current is induced
by an electric field produced by the moving magnetic field. Thus in one case a
magnetic field produces the current; in the other case an electric field
produces the current. This is an asymmetry that is not inherent in the
phenomenon itself because the exact same effect takes place no matter which
object is moved. The asymmetry results from a misinterpretation of Maxwell’s
field equations. Maxwell’s field equations state that a varying electric field
at a point produces a magnetic field in the vicinity of the point and vice
versa. However, the fields must be referred to their source (as Faraday and
Maxwell did) and not to the ether (as Lorentz and Einstein did). And since the
field of the magnet does not change with respect to the magnet when the magnet
is moved there is no electric field produced by the moving magnet. So the
current in the wire is induced by magnetic force in both cases. This is
explained clearly and in detail by Andre Assis [8,
pp.127–131 (also see 43, pp. 148-149 and 48, pp. 7-9)].

Einstein
believed that elimination of the asymmetry required elimination of the notion
of ether. If he had adopted the view of Faraday and Maxwell instead of the view
of Lorentz, he would have been able to retain both the symmetry and the ether.
Elimination of the ether was a drastic step that led to the theory of
relativity of space and time with its confused notions and inherent contradictions.

Einstein built
his theory of special relativity on two postulates. The first he called the
“principle of relativity.” It can be stated as follows: The fundamental laws of
physics (mechanical and electrodynamic) have the same
formulation on all rigid material frames of reference that move in uniform translatory motion with respect to each other. That would
make uniform translational motion through the ether undetectable by physical
experiments. However, the postulate says nothing about accelerated motion.
Accelerated motion could still be detected by inertial effects, as Newton had
observed. So the notion of ether cannot be totally ruled out by this postulate.

The second
postulate in that of the constancy of the speed of light in a vacuum. The first
postulate already implies that the speed of light is constant with respect to
the source. Otherwise, the fundamental laws of electrodynamics would differ
from frame to frame and one could detect uniform motion in the ether. But for
the speed of light to be constant with respect to the source each source would
have to be accompanied by its own ether. Einstein went a step further because
he wanted to eliminate the ether altogether. He said that the speed of a beam
of light will have the same speed for all observers that move in uniform translatory motion with respect to each other, no matter in
which frame it was emitted. Assis points out that
this postulate makes light an oddity in the physical world. The speed of
bullets shot from a gun with respect to a flatcar on which it rides does not
depend on the speed of the flatcar, but their speed with respect to any
observer depends on the speed of the observer relative to the flatcar. The
speed of a wave is constant with respect to the medium in which it travels, as
long as the medium is homogeneous. But its speed relative to an observer
depends on the speed of the observer relative to the medium. However, in
special relativity the speed of light does not depend on the speed of the
observer relative to anything. According to Assis,
that has never been empirically demonstrated. In fact, Assis
cites evidence to the contrary [8, pp. 139–140]. In physical experiments light
always shows similarities to projectiles or waves. But Einstein made light
behave differently than either projectiles or waves. That is the source of the
“paradoxes” and the counter-intuitional concepts of space and time generated by
special relativity because in order to maintain the constancy speed of light
for all observers one is forced to deny the possibility of common standards for
measuring distance and duration.

Thus Einstein’s
second postulate gives light a privileged place among physical phenomena.
Making the speed of light constant for all observers makes it simulate infinite
speed. According to classical physics only something traveling at an infinite
speed would have the same speed with respect to all observers, independent of
their states of motion. The speed of light being the same for all observers
gives rise to relativity’s bizarre notions of space and time.

One such notion
is called “relativity of simultaneity.” Classically, simultaneity can be
defined in terms of events that can be “connected” with signals that travel at
infinite speed. This means that if a clock, at a certain instant, sends out an
infinitely fast signal throughout the universe, events occurring at places
throughout the universe when that signal is received are occurring
simultaneously. But in Einstein’s relativity, such simultaneous events are also
connected by signals that travel at finite speeds. Consider a transmitter at
rest with respect to a receiver located at another distant place. Assume next
that, at a certain instant, the transmitter sends an infinitely fast signal to
the receiver that contains information about events then occurring at its
place. So the “observer” at the receiver can know what is happening at that
instant at the place of the transmitter.

Next consider an
“observer” moving at velocity v with respect to the rest frame of the
transmitter and receiver. According to classical kinematics the signals
exchanged between the transmitter and receiver would still be infinitely fast
for such an observer. But according to relativistic kinematics that would not
be so. The transmission and reception events would not be connected by a signal
of infinite speed, but by a signal of finite speed, and therefore the
transmission and reception of the signal would not be simultaneous events to
such an observer. The formulas for the addition of velocities of special
relativity transform the infinite speed of the signal sent by the transmitter
to the receiver to a signal of finite speed for such an observer. The speed of
the signal can take on a range of finite values, the value depending on the
magnitude of v and its direction with respect to the line connecting the
transmitter and receiver.

Consider a
special case in which the observer travels in a straight line at speed v in the
direction from the transmitter to the receiver. Then the infinitely fast signal
appears to the observer to be traveling at the at the finite speed c^2/v,
where c is the speed of light. Relativistic kinematics does not allow v to
exceed c because that produces mathematically imaginary effects. Therefore the
speed of the signal that the moving observer observes, although finite, is
still equal to or greater than c. Furthermore, the fourth Lorentz equation, the
time transformation, indicates that if the observer were to clock a signal
speed greater than c^2/v he would see the temporal sequence of the
events reversed; that is, the observer would see the receiver receiving the
signal before the transmitter transmits it. Since c^2/v is the
transformation of the highest signal speed possible in the rest frame of the
transmitter and receiver, it is the highest signal speed that can be clocked by
the observer, so the reversal of cause and effect in his frame is not possible.

The above
example should make it clear that although relativistic kinematics puts a limit
on the relative speed of inertial frames, it does not put a limit on the speed
of a signal sent within an inertial frame or even between inertial frames.
However, relativistic dynamics puts a limit on the speeds of signals that are
conveyed with objects that have inertial mass because a massive object cannot
move faster than the speed of light in an inertial frame.

There are
indications that some natural effects are transmitted with infinite or
near-infinite speed. Physical observations provide strong evidence that certain
gravitational, electromagnetic and quantum mechanical effects are communicated
instantly or near instantly. But these effects cannot be used by intelligent
agents to communicate information. This will be discussed at some length in the
next chapter.

Kinematical Contradictions of
Special Relativity

If something were to travel
instantaneously it would appear so to all observers because that is a property
of infinite speed. Postulating that a finite speed of light is the same to all
observers is applying a property proper to an infinite thing to a finite thing.
This is the source of contradictions in special relativity. It is analogous to
postulating that the center of every finite circle is everywhere within the
circle, a property that belongs only to infinite circles. A geometry based on
such a postulate would produce contradictions.

Two results of
special relativity are length contraction and time dilation. According to
Einstein, observers moving with uniform linear motion with respect to each
other will observe the other’s measuring rod to be shorter and clock to be
slower; both would observe the exact same effects in the other’s instruments.
This notion leads to contractions. The most famous contradiction is the “twin
contradiction.” It is usually called the twin “paradox.” But it is not a
paradox because a paradox is only an apparent contradiction. It is a genuine
contradiction if presented in the proper way. It goes as follows:

Twins occupy two
identical space rockets facing back to back. They both fire off at the same
time and follow the same flight program. They rapidly accelerate away from each
other to close the speed of light, move on uniformly for a time, slow down to a
stop, reverse direction, accelerate to close the speed of light again, move on
uniformly for some time, slow down and return together. According to special
relativity, each pilot says that the other has aged more slowly and will be
younger on the return. Because of the perfect symmetry of the arrangement, this
can be nothing other than a genuine contradiction.

This “paradox”
is usually presented in a non-symmetrical form. The one twin stays home on
earth while the other goes off in a rocket and returns. Relativists resolve the
paradox by saying that the twin who stayed at home remained at rest or in a
state of uniform motion in space while the other was subjected to forces during
acceleration and deceleration. So he’s the one who really moved, and he will
indeed be younger than his brother when he returns home. Here relativists
resort to the concept of absolute space (or ether), which Einstein’s theory was
supposed to make “superfluous.”

Here is a
contradiction involving length contraction that might be called “the incredible
shrinking bobsled contradiction”: A bobsled is made to slide in a long straight
frictionless track. At midlength along the track a
hole made equal to the length of the bobsled when the bobsled is at rest in the
track. The bobsled is then taken to the end of the track, equipped with
rockets, and accelerated down the track to close to the speed of light. An
observer sitting at rest alongside the track will observe that the bobsled is
shorter than the hole and that the bobsled will fall through the hole. The
pilot of the bobsled will find the hole much shorter than the bobsled and the
bobsled will pass right over the hole.

These and other
inconsistencies in the special theory of relativity call for a rethinking of
the problem of relative versus absolute motion.

Special Relativity without
Contradictions

The most fundamental formulae of
field electrodynamics are Maxwell’s four field equations and Lorentz’s force
equation. Maxwell’s equations describe the electric and magnetic fields of a
source relative to the source. The Lorentz force equation describes the effects
of an electromagnetic field on an electrically charged body moving relative to
the source of the field. If the principle of relativity is a genuine feature of
nature, what can we learn about nature by applying it directly to Maxwell’s and
Lorentz’s equations? That and related questions were investigated by Nizar Hamdan in a series of five
papers [30]. Hamdan conceives a dynamic relativity
that is free of the contractions inherent in Einstein’s kinematic relativity.
He obtains the verified results of special relativity without employing its
bizarre conceptions of space and time.

Hamdan distinguishes his principle of relativity from that
of Einstein. For Einstein, a fundamental physical law is one that remains
invariant (that is, retains the same mathematical form) under a Lorentz
transformation, which is a set of transformation formulas that give Maxwell’s
equations the same mathematical form in all frames of reference moving in
uniform linear motion with respect to each other. For Hamdan,
any physical equation is a candidate to describe a fundamental law. The Lorentz
transformation is a transformation of space and time coordinates that leads to
the notions of length contraction and time dilation. Hamdan
removes Einstein’s constraint and thereby eliminates the need to refer to the
Lorentz space-time transformation and its associated contradictions. For a
given physical equation, the transformation rule is not imposed; rather it is
sought.

Hamdan arrives at the constancy of the speed of light for
all observers by applying his principle of relativity to both the Lorentz force
law [30a] and to Maxwell’s field equations [30e]. He shows that the constancy
of the speed of light for all observers is a consequence of the relativity
principle alone and need not be postulated additionally as Einstein did. But he
argues that the constancy of the speed of light is not a kinematic effect, as
it is in the special theory of relativity, but a dynamic effect. That is, it is
not an effect of the properties of motion but an effect of the properties of
light itself. The wavelength (which is inversely proportional to the momentum)
and frequency (which is proportional to the energy) of a photon of light may
vary from observer to observer, but their product (which is the speed of light)
remains constant. In Hamdan’s analysis the notions of
length contraction and time dilation and the contradictions associated with
them have no physical significance. They have no significance because they are
rooted in the notion that the constancy of light is a kinematic phenomenon, as
Einstein proposed. If the constancy of the speed of light is a dynamic
phenomenon, as Hamdan proposed, then length
contraction and time dilation do not follow as necessary consequences.

In both
Einstein’s and Hamdan’s dynamics a massive body
cannot move in any inertial frame faster than the speed of light. But in both
relativities massless signals can move faster than
the speed of light within an inertial frame or between inertial frames. It
seems that gravitational and electromagnetic interactions are such massless signals and thus are not constrained to speeds
less than or equal to the speed of light.

In Hamdan’s analysis the fundamental entities in the universe
are energy and momentum. Space, time and mass are secondary. This is consistent
with the scholastic notion that matter and motion are the two fundamental
created entities. Place, time duration and quantity of matter are accidents of
matter and motion. Hamdan shows that the invariance
of the speed of light is rooted in the transformation properties of its energy
and momentum for observers in relative motion. From his application of the
relativity principle alone to the Lorentz force alone he arrives at the two
great triumphs of Einstein’s theory: the formula describing the increase of
inertial mass with velocity and the formula identifying inertial mass and
energy. Those formulas are also rooted in the transformation properties of
energy and momentum and manifest a close relationship between inertial and
electromagnetic phenomena.

Einstein altered
classical mechanics to make it compatible with the Lorentz transformation.
Newton’s second law conformed if the velocity-dependent mass formula is used to
define momentum rather than a velocity-independent mass. Hamdan
obtains the same mechanical results as special relativity without the use of
the Lorentz transformation [30c]. He first argues that his principle of
relativity calls for a variable mass in Newton’s second law. He argues that the
variation of mass with velocity is a dynamical effect, not a kinematical one,
as in special relativity. The work performed on a massive body by a force
changing its location is absorbed as kinetic energy, which is expressed in the
form of mass. The kinetic energy does not reside in the motion but in the body;
it is the material body itself that has the ability to do work, not its motion.

It must be
admitted that in Einstein’s analyses the connection of mechanics and
electrodynamics seems more natural. The speed of light enters into the
mechanical calculations by means of the Lorentz transformation, which connects
with Maxwell’s equations. However, in Hamdan’s
analyses the speed of light seems to be artificially introduced.

Proponents of
Einstein’s theory of special relativity claim that time dilation is
experimentally confirmed. They point especially to two phenomena as confirming
it: the transverse Doppler effect and the radioactive
decay of mesons. The transverse Doppler effect is a
shift in the wavelength of light that occurs to an observer viewing light from
a source moving perpendicular to his line of sight. The transverse Doppler effect is predicted by the special relativity theory. There
are explanations for the effect, however, that employ classical physics [see
citations in 30d], but relativists have long claimed it as a unique feature of
special relativity. The transverse Doppler effect is
attributed in Einstein’s relativity to time dilation. The transverse Doppler effect has been observed experimentally, and relativists
claim that time dilation is thereby empirically confirmed. In his fourth paper
[30d] Hamdan explains the effect using only the
Lorentz force law and the principle of relativity, without the notion of time
dilation. He thus shows that the transverse Doppler shift is not a kinematic
effect, that is, it is not caused by motion; but it is a dynamic effect, an
effect of the nature of light.

The transverse
Doppler effect as a dynamic effect has a mechanical
analog. The longitudinal tension in a cord held to a fixed center of rest might
be caused by one of two things. First, it might be caused by a mass at the
other end of the cord that is trying to increase its distance from the center
of rest in the direction in which the cord is stretched. Second, it might be
caused by a mass at the other end of the cord that is traveling in a circle
around the center of rest, perpendicular to the direction in which the cord is
stretched.  If the mass was moving in a circle and the cord was very long
and the speed of rotation was very slow, an observer at the center of rest
might not be able to perceive the angular rotation of the cord and would,
therefore, be unable to discern the cause of the tension.

Experiments have
been performed in which radioactive mesons are accelerated to high velocities
in particle accelerators. In those experiments it has been observed that the
half-lives of the accelerated mesons are greater than the half-lives of mesons
at rest in the laboratory. Relativists claim that those experiments are
confirmations of time dilation. They say that the experiments show that clocks
“riding” on the accelerated mesons run slower than the clocks at rest in the
laboratory. However, an analysis like Hamdan’s
analysis of the transverse Doppler effect might
possibly explain that as an effect caused by the difference in internal energy
between the speeding mesons and those at rest. The speeding mesons would have
larger masses, and the larger masses might be associated with stronger binding
forces, which mean greater half-lives.

E.A. Milne [31,
pp. 34–48] argues that the Lorentz transformation formulas of special
relativity express kinematical observational effects connected with the finite
speed of light and do not reveal any deep secrets about the nature of space and
time.

And now a few
words about energy and momentum, the fundamental entities in Hamdan’s perception of relativity: First, let us consider
the intangible nature of energy. Recall that energy is the ability of
something to do work on a material body. This “ability” is communicated,
without loss, to the body on which it works. James Clerk Maxwell observed that
energy is not capable of identification. He states:

We cannot identify a
particular portion of energy, or trace it through its transformations. It has
no individual existence, such as that which we attribute to particular portions
of matter.

The
transactions of the material universe appear to be conducted, as it were, on a
system of credit (except perhaps that credit can be artificially increased, or inflated). Each transaction consists of the
transfer of so much credit or energy from one body to another. The act of
transfer or payment is called work. The energy does not retain any character by
which it can be identified when it passes from one form to another. [9, p. 90]

The modern
notion of energy echoes the scholastic notion of prime matter, which is matter
out-of-which something exists. Prime matter is that which is in potency to
substantial existence. It is pure potency because it has the
potential to be any material thing, and it is the principle of permanence
because it perseveres through any change. It exists separately in the mind
only. It does not exist separately in reality. It has no form in its
rational character, yet it is never stripped away from form in reality. St.
Thomas Aquinas in On the Principles of Nature points out that prime
matter is “numerically one in all things.” That is, it “exists without
dispositions making it numerically different.” Prime matter, like
energy, is not capable of identification because it does not possess a
character that can be identified when it passes from one form to another. And
energy is like prime matter because it does not exist in itself but only in
physical entities; it perseveres through physical transformations without a
specific identity.

Another
important property of energy is that it is strictly relative. The calculation
of energy transfer takes into account only the communication of “parcels” of
energy between one thing and another. It makes no use of an absolute source of
energy. Maxwell points out that we cannot know the absolute energy of a body
(if indeed such a notion makes sense):

The energy of a
material system can only be estimated in a relative manner.

In
the first place, though the energy of the motion of the parts relative to the
centre of mass of the system may be accurately defined, the whole energy
consists of this together with the energy of a mass equal to that of the whole
system moving with the velocity of the centre of mass. Now this latter
velocity—that of the centre of mass—can be estimated only with reference to some body external to the system, and the value which we
assign to this velocity will be different according to the body which we select
as our origin.

Hence
the estimated kinetic energy of a material system contains a part, the value of
which cannot be determined except by the arbitrary selection of an origin. The
only origin which would not be arbitrary is the centre of mass of the material
universe, but this is a point the position and motion of which are quite
unknown to us. [9, pp. 90-91]

One could go
further and say that the notion of absolute energy is meaningless because the
notion of motion of the center of mass of the universe means its motion through
absolute space, which is meaningless.

Maxwell gives us
another reason for considering the notion of absolute energy meaningless,
although he does not reject the idea:

But the energy of a
material system is indeterminate for another reason. We cannot reduce the
system to a state in which it has no energy, and any energy which is never
removed from the system must remain unperceived by us, for it is only as it
enters or leaves the system that we can take any account of it.

We
must, therefore, regard the energy of a material system as a quantity of which
we may ascertain the increase or diminution as the system passes from one
definite condition to another. The absolute value of the energy in the standard
condition is unknown to us, and it would be of no value to us if we did know
it, as all phenomena depend on the variations of the energy and not on its
absolute value. [9, p. 91]

The relative
nature of energy is manifested in the observation that its transfer is a local
phenomenon; that is, the giver and the receiver of a “parcel” of energy are in
the same place at time of the transaction.

Adding the accidents of place and time duration to the notion of
energy leads to the complementary fundamental notion of momentum. If
energy corresponds to matter in place, momentum corresponds to matter in
motion. Momentum has the same relation to time as energy has to position, namely, the rate of change of the momentum of a
body with respect to time is the same as the rate of change of its energy with
respect to position. And like energy, it is a relative quantity that is
conserved in energy transactions.

Again, recall
that the energy possessed by a body actually resides in the body itself and not
in its position or speed, although it depends on them in an accidental way. The
same is true for momentum.

General Relativity and
Absolute Space

In his theory of general
relativity, Albert Einstein proceeded to formulate the laws of physics so that
they look the same in all coordinate systems moving relative to each other,
whether uniformly or nonuniformly, linearly or
nonlinearly. To do this the notions of absolute motion in space and absolute
rest in space had to be eliminated. This was made possible by the equivalence
of inertial and gravitational mass, which allowed for gravity to eliminate
absolute motion. Motion of massive bodies could then be looked at as being
determined by the geometry of space-time that was shaped by gravitating masses.
The first law to be formulated for all possible coordinate systems had to be
that of gravity itself because of its central importance. Einstein put a lot of
effort into this problem. His work resulted in the formulation of his famous
gravitational field equations, a set of ten differential equations for the
metric of space-time. These are the equations modern cosmologists use to model
the universe.

Einstein was
strongly influenced by the thinking of Ernst Mach. He wanted to incorporate
Mach’s ideas into his theory of general relativity but was not able to do so
satisfactorily [see 2, pp. 192-199; 8, pp. 125-159; 11, pp. 242-244; 28. p. 6;
32, pp. 284-288]. For Mach, the concept of space as an independent entity has
no place in physics, and Einstein did not succeed in removing it. In his theory
of general relativity, Einstein did not eliminate space and time as independent
entities even though he combined them into space-time. But he still
treated space and time as realities that are independent of the matter that
determines them. So one could contemplate removing all the matter from the
universe and yet have space and time remain. That is metaphysical thinking, not
physical thinking. But his space-time differed from absolute space in that it
was something that both acted and was acted upon. Masses in their passive
inertial role are “guided” by space-time and in their active gravitational role
“shape” space-time. General relativity did not eliminate space, but it did
deprive space of its Newtonian absoluteness by giving it a passive quality.

The reason that
Einstein failed to eliminate an independent space-time seems to be that he
actually started out with one. In general relativity Einstein starts out with a
four-dimensional space-time manifold that is anchored to nothing. A manifold is
a topological space (a continuous set of points with certain properties) with a
Euclidean structure. That means that it is a space on which a constant
Pythagorean metric is imposed (the metric gives a non-negative number for the
distance, or separation, between two points). That Euclidean structure is then
deformed by matter/energy imbedded in the space. This deformation is manifested
by a varying metric described by his ten gravitational field equations.
Einstein’s space-time is not generated by matter/energy but is co-existent with
it and given shape by it.

At this point
let us recall what was said about Newtonian absolute space. It was mentioned
earlier that in empty Newtonian absolute space no coordinate grid can be
established because there is no place to anchor such a grid and no standard for
the measure of distance. Therefore the concepts of trajectory and straight line
are meaningless. Newtonian absolute space might be called a reverse
abstraction. The notion of extension is abstracted from material bodies, in
which it has real intrinsic meaning, and applied to empty space, in which it
has no real intrinsic meaning. Extension is an accident of matter, whose
ultimate standard of measurement is a material measuring rod. The notion of
extension in empty space without matter is meaningless because it an accident without a subject in which to inhere.
Furthermore, the notion of three-dimensional emptiness is theologically
objectionable when it is paired with the notion that before creation empty
three-dimensional space existed alongside God as a parallel infinity. As
previously noted, sound theology informs us that before creation there was no
infinite three-dimensional void into which God injected matter. Before creation
there was nothing but God.

The Catholic
Encyclopedia (1914) nicely expresses the position of the scholastic masters
on absolute space:

The traditional
philosophy of the Catholic schools rejects absolute space. Newton's idea is
incompatible with the concept which the great doctors of the school, following
Aristotle, formed of quantity. Suarez declares that space is only "a
conceptual entity [ens rationis],
not, however, formed at will like chimeras, but extracted from
bodies, which by their extension are capable of constituting real
spaces" (Met. disp., 51). The expression ens rationis
may be equivocal, but it expresses somewhat exaggeratedly the very active part
played by the human intellect in the construction of space. Space is not
material bodies themselves, since it appears to be rather a receptacle
containing them. From this point of view it must be pure extension, an
unqualified quantity. In the strict sense of the terms a quantity without
quality is contradictory; for quantity is only the multiplicity of the
homogeneous parts in the unity of a body; it is the distribution of an essence,
simple in its formal determination. Multiplicity implies a thing that is multiplied, and distribution something that is distributed.
Every quantity is the quantity of something; all extension is therefore, in
itself, the extension of an extended substance. Yet quantity is something more
than a modal accident; it is in truth the absolute accident par excellence;
it confers on a substance a perfection such that, granted the existence of a
substance, the corporeal body is measured by its quantity. It is none the less
true that quantity postulates a quantitative substance; and, in a sense,
entirely different however from the fancies of ancient physics, it may always
be said that an empty quantity is a contradiction in terms. From this we must
conclude that extension is only a derivative of quantity; a non-qualified
extension, pure extension, pure space in the reality of the corporeal world is
contradictory. We conceive it, however, and what is, properly speaking,
contradictory is inconceivable. The contradiction arises when we add the
condition of existence to pure space. Space is not contradictory in the mind,
though it would be contradictory in the real world, because space is an
abstraction. Extension is always the extension of something; but it is not the
thing extended. Mentally we can separate extension from the substances from
which we distinguish it; and it is extension thus separated, conceived apart,
which constitutes the space of the universe. Space is therefore as real, as
objective, as the corporeal world itself, but in itself it exists apart only in
the human mind, seeing that in the reality of existing things it is only the
extension of bodies themselves. [16, article entitled “Space”]

The above
critique of Newton’s absolute space can be also applied to the inertial spaces
of special relativity because conceptually they are either simply subdivisions
of absolute space that move in absolute space or, more confusing yet, an
infinite set of independent absolute spaces that move at all speeds relative to
one another.

Einstein’s
four-dimensional space-time is also subject to the same critique. It is in no
way clear how Einstein makes the transition from topological space to physical
space. In his paper “The Foundation of the General Theory of Relativity” (1916)
Einstein states that his “introduction of a system of reference serves no other
purpose than to facilitate the description of the totality of such
coincidences.” The “coincidences” are “the meeting of the material points of
our measuring instruments with other material points” [22, p. 117]. But he
treats the reference (coordinate) system that “facilitates” the description of
such coincidence as a free agent, not as something that depends on those
coincidences for its existence. Thus it differs little in its conceptual
fundamentals from Newton’s absolute space. Further, in general relativity,
matter/energy imposes a metric, which is accidental, on the four-dimensional
manifold (system of reference), which is a mathematical (mental) object that
has no substantial existence.

General
relativity failed to give a cosmic origin to the inertia of a body. [see 8, pp. 148-159] According to Mach’s principle, a body in
otherwise empty space should possess no inertia. But Einstein was not able to
achieve that result. According to general relativity such a body would
possess inertia. Also, general relativity predicts that the surface of a
rotating pail of water would retain its concave shape if the rest of the matter
in the universe disappeared. That too violates Mach’s principle. Further,
although general relativity employs the proportionality of gravitational and
inertial mass, it is unable to give a reason for it.

St. Thomas
Aquinas said that space is a privation and not a negation, that
is, it is the absence of matter from where it ought to be and not its absolute
absence. He said that before the creation of the world there was no
space because there were no “real dimensions” and no “place” [4, p.97; 5, Part
I, Q. 46, A. 1, Reply Obj. 4]. One can apply St.
Thomas’ reasoning to the consequences of general relativity. The fact that in
general relativity a body has inertia in the absence of other masses implies
that there is a coordinate system in which acceleration is measured. But it is
impossible to construct such a coordinate system because there are no physical
objects on which to fix it (no “real dimensions”) and no measuring rod to
measure it. The isolated body itself could not be a measuring rod because to
make measurements it would have to be moved from one place to another. But in
such a situation there is no such thing as “place,” and thus moving it from
place to place is meaningless. Also, the object itself could not be the origin
of a coordinate system in which its acceleration is measured because the body
always remains at the origin.

It seems that
freestanding (independent of matter) coordinate systems have introduced immense
complications and confusion into physics that far outweigh any simplifications
they may have produced. J. B. Barbour noted:

Einstein himself
commented [citation given] that the simplest way of realizing the aim of the
theory of relativity would be to formulate the laws of motion directly and ab initio in terms of relative distances and
velocities—nothing else should appear in the theory. He gave us the reason for not
choosing this route its impracticability. In his view the history of
science had demonstrated the practical impossibility of dispensing with
coordinate systems. He therefore adopted an indirect approach and was guided,
it seems, more by gut intuition than a clear formulation of principles that
would of necessity lead to the realization of his aims. [28, p. 6]

This leads us
into the subject of the next chapter, namely, relational mechanics, in which
the laws of motion are formulated directly in terms of relative
distances, velocities and accelerations.

CHAPTER FIVE: THE LOGIC OF RELATIONAL PHYSICS

Relational Mechanics

The Catholic Encyclopedia (1914) reduces the views of
philosophers concerning space to two fundamental notions:

To recall all the successive explanations of the
nature of real space given by the great philosophers it would be necessary to
go through the history of philosophy; but, leaving aside the complete negation
of extension, all the doctrines, from Hesiod (cf. Aristotle, IV Phys., vi,
213b) to our day, fluctuate between the idea of absolute space, a real
substance independent of the bodies it contains, and purely relative space, a
mental fiction based on the real extension of material bodies. The most radical
expressions of these two conflicting views are those of Newton and Clarke, on
the one hand, who consider space as the sensorium
of God, and on the other, of Leibniz, who asserts that there is no space
independent of extended bodies, and reduces it to "the order of
co-existing things." [16, article entitled “Space”]

In his much cited foreword to Max Jammer’s Concepts
of Space: The History of Theories of Space in Physics
[2], Albert Einstein clearly and succinctly presented those two conflicting
notions of space as “container of all material objects” and as “positional
quality of the world of material objects.” Philosophers and historians of
science use the word “absolute” space when referring to the first notion and
“relational” space when referring to the second. The two notions of space give
rise to two different ways of doing physics. This first way employs the notion
of absolute space and its derivatives, such as inertial spaces, and the
consequent notion of freestanding coordinate systems, which is the cause of
much confused thinking in physical matters. The second employs only direct
physical quantities and their relations, without the intermediary of
freestanding coordinate systems.

Albert Einstein
recognized the limitations of using the elusive notion of freestanding
coordinate systems in physical systems but argued that it was unavoidable:

We want to
distinguish more clearly between quantities that belong to a physical system as
such (are independent of the choice of coordinate system) and quantities that
depend on the coordinate system. One’s initial reaction would be to require
that physics should introduce in its laws only the quantities of the first
kind. However, it has been found that this approach cannot be realized in
practice, as the development of classical mechanics has already clearly shown.
One could, for example, think—and this was actually done—of introducing the
laws of mechanics only by the distances of material points from each other
instead of coordinates; a priori one could expect that in this manner the aim
of the theory of relativity should be most readily achieved. However, the
scientific development has not confirmed this conjecture. It cannot dispense
with coordinate systems and must therefore make use in the coordinates of
quantities that cannot be regarded as the results of definable measurements.
[8, p. 147]

It seems strange
that Einstein should so readily dismiss the employment of relational
quantities, considering the conceptual simplification they offer, for
simplification is what he sought. Instead he pursued the complex way to
simplification. He describes the agony of his pursuit for the equations of
general relativity as follows: “In the light of knowledge attained, the happy
achievement seems almost a matter of course, and any intelligent student can
grasp it without too much trouble. But the years of anxious searching in the
dark, with their intense longing, their alternations of confidence and
exhaustion and the final emergence into light—only those who have experienced
it can understand that” [33, pp. 282-283].

Andre Assis seems to have accomplished what Einstein said
couldn’t be done. He eliminated the need for freestanding coordinate systems in
physics. Assis proposed a new mechanics that
implements Mach’s principle quantitatively [8]. It is a shift of paradigm away
from Einstein’s theories of relativity, of which he is quite critical. Assis applies Weber’s law for the interaction of electric
charges to the interaction of masses and posits the principle of dynamic
equilibrium. The latter states that the sum of all forces of any nature
acting on any body is always zero in all frames of
reference.

Assis calls this new mechanics relational mechanics
because it employs only relative quantities, that is, it employs only the
distances between material bodies and the relative velocities and accelerations
between material bodies. He uses the word relational to distinguish this
mechanics from Einstein’s relativistic mechanics; but relational mechanics,
unlike relativistic mechanics, is completely relativistic because all forces
are referred to relative distances, velocities and accelerations of bodies and
not to absolute space or inertial frames. According to relational mechanics,
Ptolemaic astronomy is equivalent both kinematically
and dynamically to Copernican astronomy. The choice of one or the other is one
of pure convenience since there is no such thing as absolute motion, either in
the kinematic sense or in the dynamic sense.

Relational
mechanics posits a principle similar to Newton’s third law of motion, but it
replaces Newton’s second law with the statement that the total force on any
material body is zero in every frame of reference. For example, the static
gravitational force acting on a freely falling body by the earth is cancelled
by the dynamic gravitational force acting on it by the rest of the bodies in
the universe. Since both forces are proportional to the gravitational mass, all
bodies will fall to earth at the same rate. Another example: The force of
attraction of the sun on the earth is balanced by the centrifugal force exerted
on the earth by the rest of the bodies in the universe. Because they depend
only on relative distances and motions, these forces are numerically the same
in any frame of reference even though their mathematical expressions may be
different. This contrasts with Einstein’s relativity, where the mathematical
expressions are required to be identical in different frames of reference, but
numerical values for the quantities they represent may differ.

Assis applies the mathematical expression that W. E. Weber
(1804–1891) used to express the electrodynamic force
between two electric charges to the gravitational interaction between two
masses. The expression has three terms, each of which is proportional to the
product of the two gravitational “charges” (masses). The first term is
inversely proportional to the square of the distance between the two masses.
This is Newton’s static gravitational attraction. The second term is also
inversely proportional to the square of the distances between the two masses
and proportional to the square of their relative speed along the line
connecting them. The third term is inversely proportional to the distance
between the two masses and directly proportional to the relative acceleration
along the line connecting them. The first term always represents an attractive
interaction. The second term always represents a repulsive interaction. The
third term represents a repulsive interaction if the relative acceleration of
the masses is toward each other. All interactions are along the line connecting
the two masses. Assis includes a factor that
decreases the force exponentially with distance between the masses to avoid a
paradox created by the concept of a universe infinite in extent. However, that
factor is not really needed. The only reason for postulating a universe
infinite in extent is to avoid the problem of a universe collapsing in on itself
because of gravity. And that is only a problem if one considers the universe as
having always existed. If one accepts the fact that the universe was created
only several thousand years ago, then one need not postulate a universe
infinite in extent.

Assis applies his gravitational theory to a model of the
universe that is homogeneous on a large scale, static, and in dynamic
equilibrium, using the currently accepted values for the average mass density
of the universe, the radius of the universe, and the gravitation constant. He
looks at the interaction of a mass nestled deeply within that universe with the
rest of the universe. He then shows that Newton’s second law of motion holds
with respect to “the frame in which the distant matter [in the universe] is at
rest, despite the peculiar velocities in this frame” [8, p. 178].  In his
recovery of Newton’s second law of motion the gravitational mass appears where
the inertial mass appears in Newton’s law. Thus he demonstrates the equivalence
of gravitational and inertial mass. He also recovers Newton’s first law of
motion, again with the gravitational mass in the role of inertial mass and the
above-mentioned frame of reference replacing absolute space. Relational
mechanics also predicts quantitatively that the inertia of a body would vanish
if the rest of the matter in the universe were to disappear. It further
predicts that the curvature of the surface of a pail of rotating water is
proportional to the amount of mass in the universe. The theory also yields an
expression for the precession of the perihelion of planetary orbits that agrees
to the first order with that given by general relativity. General relativity’s
ability to provide a calculated value equal to the observed value for the
precession of the perihelion of Mercury helped vault that theory into
prominence.

As mentioned
earlier, Assis also explains the null result of the
Michelson-Morley experiment in terms of relational mechanics. The
Michelson-Morley experiment failed to detect the supposed motion of the earth
through the luminiferous ether. Assis
says that the most straightforward explanation of that experiment is that there
is no ether. He says: “Only the relative motion between the light, the mirrors,
the charges in them and the earth are important, no matter what the velocity of
these bodies relative to the ether or to absolute space. In this regard the
results obtained by Michelson and Morley agree completely with Weber’s
electrodynamics, as in this theory, the ether plays no role” [8, p. 145].

Assis further proposes that observed phenomena attributed
to relativistic time dilation are better interpreted by relational mechanics.
For example, the half-lives of mesons are observed to increase with their
speed. It is usually explained that it is because the clocks “riding” on the
moving mesons run slower than clocks at rest. Assis
thinks that a simpler explanation is that “the half-lives of the mesons depend
on their high velocity relative to the distant material universe” [8, p. 133].
This way of explaining such phenomena, he says, is more in agreement with the
standard procedures of physics and suggests new avenues of experimental
research.

Applying Mach’s
principle but reasoning along different lines, Amitabha
Ghosh arrived at a similar mathematical expression to
that of Assis for the interaction of two
gravitational masses, one of which he treats as a test body [34]. He focuses in
on the second term, the term that contains the square of the relative velocity
along the line joining the masses. He adjusts this term so that it represents
an interaction that always acts in the opposite direction of the velocity in
the manner of a cosmic viscous force. Ghosh calls
this interaction cosmic drag. Cosmic drag is not easily detectable by
experiment because it is a very small effect. But, since it acts on photons of
light decreasing their energy, it gives rise to the observed galactic red
shift. Thus Ghosh gives an explanation for the red
shift and Hubble’s law without the big bang and expansion of the universe. The
notion of light losing energy as it transverses the cosmos is called tired
light. Other mechanisms for tired light have been proposed in addition to
cosmic drag, but Ghosh claims that cosmic drag is the
only testable mechanism.

Relational
mechanics cosmology easily accommodates cosmic microwave radiation. Assis and Ghosh shatter the myth
that the big bang advocate George Gamow and his
associates were the first to predict the existence of the cosmic microwave
radiation (CMR) prior to its discovery by Penzias and Wilson in 1965 and that
CMR supports the big bang hypothesis exclusively. They cite a number of
researchers that predicted CMR in a stationary, nonexpanding universe. Such
predictions not only predate those of Gamow et al. but also more accurately
predicted the temperature of the radiation. The earliest prediction discovered
in their literature searches was made in 1896 by C. E. Guillaume, who estimated
a temperature between 5 and 6 degrees Kelvin.

The major
objection physicists have to a mechanics that implements Mach’s principle is
that it requires instantaneous-action-at-a-distance. With the ascendancy of the
theory of special relativity, it has become scientific dogma that the effect of
any physical disturbance cannot be communicated faster than the speed of light,
and Mach’s principle demands that any material body and the rest of the
universe must instantly sense any change in their relative distances and
motions. However, it was argued in the last chapter that special relativity
does not necessarily rule out physical causes propagating faster than the speed
of light. More will be said about instantaneous-action-at-a-distance in a later
article.

Mach’s principle
is anathema to quantum theorists, who give great importance to fields. They
point out that the fields of elementary particles, either real or virtual,
occupy all of space-time. These fields, which they say cannot be eliminated,
possess Lorentz invariance and can be considered a modern
ether [see 11, p. 244]. In response, it can be said that those fields are not
physical entities. They are pure mathematical entities because they are
expressed in terms of complex numbers and points in Einstein’s space-time
fabric, which is a mathematical entity, not a physical one. They are
indispensable only insofar as one accepts the absolute space-time of relativity
as a working paradigm [see 2, pp. 212-213]. Also, the field concept does not
explain the quantum phenomenon of entanglement, in which physical
effects are communicated instantly without the medium of fields.

Although Assis says that the model for the universe he prefers is an
infinitely large, unbounded, eternal universe, the model he worked with was a
finite, bounded universe. It does not matter in relational mechanics how old
the universe is. The main requirement is that it is in dynamic equilibrium. So
it seems that relational mechanics cosmology can be made to harmonize with
Genesis. Furthermore, it makes it easy to place earth in its rightful position
as the center of rest in the universe. Because of its strong foundation in
fundamental physics, relational mechanics cosmology has the potential to
supplant cosmologies based on Einstein’s general relativity.

Absolute and Relational
Spaces United

The lack of resolution of the
centuries-old debate between the proponents of absolute space and the
proponents of relational space led J. Earman to make
the following conjecture: “My own tentative conclusion from this unsatisfactory
situation is that when the smoke of the battle finally clears, what will emerge
is a conception of space-time that fits neither traditional relationism
nor traditional substantivalism. At present we can
see only dimly if at all the outlines the third alternative might take” [as
quoted in 2, p. 236]. Jammer explains “substantivalism”
as denoting that “space has the ontological status of an independent reality
‘as a kind of substance’” [2, p. 216]. Jammer further cites W. E. Johnson, “[A]
theory of space conceives space as ‘substantival’ if
it ascribes spatial positions directly to the individual points of space
themselves and only in a derivative sense to material particles in virtue of
their occupation of points in space,” and “space is ‘adjectival’ if the spatial
characteristics of a material particle belong to it in a primary and underived sense” [2, p. 217]. Earman’s
third alternative, if not a completely new notion of space, would be a union of
relative space with absolute space. Often the resolution of a conflict resides
in the recognition that both sides are partially correct and reconciles them.

Relational space
and absolute space are alike in that they both require the notion of extension
in three dimensions. And both depend on physical entities as standards for the
measurement of extension. The difference is that in absolute space the
extension and its derivatives (velocity and acceleration) are referred to a
freestanding absolute mathematical frame of reference in a void while in
relational space they are referred to other material bodies. Absolute space is
spoken of in the singular, that is, there is only one frame of rest. Relationalism, on the other hand, actually requires that
one speak of space in the plural because each ponderable
body is accompanied by its own space. So there are many possible frames of
rest; the definition of rest is arbitrary.

It seems
possible to make absolute space into relational space by considering absolute
space not as a void but as a special kind of plenum that each ponderable body sees as its own [see 35 pp. 230-231]. The plenum
here proposed by the author of this essay is a continuous uniform mixture of
positive and negative charge with equal charge densities and no mass density.
Thus the plenum has overall charge neutrality. Disturbances in the medium are
propagated by local dipole-like fluctuations in the densities of charges.
Unlike the charge on massive particles, the plenum charges are substances, not
accidents.

The inspiration
for this comes from both the electrodynamics of Maxwell and Hertz and the
electrodynamics of Weber and Kirchhoff. Maxwell introduced the notion of free
space displacement current, analogous to the polarization currents produced in
a material dielectric by time-varying electric fields [see 36, pp. 84-101].
This is what paved the way to the electromagnetic wave equation and its
consequent, electromagnetic radiation propagating through absolute space at the
speed of light. However, since physicists gave reality to electric and magnetic
fields in a void, they did not view these free-space displacement currents as
real currents. Rather, they saw them in terms of time-varying electric fields
producing magnetic fields.

Weber and
Kirchhoff, employing instantaneous-action-at-a-distance electrodynamics, showed
that electromagnetic disturbances travel along wires at the speed of light.
However, their electrodynamics requires a medium containing electric charge to
propagate electromagnetic disturbances. Thus the notion of the propagation of
electromagnetic energy in an absolute void and the apparent empirical confirmation
of this notion might seem to discredit the notion of relational space, which
the electrodynamics of Weber and Kirchhoff employed.

Maxwell and
Lorentz proposed the ether to be an incompressible fluid. The model proposed
here employs a twofold electrically charged
compressible ether and will be referred to as the “twofold electrical ether
model” (TEEM). The continuous nature of the two charges insures that motion
through them is a meaningless concept because there is no operation by which
such motion in it can be detected. The charge mixture has a certain “viscosity”
that resists fluctuations in charge density. The non-zero viscosity of the
ether is a consequence of non-zero values for the permittivity and permeability
of “free space” (ε_0, μ_0). Since the charges are
not material, there are no mechanical interactions with the material bodies
immersed in them.

Changes in
distance-dependent electric forces along the line connecting two charged bodies
immersed in the medium are communicated instantly. The medium is transparent to
such instantaneous-action-at-a-distance forces. However, changes in the
electric forces caused by changes in the dispositions of the charges causing
the forces would be propagated perpendicular to the direction of change by dipole
(and possibly higher order) polarization currents induced in the
twofold-charged medium, just as in a material dielectric. Thus the propagated
disturbance is transverse.

The density
fluctuations manifest themselves as the propagation of an electromagnetic
field. They can be located on a coordinate grid fixed to any ponderable body immersed in the medium. The speed of
propagation of a fluctuation can then be measured with respect to such a grid.
Since the medium itself is unobservable anywhere and motion through the medium
meaningless, every ponderable body can be assumed to
be at rest in the medium. Therefore the speed of the propagation of the
fluctuations is the same in the coordinate grids of all ponderable
bodies immersed in the medium, whether they be the
source or the sink of a fluctuation. In other words, the speed of light is the
same everywhere in the plenum. Thus the constancy of the speed of light is not
an effect of the properties of space-time as it is in the theory of special
relativity. Rather it is a property of the uniform locally indistinguishable
nature of the medium of propagation.

The speed
of light being constant everywhere means that for a sinusoidal disturbance the
product of the frequency and wavelength is constant. But for a given
disturbance the wavelength and frequency can vary from grid to grid but their
product must remain constant. Therefore they must vary inversely to each other.
Consider now the relationship between the source of a sinusoidal emission and a
sink moving with respect to the source. The problem is to determine the
wavelength and frequency measured at the sink compared to those measurements at
the source. Since both are at rest with respect to the medium, classical
Doppler analysis does not apply. The problem seems to be one of dynamics rather
than kinematics. The solution, it seems, would call for consideration of how
the fluctuations transfer momentum and energy from the source to the sink.

The following
assumption can be made on the basis of empirical evidence: Electrical (coulomb)
force interactions along the line connecting two charged bodies are
instantaneous, Action and reaction must be instantaneous if Newton’s third law
and its consequence, conservation of momentum, is to hold globally. Otherwise,
the medium, which is equivalent to a void, would have to transfer momentum by
longitudinal waves, which is not possible according to Maxwell’s equations. (G.
Green pointed out that a longitudinal wave would not be propagated if the speed
of interaction is indefinitely great or indefinitely small [see 23, Vol. I, p.
145]. An indefinitely great velocity is supported by an incompressible medium
and an indefinitely small velocity is supported by a perfectly compressible
medium.) This instantaneous action also applies to other physical cause-effect
relationships (for example, gravitational interactions, entanglement). This
will be treated in more detail in a later article.

It can also be
safely assumed that information about physical events can be communicated to
intelligent observers only at speeds equal to or less than the speed of light.
For example, the instantly changing forces in coulomb interactions cannot be
communicated instantly to an intelligent observer because the intelligent
observer cannot observe the change in force directly; he must observe the
effect of the changing force, which does not occur instantly because of
unavoidable inertial and elastic effects in his instrument of observation.
Also, it seems that the instrumental effects are sensitive to the distance from
the source of the change to the observer, this being a holistic effect of the
universe [see 37, pp. 204-219].

The above
postulate also contains within it the implication that a massive body can
travel with respect to a coordinate grid fixed to a ponderable
body no faster than the speed of light.

In the TEEM the
“ether” is at rest with respect to all ponderable
bodies, The TEEM is similar in some respects to the dragged ether model. It
differs from the dragged ether model in that that it is purely relational;
motion through absolute space is a meaningless concept. In the dragged ether
model, on the other hand, a ponderable body “drags”
the ether with it through absolute space. W. Panofsky and N. Phillips [38, p.
282] list seven light transmission observations explainable by special
relativity theory. Only five of them are explainable by dragged ether theory.
The two that supposedly cannot be explained are stellar aberration and Fizeau convection of light. They will be considered in the
next article along with the Sagnac effect, which
cannot be explained by special relativity theory [see 25, pp. 282-284; 26, pp.
55-58; 27, pp. 41-43, 247-252; 39, pp. 389-396].

Relational Optics

Four crucial optical phenomena
will now be examined in light of the TEEM. The first concerns the behaviors of
two coherent beams of light moving on a platform fixed on earth, one beam
moving collinearly with the supposed motion of the earth through the ether and
the other moving transversely to it. The second concerns the behavior of a beam
of light from a source moving transversely with respect to the observer. The
third concerns the behavior of a beam of light in a material dielectric moving
collinearly with respect to the observer. The fourth concerns the behavior of a
beam of light on a turntable rotating with respect to the stars. Three of these
were described in an earlier chapter; they will be revisited here and reviewed
in the light of the TEEM.

The Michelson-Morley Experiment

This experiment performed in 1887
by A. Michelson and E. Morley was an attempt to measure the effect on optical
phenomena of the earth’s motion through the luminiferous
ether. A beam of light was split into two; one beam was sent in the direction
of the earth’s supposed movement through the ether and reflected back into an
interferometer; the other was sent transverse to the first and reflected back
into the interferometer. In the interferometer the two beams interfered and
produced a fringe pattern. The distance of travel was the same for both beams.
It was expected that the time of travel would be different for both beams and
so they would arrive out of phase at the interferometer and produce a shift in
the fringe pattern from that expected for no motion through the ether.
But no such shift was detected. There are only two reasonable explanations for
the null result. The first is that the earth is a rest in the ether; this is
held by those who believe in absolute space and that the earth is the center of
rest in it.  The second is that movement through the ether is a
meaningless concept, so that the ether appears to be at rest with respect to
all ponderable bodies; this is the assumption of the
TEEM. A third explanation, which asserts that the length of the apparatus
shrinks in the direction of the earth’s supposed motion through the ether, is
outlandish.

Stellar Aberration

Stellar aberration,
discovered and explained by James Bradley in 1726, is the apparent displacement
in the positions of stars attributed to the finite speed of light and to the
transverse motion of the earthbound observer with respect to the light beam
(ray, photon) from the star.

The effect
requires the slanting of a telescope at an angle away from the target star to
allow light entering the objective lens to reach the eyepiece. The telescope
must be tilted to allow the beam to travel down the axis of a transversely
moving telescope. If the speed of light were infinite, that would not be
necessary.

Classically, the
angle A at which the telescope must be tilted from the vertical for a star
directly overhead is given by

tan A = v/c, where v is the speed of the telescope with
respect to the beam and c is the speed of light in a vacuum [see 38, p. 279]

.

According to special relativity theory, using the equations for
the addition of velocities, the angle A is given by

tan A =, which
in practice [(v/c)2 small] is indistinguishable from the classical
result [see 11 pp. 57-58 and 38, pp. 303, 379-380].

Aberration
produces a displacement of 20.5 seconds of arc in the apparent positions of the
stars. Since the direction is constantly changing, a star appears to describe a
little circle 41 seconds in diameter over the course of a year.

This phenomenon
was used as evidence for motion of the earth through absolute space. But Einstein
did not see it that way. In the introduction to his 1905 paper he wrote.
“Examples of this sort [referring to an electromagnetic phenomenon], together
with the unsuccessful attempts to discover any motion of the earth relatively
to the “light medium,” suggest that the phenomena of electrodynamics as well as
of mechanics possess no properties corresponding to the idea of absolute rest.”

Panofsky and
Phillips [38, p. 282] list several theories (emission theories and special
relativity) that do not employ a stationary ether and
are consistent with the phenomenon of aberration. The phenomenon of stellar
aberration is also used as evidence to exclude ether drag as explanation for
null result in Michelson-Morley experiment [see 38, p. 279]. The argument supposes
that the light beam from the star is dragged along in the ether surrounding the
earth, which is allegedly moving through absolute space, and therefore
aberration would not occur. The drag would impart an additional transverse
component of velocity to the beam that would increase its speed with respect to
the star. That argument was contested by C. van der Togt [40], who assumed that the speed of light remained the
same both with respect to the star and the earth-dragged ether. This puts his
dragged-ether model on common ground with both special relativity theory and
the TEEM.

In the TEEM,
like the special relativity model, aberration is caused by the relative
motion of the star and the earthbound observer and not by the absolute
motion of the earthbound observer as in classical theories. Also, the equation
for tan A is the same in the TEEM as in the special relativity model because
that equation is a consequence of the fact that the speed of the light beam is
the same with respect to both the source and the observer. In special
relativity theory the cause for that lies in the relative natures of space and
time. But in the TEEM it lies in the absolute uniformity of the ether.

The presence of the Lorentz factor,

γ = ,

implies that the source and the
observer cannot have a relative speed greater that the speed of light.

In the TEEM both
the source and the observer can be thought of as possessing the ether as their
own because of the impossibility of detecting motion through the ether. Then
stellar aberration can be thought of as a kind of refraction, with the
interface along the axis of the telescope and the beam passing from a medium
with an index of refraction equal to unity into a medium with an index of
refraction equal to γ. However, there is no real interface between the two
“ethers” because they are really one.

When a beam of
light enters or exits one refracting medium into another its speed changes and
consequently its wavelength changes also. The ratio of the wavelength of the
beam in the first medium to that in the second medium is equal to the inverse
of the ratio of their indices of refraction. In the TEEM the index of
refraction for the first medium is unity and for the second medium γ. Thus
the wavelength ratio is equal to γ. This agrees with what special
relativity gives for the transverse Doppler effect,
which it attributes to time dilation [see 11, pp 55-56].

Since the speed
of light remains at c along the axis of the telescope, the frequency of the
beam must decrease by the factor 1/γ. This is not caused by time dilation,
as in special relativity theory, but by a variation in the energy of the beam.
Here we employ quantum mechanics which states that the energy of a photon in
the beam is proportional to its frequency. The energy and momentum of a photon,
like the energy and momentum of a material body, are relative quantities. They
will not be the same with respect to different ponderable
bodies moving with respect to each other.

The momentum of
a photon is inversely proportional to its wavelength. The wavelength of a
photon traveling down the telescope tube increases by the factor γ from
that emitted by the star, so the momentum of the photon decreases by the factor
1/γ in the telescope tube. Since in the TEEM the observer always sees
himself at rest in the ether he attributes the relative motion to the source.
Thus the photon at the source has additional momentum and energy because of the
motion of the source. This explains dynamically the increase in wavelength and
decrease in frequency of the photon in the telescope tube.

Also, if one
assumes that a material body emitted by the star suffers a loss in momentum in
the same way as a photon, it follows that the momentum of the body emitted from
the star is greater than the momentum observed on earth by the factor γ.
Thus the mass of the emitted body is greater than the mass of the observed body
by the factor γ. This mass increase is again attributed to the motion of
the source.

Fizeau Light Convection

In 1871 G. B. Airy observed
stellar aberration with a water-filled telescope. One who believes that the
earth moves through the ether would expect to find a larger angle of aberration
because of the longer time it takes for a beam of light to travel through water
than through air (the speed of light in water is 77% of that in air). However,
Airy found no change in the angle. This was not surprising to Airy because A.
J. Fresnel had already postulated in 1818 that there would be a “drag factor.”
Fresnel made this postulate to explain an observation of F. Arago.
In 1810 Arago observed starlight through a moving
plate of glass and concluded from his observations that the earth seems to be at
rest in the ether [for details see 39, pp. 123-124]. Fresnel assumed that the
ether was partially dragged along by the glass. The drag factor was introduced
to harmonize Arago’s observation with the notion that
the earth moves through an ether at rest in absolute
space. The drag factor of Fresnel is

f = 1 - 1/n^2,
with n being the index of refraction of the medium.

Fresnel’s drag
factor was applied to Airy’s observation. The drag factor
compensates for the expected difference in the angle of aberration. The drag
factor multiplied by the speed of the telescope through the ether is added to
the speed of the light in the medium. This brings the speed of a beam of light
in a water-filled telescope up to that in a telescope not filled with water.
Thus the angle of aberration is the same for both telescopes.

In 1851 A. H. L.
Fizeau devised an experiment to directly observe
Fresnel’s assumed ether drag. He set up two parallel tubes of equal length in
which he could make water flow at the same speed in opposite directions. He
then divided a beam of light into two coherent beams. He shined one beam in the
direction of flow in one tube and the other beam opposite to the direction of
the flow in the other tube and then reunited the beams in an interferometer.
When the water in the two tubes was not flowing both beams arrived at the
interferometer in the same phase and produced a fringe pattern. When the water
was made to flow a shift in the fringe pattern was observed. This meant that
the two beams did not take the same time to travel through the tubes. And from
his measurement of the fringe shift Fizeau claimed to
confirm Fresnel’s drag factor.

Fresnel’s drag
factor f is also called the “Fizeau convection
coefficient.” The use of the term “convection” highlights the notion that a
material medium imparts some of its speed to a beam of light traveling through
it.

Fizeau’s convection coefficient is derived in special
relativity by applying the addition of velocities formula to the following
scenario: the light moves with respect to the water, which in turn moves with
respect to the observer [see 11, pp. 54-55; 38, pp. 302-303]. In the
relativistic calculation the beam of light is dragged in inertial space in the
direction of the water’s motion. On the other hand, in Fresnel’s calculation
the ether is dragged.

Fizeau’s interpretation of his experiment and thus special
relativity’s “confirmation” of it has been cogently challenged by G. and V. Sokolov [41]. The Sokolovs argue
that Fizeau misinterpreted the interference pattern
he observed because he did not take into account the frequency changes that
occur when the beams enter and leave the water and the associated phase
changes. The frequency of the beam moving in the direction the water flowing at
speed v decreases when it enters the water by the factor 1-v/c and the
frequency of the other beam increases by the factor 1+v/c, in accordance with
the classical Doppler effect. And, with another
application of the Doppler effect, both beams emerge from the water with the
frequency decreased by the factor 1 - (v/c)2
but with different phases. The Sokolovs use a
molecular model for the water in which a photon of light in the beam moves
through the water intermittently at speed c with respect to the molecules,
being absorbed by a molecule and being re-emitted in phase with the absorbed
photon a short time later. The time delay between absorption and re-emission is
what slows down the progress of the beam giving rise to the index of
refraction. The Sokolovs conclude from their analysis
that the drag factor is unity and not f = 1 - 1/n^2, so that the
speeds of the beams in the tubes of the moving water with respect to the
laboratory  are c/n ± v and not c/n ± fv, where n is the index of refraction of water. This
means that the light beam is completely dragged by the water and not only
partially. The factor f is accounted for exactly by the additional phase
deviations in the two tubes caused by the frequency differences. The complete
dragging by the water contradicts the relativistic equation for the addition of
velocities. Furthermore, in the Sokolovs’ analysis
the expression for f is exact, whereas in the relativistic analysis it is an
approximation for small v/c.

The Sokolovs’ analysis is in accord with the TEEM. When the
water is still, the beam takes more time to move through the water than through
the ether alone because of the time delay between the absorption and
re-emission of radiation by the water molecules. Thus the beam is slowed down
when passing through the water, and moves at the average speed c/n. When the water is flowing at
a speed v, the re-emitting water molecules move an additional distance
proportional to v (either in the direction of the beam or against the beam)
during the time delay between absorption and re-emission. This additional
motion of the molecules causes the overall time for transit through the water
to decrease or increase, making the average speed of the beam through the water
equal to c/n ± v. An
additional note: the index of refraction of water is 1.33 and in Fizeau’s experiment the water flowed at seven meters per
second, so c/n ± v < c.

Finally, the
TEEM easily explains Airy’s observation if one,
following the Sokolovs, recognizes that even when
moving through the water the beam is propagated by the ether at speed c. The
molecules of the water are immersed in the ether and act as obstacles that slow
down the propagation. The water molecules do not affect the angle of aberration
because that depends only on the relative motion of the star and the telescope.

The Sagnac Effect

This effect was discovered in
1913 by G. Sagnac was in an attempt to demonstrate
absolute rotation by optical means. A beam of light was split into two; one
beam was sent around a turntable in the direction of rotation and reflected
into an interferometer; the other was sent around the turntable on the same
path as the first but opposite in direction and reflected into the
interferometer. When the turntable was not rotating the two beams arrived at
the interferometer in phase and produced a fringe pattern. When the turntable
was rotated the two beams produced an interference pattern with the fringes
shifted from that of the first pattern, which indicated that the optical
lengths of the two paths differed. Thus it is claimed that absolute rotation in
the ether was demonstrated.

The effect is
explained by the TEEM if one recognizes that absolute motion through the ether
is meaningless; but motion with respect to an ethereal disturbance, that is,
motion with respect to a light beam,  produces observable effects. First
of all, the motion has an effect on the wavelength and frequency of the beam.
This would have some effect on the interference pattern in the experiment. Secondly,
the motion of the mirrors would have an effect on the optical length (the
distance the beam travels) between mirrors, lengthening it in one direction and
shortening it in the other, thus producing a fringe shift. (All motions are
referred to the local ether, which is at rest with respect to the earth.) In
the Michelson-Morley experiment, on the other hand, there was no movement of
the mirrors with respect to the beam, so no fringe shifts were observed.
Thus, according to the TEEM, the Sagnac effect is not
a demonstration of absolute rotation but only one of relational motion.

Instantaneous Action at a
Distance, Cause Propagation, and Communication

The notion of
instantaneous-action-at-a-distance (IAD) is really a combination of two
notions, namely, “action-at-a-distance” and “instantaneous.” The first implies
the absence of a material medium for the propagation of a physical cause; the
second implies an infinite speed of propagation of a physical cause. The first,
however, would seem to imply the second if the subject (source of the cause)
and the object (recipient of the effect) were somehow linked across space since
the beginning of time; for without a physical medium there would be nothing to
resist the instantaneous propagation of a physical cause. How could a void have
the power to slow down the propagation of a cause? For example, it is
impossible to move a massive body across space instantly not because the
intervening space resists such movement but because of the inertia of the body
resists it. But this inertia could very well be caused by an instantaneous
interaction of the body with the rest of the bodies in the universe, a la Ernst
Mach.

Unlike
relativistic physics, relational physics, of which the TEEM is a part,
integrates IAD with non-instantaneous communication of physical disturbances.
The notion of IAD accords well with relational mechanics because it does not
require the notion of absolute space but only that of relational space. It only
concerns the relational aspects of a source and a detector. The properties of
the medium have no significance other than providing parameters for the
detector’s reaction. IAD effects are also called “non-local” effects. In
relativistic jargon, non-local effects lie in the extreme “space-like” region of
space-time (events connected by speeds greater than that of light and thus
considered unrelated causally). This is the polar opposite of everyday local
effects, which lie in the extreme “time-like” region of space-time (events
connected by speeds much less than that of light and considered possibly
related causally).

The
notion of action-at-a-distance probably entered human consciousness with the
ruminations of the early astronomers. They believed that the stars directly
influence physical processes on earth. In his Breviloquium,
St. Bonaventure, following the ancient astronomers, said that heavenly
bodies influence “the effective production of things generable and corruptible,
namely mineral, vegetative, and sensitive life and human bodies.” But “they are
not certain signs of future contingencies, nor do they exert influence upon the
freedom of choice through the power of the constellation, which some
philosophers say is fate” [Part II, Chapter 14.1]. So he, like other medieval
theologians, believed that the stars influenced things on earth. The influences
he spoke of were purely physical causes, not occult influences, which could
very well be instantaneous.

The notion of
IAD was put on firm physical ground by Isaac Newton in his theory of gravity.
And the notion is still employed successfully today in the calculation of
celestial movements. Newton, although he employed the notion
action-at-a-distance because of its usefulness, nevertheless despised it, as
the following quotation in a private letter to Richard Bentley reveals:

It is inconceivable,
that innate brute matter, should, without the mediation of anything else, which
is not material, operate upon and affect other matter without mutual contact,
as it must be, if gravitation, in the sense of Epicurus, be essential and
inherent in it. And this is one reason why I desire you would not ascribe
innate gravity to me. That gravity should be innate, and essential to matter,
so that one body may act upon another at a distance through the vacuum, without
the mediation of anything else, by and through which their action and force may
be conveyed from one to another, is to me so great an absurdity, that I believe
no man, who has in philosophical matters a competent faculty and thinking, can
ever fall into it. [37, p. 14]

However,
Newton’s objection was only a personal prejudice. There is no problem with the
concept of gravitational action-at-a-distance if one assumes that gravitational
interactions always existed. Such interactions could have easily been set up by
God at creation because they contain no contradictions.

When Newton
formulated his third law he was apparently thinking of interactions by physical
contact at the same place. Thus, it makes sense that to him even the
transmission of gravitational effects required a medium in contact with massive
bodies that conducts their gravitational effects. Thus the change in the
disposition of a massive body produces an effect immediately on the medium
surrounding it, which in turn propagates that effect to other material bodies.
And the medium instantly reacts to that change thus preserving Newton’s third
law in gravitational interactions. However, instantaneous reaction does not
logically require physical contact. This notion that it does require physical
contact is a consequence of entrenched mechanical thinking.

There is
evidence from astronomy and empirical physics that there is instantaneous
action-at-a-distance in nature. That is, there are physical causes acting over
a distance that do not appear to be propagated but rather appear to be
communicated as if by contact. Thus the universe in some respects appears to be
instantaneously holistic, like a perfectly rigid body. IAD is displayed in
gravitational, electromagnetic and quantum phenomena. The evidence from each of
those will now be considered:

Gravitation

There is solid evidence that
gravitational effects are communicated instantly. E. Mach made a point of this
[10, pp. 234-235]. Marquis de Laplace concluded from evidence within the solar
system that the propagation of gravity has to be at a speed at least a hundred
million times that of light [see 23, Vol. I, p. 207]. Further research has
driven that factor even higher. Astronomer T. van Flandern
explains why gravitational effects must propagate almost instantly:

Anyone with a
computer and an orbit computation or numerical integration software can verify
the consequences of introducing a delay into gravitational interaction. The effect
on the computed orbits is usually disastrous because conservation of angular
momentum is destroyed. Expressed less technically by Sir Arthur (Eddington), this means: “If the Sun attracts Jupiter toward
its present position S, and Jupiter attracts the Sun toward its present
position J, the two forces are in the same line and balance. But if the Sun
attracts Jupiter to its previous position S’ and Jupiter attracts the Sun
toward its previous position J’, when the force of attraction started out to
cross the gulf, then the two forces give a couple. This couple will tend to
increase the angular momentum of the system. And, acting cumulatively,
will soon cause an appreciable change of period, disagreeing with observations
if the speed is at all comparable with that of light.” [as
quoted by G. Galeczki in 29, p. 136]

It should be
noted here that instantaneous gravitational effects cannot be used by
intelligent agents to communicate information instantly because inherent
inertial effects in any physical communications system would prevent it.

Also telling is
the failure of physicists to discover gravitational waves, something predicted
by the theory of general relativity. Much expense and effort has been put into
detecting such waves but they have not been observed [see 42]. They are
expected to be very weak and therefore very difficult to detect. But perhaps
the truth is that they simply do not exist. If they do exist, what is the
medium that carries them? There is no medium comparable to the TEEM ether for electromagnetic
waves that could do so. And so it seems that, despite Newton’s objection and
general relativity, IAD remains the only plausible explanation for
gravitational interactions.

Electrodynamics

In 1785 Charles-Augustin de Coulomb (1736-1806) formulated a law for the
interaction of electric charges that imitated Newton’s law of gravitation.
Coulomb’s law stated that two electric charges attracted or repelled each other
in proportion to the product of the magnitudes of their charges and inversely proportional
to the square of the distance between them. He assumed no intervening medium
and thus introduced action-at-a-distance into electrostatics.

In 1820
André-Marie Ampère (1775-1836) discovered an
action-at-a-distance law for the force of interaction between two
current-carrying wire elements. In Ampère’s law the
force of interaction, like that of gravity, varies inversely as the square of
the distance between the wire elements [for details see 43].

The idea that
electromagnetic IAD (or near IAD) and the finite propagation at the speed of
light coexist goes back to the early nineteenth century. A. J. Fresnel believed
that the ether behaves like an elastic solid that transmits both longitudinal
and transverse waves. Fresnel hypothesized “that the velocity of the
longitudinal waves in the ether is indefinitely great compared with that of the
transverse waves; for it is found by experiment with actual substances that the
ratio of the velocity of propagation of longitudinal waves to that of
transverse waves increases rapidly as the medium becomes softer and more
plastic” [23, Vol. I, p. 128].

Michael Faraday
(1791-1867) believed that all space was permeated with electric and magnetic
lines of force. He proposed that these lines of force replaced the ether and
that light and radiant heat might be transverse vibrations propagated along
these lines of force [see 23, Vol. I, p. 193]. It seems consistent with his
thinking that changes in the dispositions of the sources and sinks could cause
instantaneous changes in the lines of force throughout all of space.

Faraday also
discovered the phenomenon of electromagnetic induction, a phenomenon that seems
to display IAD.  Consider a loop of metal wire encircling a magnetic flux.
According to the standard formulation of electromagnetic theory, based on
Faraday’s law of induction, a change in the flux anywhere in the loop is sensed
instantaneously in the wire loop by means of an induced current, no matter the
size of the loop. So, according to standard electromagnetic theory, a conducting loop light-years in diameter, would instantly
have a current induced in it by a change of magnetic flux at its center. T. E.
Phipps pointed this out, noting that classical electromagnetic induction theory
is “deficient” according to special relativity because it is (wrongly) supposed
that special relativity rules out IAD [44, p. 15].

It should be
noted here that electromagnetic induction cannot be used to communicate
information instantly because the current induced in the wire loop instantly
produces a flux at the center of the loop that opposes the flux change there.
The net result is that if an instantaneous change in flux at the center of the
loop is used to communicate a bit of information to the loop, this
communication will be retarded, even though the processes of induction and
counter-induction are instantaneous.

J. C. Maxwell,
the formulator of classical electromagnetic wave theory, did not rule out the
notion of action-at-a-distance. In the preface to the first edition of his
famous treatise on electricity and magnetism he distinguishes Faraday’s
approach (which he adopted) with the action-at-a-distance approach to
electromagnetic phenomena:

… Faraday, in his
mind’s eye, saw lines of force traversing all space where the mathematicians
saw centres of force attracting at a distance:
Faraday saw a medium where they saw nothing but distance: Faraday sought the
seat of the phenomena in real actions going on in the medium, they were
satisfied that they had found it in a power of action at a distance impressed
on the electric fluids.

When
I had translated what I considered to be Faraday’s ideas into mathematical
form, I found that in general the results of the two methods coincided, so that
the same phenomena were accounted for, and the same laws of action deduced by
both methods, but that Faraday’s methods resembled those in which we begin with
the whole and arrive at the parts by analysis, while the ordinary mathematical
methods were founded on the principle of beginning with the parts and building
up the whole by synthesis. [45, Vol. 1, p. ix]

Maxwell
continues on in the preface to compare the work of electromagnetic theorists,
W. Weber et al, who interpret electromagnetic phenomena in terms of action-at-a-distance
with his own field approach:

These physical
hypotheses [of the action-at-a-distance theorists], however, are entirely alien
from the way of looking at things which I adopt, and one object which I have in
view is that some of those who wish to study electricity may, by reading this
treatise, come to see that there is another way of treating the subject, which
is no less fitted to explain the phenomena, and which, though in some parts it
may appear less definite, corresponds, as I think, more faithfully with our
actual knowledge, both in what it affirms and in what it leaves undecided.

In
a philosophical point of view, moreover, it is exceedingly important that two
methods should be compared, both of which have succeeded in explaining the
principal electromagnetic phenomena, and both of which have attempted to
explain the propagation of light as an electromagnetic phenomenon and have
actually calculated its velocity, while at the same time the fundamental
conceptions of what actually takes place, as well as most of the secondary
conceptions of the quantities concerned, are radically different.

I
have therefore taken the part of an advocate rather than that of a judge, and
have rather exemplified one method than attempted to give an impartial
description of both. [45, Vol. 1, pp. x-xi]

In the last
chapter of his treatise Maxwell  treats the
subject of action-at-a-distance in detail.

In his famous
tractate on the principles of dynamics, Maxwell neatly summarizes the
difficulty of satisfactorily explaining action-at-a-distance phenomena in terms
of an intervening medium. Considering the interaction of two magnets, he
concludes:

Attempts have been
made, with a certain amount of success, to analyse
this action at a distance into a continuous distribution of stress in an
invisible medium, and thus to establish an analogy between magnetic action and
the action of a spring or a rope in transmitting force; but still the general
fact that strains or changes of configuration are accompanied by stresses and
internal forces, and that thereby energy is stored up in a system so strained,
remains an ultimate fact which has not yet been explained as the result of any
more fundamental principle. [9, p. 67]

The ether that
Maxwell apparently envisioned was one with mechanical properties adjusted to
provide a consistent theory. It was assumed to pervade all space and matter. It
was extremely light and extremely elastic with regard to shear so that it could
propagate transverse waves. However, it was incompressible because according to
his equations it is incapable of propagating longitudinal waves; yet it could
transmit a longitudinal electrical effect instantly. Maxwell’s custom was to
treat matter as a modification of the ether, so it can be said that he assumed
that matter and ether move together [see 23, Vol. I, p. 259]. In his essay A
Dynamical Theory of the Electromagnetic Field, Maxwell identifies the
electromagnetic field with the ether, saying: “The electromagnetic field is
that part of space which contains and surrounds bodies in electric or magnetic
conditions” [46, p. 34]. Further on he attributes capabilities to the ether
other than the transmission of light, which could include IAD:

A medium having such
a constitution may be capable of other kinds of motion and displacement than
those which produce the phenomena of light and heat, and some of these may be
of such a kind that they may be evidenced to our senses by the phenomena they
produce. [46, p. 35]

Maxwellian field theory has its critics. P. W. Bridgman
examined the modern concept of light from an operational point of view, that
is, from the point of view of what actually can be measured by physical
instruments. He concluded:

Hence from the point
of view of operations it is meaningless or trivial to ascribe physical reality
to light in intermediate space, and light as a thing traveling must be
recognized to be pure invention. [47, p. 153]

The great
success of Maxwell’s electromagnetic field theory is its ability to predict
electromagnetic radiation in free space: According to Phipps, this success lies
in predicting the time delay between cause (by the subject) and effect (at the
object) and not in describing what is happening between the subject and object:

Wherein lay the
superiority of the field mode of description? Simply in its
ability to predict the time delays of causal “propagation.” Causes at
point A produced later effects at point B, the two being linked by an
appearance of something moving from A to B at speed c. (This applies to
radiation. Many assume that it applies also to electromagnetic forces, but
there is no empirical evidence to back this.) [44, pp. 115-116]

Phipps points
out that instant-action models are not limited to
instant-action predictions. He cites the work of Gustav Kirchhoff (1824-1887),
who, using an instantaneous-action-at-a-distance, many-body interaction model,
proved that voltage and current waves travel along wires with the speed of
light [see 44, pp.40-41]. He further cites the work of N. Graneau
[37, 214-219], “who made computer calculations, using Ampère’s
original force law… to show that instant actions of large numbers of coherent
current elements separated by distance D in free space from large numbers of
coherent elements induce a coherent response in the latter that grows in time
and that is delayed in onset proportionally to D. (The delay results jointly
from inertial sluggishness of the material current elements and from
inverse-square weakening of the Ampère force with
distance.) These, broadly speaking, are the characteristics of far-zone
radiation, as measured, e.g., by antennas” [44, p. 116]. In order to
adequately explain electromagnetic radiation in terms of instantaneous action
at a distance Phipps suggests “to follow the Kirchhoff clue and look for some
altogether new conceptualization of the many-body problem” [44, p. 120]. J. Fukai made a similar suggestion. He said that Weber’s
equation (which was the basis for Kirchhoff’s calculations) can be applied to
the propagation of radiation in a vacuum by considering the vacuum as a
“virtual coaxial cable” comprised of virtual positive and negative particles.
The “telegraphers” equation of Kirchhoff can then be applied [see 48, pp.
79-82]. Assis made a similar suggestion, using a
“photon gas” as a medium of propagation [see 35, pp. 230-231].

J. P. Wesley
transformed the IAD Weber equation for the interaction of two charged particles
in relational space to field equations in absolute space. [see
26, pp. 217 ff]. In doing so he introduced two new potentials, in addition to
the traditional scalar and vector potentials. He maintains that his equations
reduce to Maxwell’s equations when those new potentials are made to vanish, and
when certain restrictions are placed on the traditional scalar and vector
potentials. Assis has also shown the compatibility of
Weber’s equation with Maxwell’s equations [see 35, pp. 223 ff].

Graneau’s work offers another mode for the communication of
physical disturbances in addition to propagation, propulsion and projection. It
might be called “postponement” (postponed action). In postponement a physical
disturbance is communicated instantly without a medium, but its observable
effects are postponed. Inertial and other instantaneous reactionary phenomena
and many-body effects delay and weaken the observable effects. Thus a physical
disturbance at one place can be communicated instantly to another place in the
universe where there is a detector, but the detector will not communicate it
instantly to an intelligent observer. Detectors further from the source of
disturbance may receive weaker and later effects than detectors closer to the
source. Postponement is not the principal mode of communication of the TEEM,
but it does play a role in the mechanism of ethereal propagation.

The prediction
by Maxwell’s equations of far-zone radiation that transports energy has long
been used as “proof” of the independent reality of the electromagnetic field.
However Graneau’s work has weakened that argument. He
essentially showed, using Ampère’s law for the force
between current-carrying elements, which is an IAD law, that the propagated
field may be an illusion caused simply by a delay that increases with distance
in the observable effects of an electromagnetic disturbance. This delay is
caused jointly by the material inertia of the detector charge and the inverse
square weakening of the reaction with distance between the source and detector.
Thus “propagated” effects are simply “delayed” effects and not effects
transported by the intervening medium.

P. and N. Graneau see hope for such a theory that explains
“propagation” in terms of delayed effects:

Two significant
facts emerged from the early investigation [into eddy currents and dynamic
induction] which ultimately became responsible for this book. The first was
that a Newtonian action at a distance theory could explain precisely the same
facts, related to relative motion, as electromagnetic field theory with
Einstein’s special relativity. The second fact concerned the time delay between
the cause of induction and the induced effect itself. This time delay, or the
corresponding AC phase shift, could be explained with equal precision by the
energy transport time lag of field theory or the many-body simultaneous matter
interaction process of Newtonian electrodynamics. The second fact suggests that
a time may come when the eight minutes it takes sunlight to reach the earth can
be accounted for by a simultaneous far-action theory. [43, p. 140]

Effects that are
transmitted instantly are changes of force. Effects that are postponed are
changes in energy. Forces produce changes in energy but not instantly because
of the inertia of matter. And observers observe the effects of forces (changes
of speed, position), not the forces themselves. These effects require time to
come about and are therefore delayed. Information is communicated by those
effects and not the forces.

It may be that
we will not come to understand postponement. But neither do we understand
Maxwell’s ad hoc vacuum displacement current, which underlies the propagation
of electromagnetic waves in free space [see 36, Chapter III] (unless it is
indeed as the TEEM proposes), nor do we understand the nature of the photon,
which is often pictured more as a projectile than a wave. It is reasonable to
believe that postponement can be the basis for a consistent theory for the
communication of electrical energy over distance that is as satisfactory as the
phenomenon of far-field radiation derived from Maxwell’s equations. It may even
give insight into the nature of the photon because it, like the
quantum-mechanical photon, is connected with instantaneous action at a
distance.

Phipps made
another pertinent observation about Maxwell’s electromagnetic field theory. He
said that that theory is in a sense incomplete because it does not provide a
force law, a point recognized by Maxwell himself [see 44, pp. 118-120].
Phipps sees no way to get from it to Ampère’s force
law for current elements or Weber’s force law for electric charges (the former
can be derived from the latter [see 43, pp. 35-36]). Both Ampère’s
and Weber’s laws presume IAD; and they incorporate Newton’s third law with
equal and opposite forces acting on the line connecting the two interacting current
elements or charges. Traditional electromagnetic field theory requires the
addition of a separate force law, which was supplied by H. A. Lorentz
(1853-1928). The Lorentz force law violates Newton’s third law because the
force on a moving charged particle by the field produced by a current element
and the reactive force on the current element are not, in general, along the
same or parallel lines. The magnetic component of Lorentz’s force law is based
on the force of interaction between two current elements proposed by H. G. Grassmann (1809-1877). In Grassmann’s
law, which Grassmann proposed in objection to Ampères law, the forces of interaction between two current
elements are generally not collinear or parallel. This non-Newtonian
electrodynamics of Grassmann and Lorentz is the
electrodynamics employed by Einstein in his special relativity theory [see 43,
pp. 28 ff.]. Since the law of conservation of linear momentum is a consequence
of Newton’s third law, it would seem inconsistent to apply the law of
conservation of linear momentum to any inertial situation in special relativity
if it does not apply to electromagnetic forces. Special relativity theory gets
around this problem by redefining the electric and magnetic fields according to
the inertial frame of the observer, thus eliminating the absoluteness that the
fields have in Maxwell’s theory [see 48, pp. 2-4].

Despite its
being a field theory IAD is actually built in to Maxwell’s electromagnetic
theory by means of Faraday’s law of electromagnetic induction and Maxwell’s
introduction of vacuum displacement current. The wave equations in free space
derived from Maxwell’s equations are known to produce “retarded” and “advanced”
solutions, and the equations themselves show no inherent preference for either
one. The retarded solutions represent electromagnetic disturbances traveling
from the source of the disturbance to the detector (absorber) at the speed of
light. The advanced solutions, on the other hand, proceed backward in time from
the detector to the source and arrive at the source at the time of emission, as
if their reaction were an instantaneous reaction. The two solutions are
consequences of the time symmetry of Maxwell’s equations, and the advanced
solution cannot simply be rejected because that would destroy the symmetry. J.
A. Wheeler and R. P. Feynman proposed a theory that formulated a combination of
both fields and gave the universe as a whole a role as perfect absorber of
electromagnetic radiation [see 49, pp. 29-48].  As Feynman explained it:
“The combination of the advanced and retarded waves means that at the instant
it is accelerated an oscillating charge feels a force from all the charges that
are ‘going to’ absorb its radiated waves” [50, Vol. II, p. 28-8]. This is not
strictly IAD because both the advanced and retarded waves travel at the speed
of light, one forward in time, the other backward in
time. However, it simulates instantaneous action at a distance to the emitter
because it receives the reaction of the absorber at the instant of emission.
Wheeler and Feynman further affirmed that the electromagnetic field does not
have an independent physical existence. They stated: “There is no such concept
as ‘the’ field, an independent entity with degrees of freedom of its own” [51,
p. 31, also see pp. 75-79].

A notion
introduced into electromagnetic theory after Maxwell is that of retarded
action-at-a-distance. This idea admits the absence of a medium but denies
instantaneous interactions. Thus the interaction is the transmission of a
physical effect by projection somehow. Specifically, impressed forces
are delayed at the speed of light. It seems that retarded force actions and
reactions would wreak havoc with Newton’s third law.

Wesley showed
that Weber’s theory applied to time-retarded fields in free space yields
electromagnetic radiation. He concludes:

Without time
retardation the field variables for an action at a distance theory must be
regarded as merely a convenient mathematical representation of the direct
interaction between the particles. But once the retardation is introduced, a
very different physical interpretation becomes necessary. In this case the
field must be viewed as having a true physical existence of its own, capable of
transmitting energy and momentum. For example, light, as electromagnetic
radiation, makes the independent existence of fields evident, quite apart from
original sources and final sinks. [26, p. 219].

However, Wesley
also makes it clear that one must begin with fields and not forces in order to
successfully introduce retardation:

Although there
have been attempts from time to time to introduce the retardation directly into
the force laws between two particles without an intermediate field … these
attempts have not been successful. The only way to introduce time retardation
is apparently via fields! [26, p. 219]

Phipps says that
the notion of retarded action-at-a-distance is theoretically arbitrary, not a
necessary consequence of Maxwell’s equations, and “is utterly devoid of
empirical support” [44, pp. 230-231].

Now for some
considerations regarding electromagnetic energy: In instantaneous action
at a distance (Newtonian) electrodynamics electromagnetic energy is conserved
non-locally. In contrast, modern electrodynamic field
theory assumes that energy is conserved locally. It assigns energy to
the electromagnetic field, energy that flows through space like a fluid. This
is not a direct consequence of Maxwell’s equations, but rather it an
application of Maxwell’s field equations and the Lorentz force law to a
postulated continuity equation for the assumed flow of energy in the
electromagnetic field. This is the place in the development of electromagnetic
field theory where universal IAD is eliminated, thus bringing field theory into
concord with special relativity. (Universal instantaneous-action-at-a-distance
implies absolute simultaneity, which is not allowed by special relativity
theory.) The concept of continually flowing field energy produces bizarre
notions, such as attributing ohmic heating in a
current-carrying wire to energy flowing into the wire from the field
surrounding it (which is produced by distant charges), rather than to the
charge flowing through it. And it produces a plethora of conflicting
mathematical expressions for the energy density and energy flow, an ambiguity
that Feynman clearly points out. Feynman further points that the actual
location in space of the electromagnetic energy is not known with certainty
[see 50, Vol. II, Ch. 27].

Electromagnetic
field theory has triumphs to its credit; but it has also failed, in both the
macroscopic and microscopic domains. P. and N. Graneau
show that electromagnetic field theory gives answers that are in conflict with
empirical facts. A dramatic example is the measured energy consumption of a
rail gun, which differs by orders of magnitude from the value
calculated using relativity and field theory [see 43, esp. Ch. 5]. Feynman
points out that electromagnetic field theory also fails when it is applied to
the electron or any charged particle. It produces an infinity
for the self-energy of an electron or point charge, in both the classical and
quantized versions, and there is no satisfactory field theory that describes a
non-point charge [see 50, Vol. II, Ch. 28].

R. R. Hatch has resurrected
the nineteenth-century elastic solid ether concept in a form that he says
explains the experimental data and is an alternative to both relativity theory
and IAD [see 52].

It may be that
instantaneous-action-at-a-distance is the Cinderella of electrodynamics. She in
her straightforward unpretentious simplicity has been mistreated and kept out
of sight by her ugly but elegantly attired stepsisters, electromagnetic field
theory and special relativity. The mathematics of instantaneous-action-at-a-distance
is simple and straightforward but awkward and inelegant, while the mathematics
of electromagnetic field theory and special relativity is clever and elegant
but conceptually deceptive. Perhaps sometime during the twenty-first century a
fairy godmother (in the guise of insightful young physicist) will come forth to
dress her up in elegant clothing and display her beauty to the world.

Quantum Mechanics

IAD is part and parcel of quantum
mechanics. This is especially evident in the phenomenon of entanglement, in
which a quantum measurement in one part of the universe has an instantaneous
effect on a measurement in another part of the universe, no matter how far away
[see 53]. Two objects are “entangled” if they are connected in such a way that
the outcome of a measurement of a given quantum variable for the first object
instantly determines the outcome of a measurement of the same variable for the
second object. For example, if the measurement of a quantum variable for an
entangled object in the first location yields “up,” a measurement of the same
variable will necessarily yield “down” for its partner in the second location.
And if the measurement of a quantum variable for an entangled object in the
first location yields “right,” a measurement of the same variable will
necessarily yield “left” for its partner in the second location.

Here is a
parable to illustrate the phenomenon: Twin brothers are each given identical
magic coins at birth. If one flips his coin and gets heads, the other will get
tails when he flips his and vice versa, no matter what their separation.

First observe
that the effect must be instantaneous. If it were not, it could be
contradicted. Consider what would happen if the communication between the two
coins was retarded. The first twin could flip his coin and get a result, say
heads. The coin would communicate this result to the second coin, but it would
take some time. During the interval of communication the second twin could also
flip his coin and get heads thus destroying the effect.

Also observe
that the two brothers when separated can never use their coins to communicate
with each other because the first must flip his coin; he cannot choose the
outcome. All he knows is that when his faraway brother flips his coin he will
get the opposite side. One brother can cause something to happen at the other
brother’s end, but he cannot control what will happen.

The so-called
Copenhagen interpretation of quantum mechanics, championed by Niels Bohr and Werner Heisenberg, implies that things in the
submicroscopic world of electrons and other elementary particles behave with
pure spontaneity, as if they had free will. Innate randomness is inferred to be
part of their nature because some information about them is indeterminate in
principle. This view was opposed by the so-called hidden variables
interpretation, championed by Albert Einstein and David Bohm,
which sees the probabilities of quantum mechanics as caused by an
incompleteness of the theory. This incompleteness manifests itself in a lack of
information conveyed to intelligent observers of nature. Hidden variables carry
the missing information. John Bell provided a theoretical basis on which
experiments could be made to test whether quantum mechanics is complete or
incomplete. Such experiments seem to demonstrate that quantum mechanics is
complete and that there are no hidden variables, unless the information hidden
variables carry could be communicated instantly over any distance
(non-locality), which would violate the tenet of relativists that the speed of
light is the ultimate speed in the universe. David Bohm
formulated a theory employing hidden variables that is equivalent to standard
quantum mechanics and retains causality. It is a non-local theory, but the
non-locality is not “signal non-locality,” that is, intelligent agents cannot
use non-locality to communicate instantly because they cannot control the
phenomenon [see 54].

Extension, Timekeeping and
Mass

The most fundament concepts in
physics are space and time. They are treated differently in the logics of
Newtonian physics, relativistic physics and relational physics. In Newtonian
physics space and time are absolute independent entities with absolute, and not
necessarily material, standards of measurement. In relativity, space and time
are not absolute but rather relative; different observers will measure
different spatial or temporal intervals between events depending on the
relative motion of the observers of the events and the presence of
gravitational fields. In relational physics, space and time have meaning only
in respect to physical objects and physical processes that can be observed and
measured. They are not absolute in the Newtonian sense, but they are absolute
in the sense that measuring rods and clocks do not, in principle, change
according their state of motion or location, as they do in relativity. They can
change accidentally, however, because of a change in their specific physical
properties because of motion or change of place. Relational physics is
down-to-earth because its lengths and time intervals are as invariant as the
physical objects and processes that standardize them. Relativity, on the other
hand, is cerebral because it is based on mathematical ideas rather than
material objects, the forms of equations being invariant rather than standards
of length and time.

The measurement
of space (extension), time (timekeeping) and the third fundamental concept in
physics, mass, will now be discussed in turn.

Extension

Relational physics rejects
coordinate systems that “hang loose” in absolute or inertial spaces. Such
coordinate systems are sources of much confusion in physics. Relativistic
principles, either Galilean or Lorentzian, lead to
confusing notions of extension. Extension is ill-defined in relativistic
theories; lengths are tenuous, intangible entities. The measuring rods of
special relativity are phantom objects, the ghosts of real things.

The relational
standard for measuring extension in the laboratory is a rigid rod under given
physical conditions, as, for example, pressure and temperature. All other
methods of measuring extension are somehow referred back to the rigid rod.

The earth serves
as a rigid base on which to construct a coordinate system employing a rigid rod
standard. The earth itself approximates a rigid body for laboratory purposes.

The earth also
serves as a mini-universe with respect to elementary particles. The relation of
elementary particles to the earth is the relation of individual particles with
a huge mass of particles bound together rigidly. Thus it is a many body
relationship. The earth, being a huge and massive rigid body, is rightly seen
as a frame of reference at rest for measurements for distances traversed by
elementary particles. Also the elementary particles may have a Machian connection with earth, just as earth has with the
rest of the universe. But the motion of an elementary particle with respect to
the earth is not reciprocal or relative. One cannot take the elementary
particle to be at rest and the earth as moving with respect to it because the
physical situation is greatly asymmetric. This does not belie the principles of
relational mechanics because relational principles only apply to symmetric
situations.

Timekeeping

Relational physics also rejects
the ill-defined notion of time in relativity theory. Relativity treats time,
like it does space, as a mathematical abstraction. Relational physics, however,
treats time as a genuine measure of change in the physical world. And thus it
employs real physical clocks, not the nebulous non-physical “clocks” of
relativity theory.

Different clocks
behave in different ways because of the physical construction. Their
timekeeping must always be calibrated against a standard clock, the physical
conditions of which are strictly maintained.

Different kinds
of clocks behave in different ways and must be compensated in different ways.
Following are various kinds of clocks:

1.
Astronomical: Employs regular motions of the heavenly bodies relative to earth.
Example: sundial.

2.
Gravitational: employs regularity produced by constant gravitational force.
Examples: pendulum clock, water clock (clepsydra), hourglass.

3. Mechanical:
Employs regularity of mechanical process. Example: mass-spring mechanism.

4.
Electromechanical: Employs mechanical means for producing regular pulses of
electricity. Example: crystal-regulated clock.

5. Electronic:
Employs regularity of electronic oscillations. Example: tuned (LC) circuit.

6. Optical:
Employs light beam. Example: light clock (consists of two mirrors separated by
a rigid rod with a light pulse moving back and forth between them).

7. Atomic:
Employs radiation emitted by atoms. Example: cesium clock.

In addition to
these are biological “clocks,” those inner timekeepers of living organisms that
direct maturation of the organisms.

Clock rates are
affected by difference in place (gravitational potential energy) and states of
motion (kinetic energy) with respect to a master clock, but these effects are
not universal for all clocks; they differ from clock to clock, depending on the
physical nature of the clock. Following are two examples:

1. The pendulum
clock: The period of a pendulum clock is directly proportional to the square
root of the length of the pendulum and inversely proportional to the square
root of the gravitational acceleration. A pendulum clock that is to be taken to
the top of a mountain has to be “compensated” by shortening the pendulum
because gravitational acceleration is less at the top of the mountain. If this
is not done it will run at a slower rate when it is at the top of the mountain
than a “standard” pendulum clock at the bottom of the mountain.

The pendulum clock taken to the top of a mountain will take a definite
period of time (duration) according the pendulum clock that remains on the ground.
But the period of time registered on the clock traveling up the mountain will
depend on the path it takes. That is, different paths that register the same
duration for the trip according to the ground clock will register different
durations for different paths taken by the traveling clock. This is because the
rate of the clock varies as it is taken up the mountain. However the rate of
the clock at the top of the mountain will be independent of the path taken.
Once the traveling clock reaches the top of the mountain and is synchronized
with the ground clock by a light or radio signal, it will remain in
synchronization.

2. The atomic
clocks of the Global Positioning System (GPS): Like the pendulum clocks, the
rates of the cesium clocks in the GPS system also have to be compensated for
the difference in gravitational potential between the satellites and the
ground. In addition their rates have to be compensated because they are moving
with respect to clocks on the ground. The rates of the satellite clocks have to
be compensated by the reciprocal of Lorentz factor (1/γ) in order to
remain in synchronization with the ground clocks. However, the corrections are
dynamic and not kinematic, as asserted by special relativity theory. That is,
compensation is required because of the physical properties of the clock, not
because of “time dilation.” This is evident because the timekeeping is
asymmetric; to earthbound observers the clocks in orbit run slower than the
clocks on earth but not vice-versa. If relativistic “time dilation” were the
cause then clock slowing would be symmetric. The slowing of the orbiting clocks
is probably connected to the increased mass of the moving cesium atoms. The
increased mass is attributed to the work done on them to put them in orbit [see
44, pp. 139-146, 155-163].

Special
relativity theory makes much ado about the synchronization of distant clocks.
But it generates complications because it gives a synchronization signal
traveling at a finite speed the role of a synchronization signal of infinite
speed thus making simultaneity relative. Relational physics also recognizes
that compensated distant clocks cannot be synchronized instantly with a master
clock because information cannot be communicated instantly, as already
indicated. The fastest synchronization signal speed that can be used is the
speed of light in a vacuum. However, that does not destroy the notion of
absolute simultaneity as it does in special relativity theory. Compensated
distant clocks can be synchronized by a light or radio signal with a master
clock as follows: The clock to be synchronized sends a light or radio signal to
the master clock. The master clock instantly responds with a light or radio
signal that contains the time. The time on the distant clock is set in synchronization
with the master clock by correcting for the time delay between the sent and
received signal. (The speed of the light signal is the same in both directions
because of the dynamical constancy of the speed of light.) The time delay is
the time difference from absolute simultaneity. The rate of a distant clock can
be compensated in the same way, using more than one signal.

Mass

Mass is measure of the “quantity”
of matter in a corporeal body. It is either a measure of the resistance of a body
to a change in its state of motion (inertial mass) or a measure of its
interaction with other corporeal bodies (gravitational mass). The properties of
mass that make it useful as a measure of the quantity of matter are that
it is universal, that is, it applies to all material bodies, and that it is
additive; that is, the mass of an aggregate of two bodies in identical physical
states is the sum of the masses of the individual bodies.

The theory of
special relativity predicts that the inertial mass increases by the Lorentz
factor γ with the speed of a body with respect to the observer. This is
consistent with relational physics, for it was shown in a previous article that
the relational interpretation of stellar aberration suggests it. The increasing
of mass with speed was inferred before the advent of the theory of relativity
from electromagnetic considerations. It is significant only at speeds
approaching the speed of light and has been experimentally confirmed.

Newton’s second
law states that the force exerted on a body is equal to the rate of change of
its momentum; with its momentum, in general, being the product of the Lorentz
factor, the rest mass, and the velocity. A simple mathematical integration of
the rate of change in momentum with respect to distance from a body at rest to
a speed v yields an expression for the kinetic energy imparted to the body. The
kinetic energy so calculated manifests itself as an increase in
its inertial mass, being expressed by the formula KE = mc2 _ m_0c^2
= γm_0c^2 –  m_0c^2
. When expanded in powers of v, the term m_0c^2 cancels
out. The presence of that term led Einstein to propose that even at rest a
material body possesses energy by virtue of its inertial mass..
However, relativistic (or relational) dynamics alone cannot verify universal
identity of mass and energy (that is, whether they are synonyms for the same
underlying physical substratum), nor can it say whether inertial mass can be
completely transformed into energy. Those questions were answered in the
affirmative only by further investigations in theoretical and experimental
physics.

Although mass is
a very important fundamental concept in physics, it is not well understood. Max
Jammer concludes his Concepts of Mass with the acknowledgment:

One has to admit
that in spite of the concerted effort of physicists and philosophers,
mathematicians and logicians, no final clarification of the concept of mass has
been reached. The modern physicist may rightfully be proud of his spectacular
achievements in science and technology. However, he should always be aware that
the foundations of his imposing edifice, the basic notions of his discipline,
such as the concept of mass, are entangled with serious uncertainties and
perplexing difficulties that have as yet not been resolved. [55, p. 224]

In relational
physics, mass is not understood to be an innate property of a body; rather, it
is a collective effect on a body caused by its interaction with all the other
bodies in the universe [see 8, 29, 34, 37].

Chapter SIX:
Conclusion—Principles for Relational Cosmology

A Catholic creation cosmology is
one that is totally consistent with empirical facts, with the biblical record,
and with the authentic teachings of the Catholic Church. Further, it employs
the sound philosophy of nature developed by medieval scholasticism. Cosmologies
in vogue today, unfortunately, do not fulfill those requirements. They are
based on more on human ideas than on empirical facts, and they do not recognize
certain divinely revealed truths about the cosmos and its origin. A cosmology
can be genuine only if it starts from true principles, even though such
principles may yield more than one consistent cosmology. Following is a set of
principles for Catholic creation cosmology that are gleaned from the material
presented in this book:

Principle 1: Extension is
an absolute accident that depends on matter for its meaning.

The first of the modern
philosophers, René Descartes (1596-1650) believed that matter and extension are
the same. He held that the concept “void” is a contradiction in terms because
where there is space there is by definition extension and therefore matter.
Thus for Descartes the universe is a plenum; it is filled, that is all of the
places for matter are occupied by matter. This contrasts with the position of
St. Thomas Aquinas, who held that the void is a privation, that is, it is a
place for matter that is not filled.

The traditional
Catholic position, informed by the doctrine of the Eucharist, holds that
extension is an “absolute accident.” Being an “accident” means that it depends
on matter for its meaning, that is, its existence must always be referred to a
material substance. Being “absolute” means that it is separate from a substance
in which it inheres, that is, it does not contribute to the essence of a
substance. This is in opposition to the doctrine of Descartes, who held that
extension is the very essence of material substance. The Catholic
Encyclopedia (1914) explains this nicely:

Extension is an
“absolute accident,” that is not a mere mode in which the substance exists, as,
for instance, are motion and rest. It seems to have a
certain distinct entity of its own. This, of course,
would most probably never have been suspected by the human mind unaided by
Revelation. But given the doctrine of the Real Presence of Christ in the
Sacrament of the Eucharist, wherein the extensional dimensions and sensible
qualities of bread and wine persist after the conversion of the substance of
bread and wine into His Body and Blood, reason, speculating on the doctrine,
discerns some grounds for the possibility of the real distinction and even
severance between substance and local extension. In the first place there are
motives for inferring a real distinction between substance and extension
(actual and local), or, in other words, that extension does not constitute the
essence of material substance (as Descartes maintained that it does):

1. Substance is the
root principle of action; extension as such is either inactive or at most a
proximate principle.

2. Substance is the
ground of specification; extension as such is indifferent to any species, since
shape or figure which is the dimensional termination of extension depends upon
the specific form.

3. Substance is
identical in the entire mass and in each of its parts (e.g. in gold), while
extension is not the same in the whole and each of its parts.

4. Substance is the
principle of unity; extension is the formal principle of plurality.

5. Substance
essentially demands three dimensions; extension may be realized in one or two.

6. Substance
remaining the same; extension may increase or decrease.

Given a real
distinction between extension and substance, no intrinsic impossibility can be proven
to exist in the separation of one from the other, for although internal
extension naturally demands external, there is no evidence that the demand is
so essentially imperative that Omnipotence cannot supernaturally suspend its
realization and by other means afford the accidents—extension and the rest—the
support which the substance naturally supplies. Since material substance owes
the distribution of its integral parts to extension, the question arises
whether, independently of extension, it possesses any such parts (it, of
course, possesses parts essential to corporeal substance, matter and form), or
is simple, indivisible. St. Thomas and many others maintain that substance as
such is indivisible. Suarez and others hold that it is divisible. [16, article
entitled “Extension”]

It is clear that
extension does not contribute to the nature of an object if one considers, for
example, that the properties a square do not depend on its size and the nature
of a bird does not depend on its size. However, relationships with other
objects do depend on extension. For example, one can place smaller squares
inside a square, and a bird’s size will affect how it interacts with its
environment. Therefore extension can be said to be “relational.”

Principle 2: Interbody extension (space, void) is relational, not
absolute.

The first principle applies to a
“local” physics, in which the earth (or other ponderable
body) is treated as a rigid frame of reference at rest. This second principle
applies to a “cosmic” physics, which considers relations between those ponderable bodies. In these relations the void surrounding
a ponderable object is considered as an extension of
the object. The object thus lends its three-dimensionality to the void
surrounding it. The interaction of different objects involves the unifying
interpenetration of their individual voids. In such a holistic universe, each ponderable body can be thought of as the core of the
universe, the void surrounding it containing the rest of the universe.
Nevertheless, Catholic tradition teaches that the earth holds a special place,
having been created first; so the universe is not perfectly “democratic,” a
notion espoused by those who embrace the cosmological principle.

*

Despite its few successes,
general relativity has serious deficiencies that call into question its
suitability for modeling cosmologies. These deficiencies follow from the fact
that general relativity is rooted in the notion that space-time is an
independent physical entity. It was pointed out earlier how general relativity,
like Newtonian mechanics, gives inertia to a body alone in empty space. This is
an operationally meaningless concept. Einstein himself realized this. He said:
“In a consistent theory of relativity there can be no inertia relatively to
“space,” but only an inertia of masses relatively
to one another. If, therefore, I have a mass at a
sufficient distance from all other masses in the universe, its inertia must
fall to zero” [22, p. 180]. Einstein at first thought that this result
followed from the general theory of relativity but soon found out that it did
not [see references in 8, p. 149]. A. Assis points
out other notable defects [8, pp. 146-159]:

1. The requirement of general
relativity that the laws of physics have the same mathematical form in all
frames of reference, non-accelerated or accelerated, causes confusion and
ambiguities. “We need to change many concepts of space, time, measurements,
etc. in order for the theory to correctly predict the facts in different
accelerated frames of reference. It would be much simpler, more coherent and in
agreement with the previous knowledge of the laws of physics to require that
each two-body force have the same numerical value
(although not necessarily the same form) in all frames of reference.” Assis gives the example of a frame rotating with respect to
an inertial frame in Newtonian physics. The mathematical expression for the
force on a body is different in both frames but the numerical value is the
same. He goes on to say that numerical invariance is implemented in relational
mechanics.

2. Einstein wanted to obtain from
general relativity the classical centrifugal and Coriolis
forces in a body by its rotation relative to the universe. But he was not able
to derive the centrifugal force and the correct Coriolis
force simultaneously The Coriolis force was five
times too large. Also, in such a situation, general relativity yields a
spurious axial force that does not appear in Newtonian theory. Thus general
relativity cannot yield the correct Newtonian forces in non-inertial frames of
reference.

3. Erwin Schrödinger (1887-1961)
questioned the equivalence of the precession of the perihelion of Mercury as
measured by the astronomers and that calculated by Einstein. Schrödinger said:
“After the secular precession of the perihelion of Mercury was deduced, in
amazing agreement with experiment, from it, every naïve person had to ask: With
respect to what, according to the theory, does the orbital
ellipse perform this precession, which according to experience takes
place with respect to the average system of the fixed stars? The answer that
one receives is that the theory requires this precession to take place with
respect to a coordinate system in which the gravitational potentials should
satisfy certain boundary conditions at infinity. However, the connection
between these boundary conditions and the presence of the masses of the fixed
stars was in no way clear, since these last were not included in the
calculation at all” [8, pp. 151-152]. Since the calculation does not take into
account the stars and the measurements of the astronomers are with respect to
the background of the fixed stars, it would seem that the agreement of Einstein
with the astronomers is coincidental.

4. Concerning Newton’s bucket experiment:
As in Newtonian physics, general relativity does not attribute the concave form
of the water surface to the relative rotation of the water with respect to
either the bucket or the earth. In addition, general relativity does not
attribute the concavity to the relative rotation of the water to the fixed
stars and distant galaxies. The consequence is that, in general relativity, the
concavity of the water is caused by rotation of the water relative to something
completely disconnected from matter. According to the apologetic of general
relativity the concavity should be caused by a local curvature of space. But
what curves the space in an otherwise empty universe? Furthermore, in the
reference frame that rotates with the bucket and the water (when the rotational
speed of the water catches up with the bucket) with respect to the fixed stars
Newtonian physics adds a centrifugal force term that accounts for the
concavity. But general relativity yields in addition to a centrifugal force an
axial force that has no analogue in Newtonian theory. The fixed stars do not
exert this axial force in a frame at rest with respect to them but does exert
it in a frame rotating with respect to them. Since the axis is common to both
the non-rotating and rotating frames, this is a contradiction: the same pail of
water has a force exerted along its axis and does not have a force exerted
along its axis. Also, according to general relativity, in the frame at rest the
distant galaxies have no effect on the concavity of the water but in the
rotating frame the amount of concavity depends on the mass of the distant
galaxies.

5. The parameters of Foucault’s
pendulum and the flattening of the earth, when calculated according to general
relativity in the earth’s frame of reference with the distant galaxies
rotating, are different from those observed experimentally.

6. The inertial mass is not well
defined in general relativity.

If general
relativity cannot give us correct answers about genuine physical phenomena,
what credibility are we to give to the exotic notions it inspires, such as the
big bang, black holes, white holes and worm holes?

Assis comments on the intricate and cumbersome conceptual
and mathematical apparatus of relativity:

In our view, the
theoretical concepts of length contraction, time dilation, Lorentz invariance,
Lorentz’s transformations, covariant and invariant laws, Minkowski
metric, four-dimensional space-time, energy-momentum tensor, Riemannian
geometry applied to physics, Schwarzschild line element, tensorial
algebras in four-dimensional spaces, quadrivectors,
metric tensor gmn, proper time,
contravariant, four- vectors and tensors, geodetic
lines, Christoffel symbols, super strings, curvature
of space, etc. have the same role as the epicycles in the Ptolemaic theory. [8,
p. 159]

Assis, following the suggestion of several authors,
dispensed with coordinate systems and applied the relational force W. Weber
proposed for electrical interactions to gravitational interactions. He was able
to implement a mechanics without absolute space and time and without frame
dependent forces that gives a clear notion of inertial mass and explains, among
other things, centrifugal and Coriolis forces as real
forces produced by relative rotation of a body with the distant universe. Assis’ relational theory of gravity produces results that
are in agreement with experience and are free of contradictions, confusion and
ambiguities.

In relational
mechanics the measurement of distance on rigid bodies in made with rigid rods.
A taut cord can be used to define a straight line. The measurement of distance
between rigid bodies is done by laser clocks. In a laser clock a laser beam is
reflected back and forth along a measuring rod. To measure a distance between
two bodies a light signal is sent from on body to the other and returned. The
distance is indicated by the number of cycles recorded by the laser clock
during the period of transmittal of the signal and return. The constancy of the
speed of light allows this, the time for the transmitted signal and return
signal being the same. These procedures may not always be capable of being
performed because of practical considerations. Their purpose is to serve as
operational definitions with clear physical meaning.

Relational space
(interbody extension) may be Euclidean or
non-Euclidean. Operationally, the local geometry of relational space is
determined by the communication of three light beams from/to three bodies. The
geometry determined by the sum of angles in triangle formed by the three light
beams with three bodies at vertexes. If the sum is two right angles then the
three bodies define a Euclidean surface, if not, they define a non-Euclidean
surface. The geometry would probably depend on the relation of the three bodies
with respect to the rest of the massive bodies in the universe. The precession
of the perihelion of Mercury might be explained as the result of the triangles
formed by the sun, the earth and Mercury defining non-Euclidean surfaces. Thus
the precession might be an observational (optical) phenomenon caused by
non-Euclidean light trajectories, and not a “curvature of space-time.”

Notice that,
although on the Euclidean plane the straight line is a unique path, in general
the path defining the shortest distance between two points may not be unique.
For example, consider a sphere on an axis: There are an unlimited number of
shortest paths from the north pole to the south pole
on its surface, all arcs of a great circle. Since the interbody
extension between celestial bodies might be defined by non-Euclidean light
trajectories, different stellar objects may be the same object viewed along
different light trajectories.

Principle 3: Time is
relational, not absolute.

Time is not an entity itself.
Rather, it is a means of comparing physical changes in different physical
objects and is measured by physical devices. Both Newton and Einstein treated
time as if it were a substance. For Newton it is a rigid substance which is the
same for all who observe it. For Einstein it is a flexible substance that can
vary from observer to observer.

Relational
physics retains the commonsense notion of absolute simultaneity, even though it
cannot be verified directly over large distances by a signal of infinite speed.
Two events, no matter how distant from each other have the same temporal
sequence and separation to all observers because all observers can refer their
observations to a standard clock, no matter where it is located. The
synchronization of clocks presents, in principle, no problem. Clocks can be
synchronized unambiguously a by light beam, which has the same speed for all
observers because of its dynamical nature.

Principle 4: The speed of
light is the same for all moving observers because of its dynamic properties
and not because of kinematic properties of clocks and measuring rods.

The speed of light is constant
(in uniform gravity) because it is impossible to determine motion though the
twofold electrical ether, because of it very nature. If the speed of a light
beam varied from body to body, this would imply that that there is a frame of
reference in which the beam is at rest. Such a frame of reference would define
an absolute space, in which ponderable bodies move at
various absolute speeds. Relational physics rejects such a space.

Relative motion
is reflected in the change of wavelength and frequencies of a light beam
exchanged by two observers on two ponderable bodies
moving relatively. The period and wavelength differ by the same factor (γ)
resulting in a constant speed. (In quantum terms this means that the
energy and momentum of a photon are not fixed but its speed is.) This involves
a twofold Doppler effect. Both the frequency and wavelength of a beam of light
change from physical observer to another physical observer moving with respect
to the first but such that the speed of the beam remains fixed. In the
classical Doppler effect the wavelength of a
disturbance changes when the source moves through the medium and the frequency
changes when the detector moves through the medium but the speed through the
medium remains constant. However, in relational physics both the source and the
detector find themselves at rest in the medium.

*

The TEEM allows for the
permittivity and permeability of “free space” to be altered by strong
gravitational interaction, giving rise to refraction in the proximity of large
massive objects. This would account for the bending of starlight around the sun
and gravitational red shift. This seems to be a more straightforward and
natural way to account for such effects than by the distortion of a space-time
continuum.

A. K. T. Assis has made a natural connection between gravitation and
electromagnetism that makes gravitational effects on the permittivity and
permeability of “free space” plausible. He formulated a generalized Weber force
law for electromagnetism that includes terms of fourth and higher orders in
v/c. He showed that the extra terms yield an attractive force between two
neutral dipoles in which the negative charges oscillate around the positions of
equilibrium. He concludes: “This attractive force can be interpreted as the
usual Newtonian gravitational force as it is of the correct order of magnitude,
is along the line joining the dipoles, follows Newton’s action and reaction
law, and falls off as the inverse square of the distance” [56a, b].

Principle 5: Natural
forces act instantaneously over distance.

Ever since Isaac Newton
introduced his law of gravity there has been strong opposition to the notion of
instantaneous-action-at-a- distance. Newton himself, even though he framed his
law of gravity in a way that implies instantaneous-action-at-a-distance, did
not believe in it. However, the stability of a planetary orbit depends on the
instantaneous (or near-instantaneous) sensing by both bodies of the change in
distance between the sun and the planet. Since Newton believed that
gravitational effects were transmitted by an ether,
his ether would have to be perfectly rigid in order to communicate changes in
force instantly. It seems just as easy to believe that changes in gravitational
forces are communicated instantly over space as to believe that they are
transmitted by a rigid ether. The former only requires
acceptance of the notion that the universe is holistic and not analytic. Although
separating the universe into parts has been helpful in explaining some of its
features, its complete understanding requires knowledge of the whole.

The same
reasoning can be applied to electric and magnetic forces that act along
geodesics connecting electric or magnetic objects. Disturbances in the twofold
electrical ether are propagated perpendicular to the disturbance at the speed
of light. No such propagation exists for gravitational interactions because
there is no twofold medium for them, there being only one kind of gravitational
“charge.”

W. D. Walker has
shown that, according to Maxwell’s equations, the propagation speed of
electromagnetic fields is nearly infinite in the near field and reduces to the
speed of light in the far field [57].

Principle 6: Intelligent
agents can physically communicate information no faster than the speed of
light.

Although longitudinal natural
force variations are transmitted over any distance instantly, intelligent
agents cannot use them to communicate information instantly. A force can
transmit information only by its observable effects (for example, displacement,
acceleration). Observable effects take time to
manifest themselves. Nature conspires to make us unable to communicate
information faster than the speed of light, lest we come to think that we are
gods.

Principle 7: The inertia
of a material body is caused by gravitational interaction with all the other
bodies in the universe.

It was recounted how A. K. T. Assis explained inertia as being the effect of real
instantaneous-action-at-a-distance gravitational forces. Applying this notion
he recovered Newton’s first and second laws of motion, demonstrated the
equivalence of inertial and gravitational mass, and even produced an expression
for the precession of the perihelion of Mercury.

Assis’ model of the universe was Euclidean. But logically
it need not be so. His notion applied to a non-Euclidean universe would require
distances to be measured along geodesics. The equivalence of gravitational and
inertial mass insures that the geodesics will be the same for all masses.

Assis’ model is classical; it does not yield an inertial
mass that increases with speed, which, apparently, has been experimentally
verified. However, a modification of the gravitational interaction might
achieve this. The physical problem confronted in determining this term is how
to connect optics with mechanics. This is necessary because the mass variation
factor, γ, contains the speed of light. Einstein achieved this connection kinematically at the expense of
Newtonian notions of space and time. The connection can be made in
relational mechanics dynamically in terms of the force of interaction
between a mass and the rest of the universe. This had already
been done by E. Schrödinger in 1925 and independently by J. P. Wesley in 1990
[see 8, pp. 233-236].  However, a good physical explanation should
be provided for that interaction. Their introduction of the speed of light
seems ad hoc and does not seem to reveal a natural connection between optics
and mechanics. Even so, they showed that relational mechanics is capable of
explaining mass variation without the bizarre notions of space and time
introduced in special relativity.

Appendix A:
Spectroscopic Binaries

A spectroscopic binary star
system is composed of two very close stars rotating about each other. Often a
spectroscopic binary cannot be resolved optically into two distinct stars and
so appears as a single star in the sky. But its optical spectrum contains lines
shifted both up and down, from which astronomers deduce that the star is
binary. Because of the Doppler effect, the member of
the pair moving toward the observer has lines shifted toward shorter
wavelengths and the member moving away from the observer has lines shifted to a
longer wavelength. The observed wavelength shifts indicate considerably large
rotational speeds.

The observations
of binary systems have been used to refute Einstein’s notion that stellar
aberration is caused by the relative motion of the earthbound observer and the
observed star and not by the motion of the observer through the ether. Critics
of Einstein’s view argue that if relative motion causes stellar aberration then
the stars in a binary system would not look as close to each other as they do.
This is because their great rotational speeds in opposite directions would
produce a great difference in their angles of aberration so as to make them
look widely separated. [See 58, chapter 11, for a historical summary on
spectrographic binaries.]

That argument
does not apply to the TEEM, however, because both stars in the binary system
can be construed as one star because, being so close together, they produce one
ray of light that travels down the telescope tube to the observer. Thus the
speed in the angle-of-aberration equation is the speed of the center of mass of
the system.

Appendix B:
Observations Pertaining to the Relative Rotation of the Earth and the Stars

Several experimental observations
seem to have been influenced by the relative rotational motion of the earth and
stars. The most notable of these is the Hafele and
Keating experiment in which atomic clocks were transported in opposite
directions around the globe on commercial airline flights. The clocks flown
eastward slowed down losing 59 nanoseconds with respect to the clocks at rest
on the surface of the earth; and the clocks flown westward sped up gaining 273
nanoseconds. This can be explained relationally by considering the masses of
the atoms in the clocks as they move with respect to the stars. The clocks
moving eastward have a greater speed with respect to the stars than the clocks
at rest. Therefore the masses of the atoms will increase and the clocks
correspondingly slowed. Similarly, the clocks moving westward will have a
lesser speed with respect to the stars. Therefore their masses will decrease
and the clocks correspondingly sped up. [See 58, chapter 16, for a historical
summary of this experiment.]

Another
pertinent experiment is the Michelson-Gale experiment. In that experiment two
beams of light were sent in opposite directions around a large east-west
oriented rectangle back to their point of origin. The interference pattern
indicated that the optical lengths of the two paths were different. This was
interpreted to mean that the speed of the beam travelling east to west was
different from that travelling west to east. However, this too might be
interpreted relationally. Perhaps it was not the speed of the opposing beams
that differed but rather their frequencies and wavelengths. That would also
have an effect on the interference pattern. [See 58, chapter 14, for a
historical summary of this experiment.]

Bibliography

1.  Richard Mc Keon. The Basic Works of Aristotle. Random House, New York,
1941.

2.  Max Jammer. Concepts of Space: The History of Theories of Space in Physics, 3rd
edition. Dover, New York, 1993.

3.  Pierre Duhem. Medieval
Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds,
edited and translated by Robert Ariew. The University
of Chicago Press, Chicago, 1985.

4.  Steven E. Baldner
and William E. Carroll. Aquinas on Creation: Writings on the
“Sentences” of Peter Lombard 2.1.1. Pontifical Institute
of Medieval Studies, Toronto, 1997.

5.  Thomas Aquinas. Summa Theologica,
English Dominican Fathers translation. Benzinger, 1947.

6.  James A. Weisheipl,
O.P. Nature and Motion in the Middle Ages, edited by William E. Carroll.
The Catholic University Press, Washington, D.C., 1985.

7.  Titus Lucretius Carus.
The Way Things Are. Indiana University Press,
Bloomington, IN, 1968.

8.  Andre K. T. Assis. Relational Mechanics. Apeiron,
Montreal, 1999.

9.  James Clerk Maxwell. Matter and Motion. Dover, New York, 1991.

10. Ernst Mach. The Science of
Mechanics: A Critical and Historical Account of its Development,
sixth American edition. Open Court, LaSalle, IL, 1960.

11. Wolfgang Rindler.
Essential Relativity: Special, General, and Cosmological, revised second
edition. Springer-Verlag, New York, 1977.

12. Edith
Hamilton and Huntington Cairns, editors. The
Collected Dialogues of Plato. Princeton University
Press, Princeton, NJ, 1973.

13. Maria Boulding, O.S.B., translator. The
Confessions [of St. Augustine]. New
City Press, Hyde Park, NY, 1997.

14. Henry Bettenson, translator. St. Augustine: Concerning
the City of God against the Pagans. Penguin, New York,
1984.

15. Henry Denzinger.
The Sources of Catholic Dogma, thirtieth edition, translated by Roy. J. Deferrari. Loreto Publications, Fitzwilliam, NH, reprint of
1954 edition.

16. The Catholic Encyclopedia: Classic 1914 Edition, CD. New Advent, www.NewAdvent.org.

17. H. S. Thayer, editor. Newton’s
Philosophy of Nature: Selections From His Writings.
Hafner Press, New York, 1974.

18. Bernard Wuellner,
S.J. Dictionary of Scholastic Philosophy. Bruce Publishing Company,
Milwaukee, 1956.

19. Saint Augustine, On
Genesis: A Refutation of the Manichees; Unfinished
Literal Commentary on Genesis; The Literal Meaning of
Genesis (The Works of St. Augustine: A Translation for the 21st
Century, Part I, Volume 13). New City Press, Hyde Park,
NY, 2002.

20. Thomas C. Oden
and Andrew Louth, editors. Ancient
Commentary on Sacred Scripture, Old Testament, Vol. I, Genesis
1–11. InterVarsity Press, Downers    Grove, IL, 2001.

21. Edwin Arthur Burtt. The Metaphysical Foundations of
Modern Science. Doubleday, Garden City, NY, 1954.

22. H. A. Lorentz, A. Einstein,
H. Minkowski, and H. Weyl, The Principle of Relativity: A Collection of
Original Memoirs on the Special and General Theory of Relativity. Dover,
New York, 1952.

23. Sir Edmund Whittaker. A History of the Theories of Aether
and Electricity, Volumes I and II. Dover, New
York, 1989 (reprint of 1951 and 1953 editions bound as one).

24. J. S. Bell. Speakable
and Unspeakable in Quantum Mechanics. Cambridge University
Press, New York, 1987.

25. Gerardus D. Bouw. Geocentricity. Association for Biblical
Astronomy, Cleveland, OH, 1992.

26. James Paul Wesley. Selected Topics in Advanced Fundamental Physics. Benjamin Wesley, Publisher; Blumberg, West Germany, 1991.

27. D. Turner and R. Hazelett, editors. The Einstein Myth
and the Ives Papers. Hope Publishing House,
Pasadena, CA, 1979.

28. Julian B. Barbour. The
Discovery of Dynamics: A Study from a Machian Point
of View of the Discovery and the Structure of Dynamical Theories. Oxford
University Press, New York, 2001.

29. M. Sachs
and A. R. Roy, editors. Mach’s Principle and the Origin of Inertia.
Apeiron, Montreal, 2003.

30. Nizar
Hamdan. a) “Abandoning the Ideas of Length Contraction
and Time Dilation,” Galilean Electrodynamics 14:5, 83 (2003); b)
“Abandoning the Idea of Relativistic Length Contraction in 31. Relativistic
Electrodynamics,” Galilean Electrodynamics  15:4, 71 (2004); c)
“Newton’s Second Law is a Relativistic Law without Einstein’s Relativity,” Galilean
Electrodynamics 16:4, 71 (2005); d) “On the Interpretation of the Doppler
Effect in Special Relativity Theory,” Galilean Electrodynamics 17:2, 29
(2006); e) “On the Invariance of Maxwell’s Field Equations under Lorentz
Transformations,” Galilean Electrodynamics  17:6, 115 ( 2006).

31. E. A. Milne. Modern
Cosmology and the Christian Idea of God: Being the Edward Cadbury Lectures in
the University of Birmingham for 1950. Oxford University
Press, Oxford, UK, 1952.

32. Abraham Pais.
‘Subtle is the Lord …’: The Science and Life
of Albert Einstein. Oxford University Press New York,
1982.

33. Albert Einstein. Ideas and Opinions. Dell, New York, 1954.

34. Amitabha
Ghosh. Origin of Inertia: Extended Mach’s
Principle and Cosmological Consequences. Apeiron,
Montreal, 2000.

35. André Koch Torres Assis. Weber’s Electrodynamics. Kluwer Academic Publishers, Boston,
1994.

36. Alfred O’Rahilly.
Electromagnetic Theory: A Critical Examination of the Fundamentals (in
two volumes).  Dover, New York, 1965.

37. Peter Graneau and Neal Graneau. In the Grip of the Distant Universe. World Scientific Publishing, Hackensack, NJ, 2006.

38. Wolfgang K.
H. Panofsky and Melba Phillips. Classical Electricity and Magnetism,
second edition. Dover, New York, 2005.

39. Robert A. Sungenis and Robert J. Bennett. Galileo Was
Wrong: The Church Was Right, Volume I: The Scientific Case for Geocentrism. Catholic Apologetics International
Publishing, State Line, PA, 2007.

40. Carel
van der Togt. “Stellar Aberration and the Unjustified Denial of Ether,” Galilean
Electrodynamics 16: 4, 75 (2005).

41. Gennady Sokolov and Vitali Sokolov. a) “The Fizeau
Experiment with Moving Water: A New Explanation,” Galilean Electrodynamics,
18: Special Issues 1, 7 (2007); b) “A Classical Explanation of the Fizeau Experiment with Moving Water,” Galilean
Electrodynamics 22:6, 110 (2011).

42. Marcia Bartusiak.
Einstein’s Unfinished Symphony: Listening to the Sounds of Space-Time. Berkley Books, New York, 2000.

43. Peter Graneau and Neal Graneau. Newtonian Electrodynamics. World
Scientific Publishing, River Edge, NJ, 1996.

44. Thomas E. Phipps, Jr. Old
Physics for New: A Worldview Alternative to Einstein’s
Relativity Theory. Apeiron, Montreal, 2006.

45. James Clerk
Maxwell. A Treatise on Electricity and Magnetism, 2 Volumes.
Dover, New York, 1954.

46. James Clerk
Maxwell. A Dynamical Theory of the Electromagnetic
Field. Wipf and Stock Publishers, Eugene, OR, 1996.

47. P. W. Bridgman. The Logic of Modern Physics. The Macmillan Company,
New York, 1960.

48. Junichiro
Fukai. A Promenade Along
Electrodynamics. Vales Lake Publishing, LLC, Pueblo West, CO, 2003.

49. F. Hoyle
and J. V. Narlikar. Action
at a Distance in Physics and Cosmology. W. H. Freeman and Company, San
Francisco, 1974.

50. Richard. P. Feynman, Robert
B. Leighton, Matthew Sands. The Feynman Lectures on Physics, Volumes
I-III. Addison Wesley, Reading, MA, 1963.

51. Carver A. Mead. Collective
Electrodynamics: Quantum Foundations of Electromagnetism. The MIT Press, Cambridge, MA, 2000.

52. Ronald R. Hatch. Escape from Einstein. Kneat Company, Wilmington, CA,
1992.

53. Amir D. Aczel.
Entanglement: The Greatest Mystery in Physics. Four Walls Eight Windows,
New York, 2001.

54. James T. Cushing. Quantum
Mechanics: Historical Contingency and the Copenhagen Hegemony. The
University of Chicago Press, Chicago, 1994.

55. Max Jammer. Concepts of Mass. Dover, New York, 1997.

56. A. K. T. Assis.
a) “Deriving gravitation from magnetism” Canadian Journal
of Physics, 70:5, 330-340 (1992); b) “Gravitation as a fourth-order
electromagnetic effect,” Advanced Electromagnetic Foundations: Theory and
Applications, pp. 314-331. World Scientific,
Singapore, 1995.

57. William D. Walker. “Near-Field Electromagnetic Effects on Einstein’s Special
Relativity,” Galilean Electrodynamics 23:1, 13 (2012).

58. Tom Bethell,
Questioning Einstein: Is Relativity Necessary? Vales Lake Publishing,
LLC, Pueblo West, CO, 2009.

Additional
Resources

Henri Bortoft.
The Wholeness of Nature: Goethe’s Way toward a Science of Conscious
Participation in Nature. Lindisfarne Books, 1996.

Mary B. Hesse.
Forces and Fields; The Concept of Action at a
Distance in the History of Physics. Dover, NY, 2005.

Wolfgang Smith. The Wisdom of
Ancient Cosmology: Contemporary Science in Light of Tradition. The
Foundation for Traditional Studies, Oakton, VA, 2004

About the Author

Father Warkulwiz’s
first technical experience was in electronics. He studied radio and television
technology in high school. His first job out of high school was with Remington
Rand Univac, where he worked as an electrical draftsman on the first
transistorized computer. He went on to become an electronic designer and also
worked as an electronic technician at Univac. He continued his study of
electronics in the U.S. Naval Air Reserve, specializing in antisubmarine
warfare technology. He worked at General Electric Corporation as a mathematics
technician doing vibrations studies of reentry vehicles. He received a B.S. in
electronic physics from La Salle College. After graduation from college, he
worked as an electromagnetics physicist for General
Electric Corporation, where he studied the effects of electromagnetic pulse
radiation on semiconductor diodes.

Mr. Warkulwiz’s interest in electronics led him to physics. He
received a Ph.D. in physics from Temple University. At Temple he did
experimental work in holography, theoretical work in statistical mechanics, and
operated a planetarium. He did his dissertation research at the National Bureau
of Standards research reactor, where he gained experience in the fields of
precision thermodynamic measurements, cryogenics, vacuum
technology, critical phenomena in fluids, neutron diffraction and nuclear
instrumentation.

After receiving
his Ph.D., Dr. Warkulwiz went to work for the Central
Intelligence Agency as a physical scientist/intelligence officer, where he
specialized in ballistic missile systems. From there he went on to Magdalen College, NH (now The College of Saint Mary Magdalen) to teach science and mathematics in a “great
books” program. At Magdalen he conducted seminar
courses in classical mathematics, natural philosophy, astronomy, atomic
chemistry and physics, logic, and philosophical biology. He lectured on ancient
and medieval history, the history and nature of communism, and creationism vs.
the theory of evolution.

Dr. Warkulwiz then went to work for aerospace consultant firms.
He worked at Quest Research Corporation, where he did a study of techniques for
producing moving infrared images, and at Analytic Services Corporation, where
he specialized in space technology. While at Analytic Services, Dr. Warkulwiz heard the call to the priesthood.

In preparing for
the priesthood, Fr. Victor received an M.Div. from
Mount St. Mary’s Seminary and an M.A. in theology from Holy Apostles Seminary.
He taught courses in literature, mathematics and physics in the college
seminary at Holy Apostles and courses in philosophy and religion at the
Franciscan Friars of Mary Immaculate scholasticate.
He also conducted Bible and catechism classes in a summer program for youth.

Fr. Victor was
ordained a Roman Catholic priest in 1991. He is a member of the Missionary
Priests of the Blessed Sacrament and has helped hundreds of parishes in the
U.S. and elsewhere to start or maintain perpetual Eucharistic adoration. He was
named national director of the Apostolate for Perpetual Eucharist Adoration in
October 1998 and theological reviewer for the Kolbe Center for the Study of
Creation in 2001. He is profiled in the 2003 and 2004 editions of Who’s Who
in America.

A recent work of
the author is The Doctrines of Genesis 1-11: A Compendium and Defense of
Traditional Catholic Theology on Origins (first printing published by iUniverse, Inc., 2007, www.iuniverse.com; second printing
published by The John Paul II Institute of Christian Spirituality, 2009,
www.genesis1-11.org). He also edited St. Lawrence of Brindisi
on Creation and the Fall: A Verse by Verse Commentary
on Genesis 1-3 (The Kolbe Center for the Study of Creation, 2009,
www.kolbecenter.org).