Communicative Rationality of the Maxwellian Revolution

According to a widespread opinion, Maxwellian electrodynamics was a stage of the Faraday programme development based on the field concept (see, for instance, Chalmers 2007 and references cited therein). The latter had provided prediction and verification of the electromagnetic waves phenomenon and finally superseded the Ampère–Weber research programme founded on the action at a distance concept.

Hence it is not surprising that even at the beginning of his electrodynamics studies, on May 1855, a post-graduate student at Cambridge writes a letter to his father, stressing the importance of studying the theories of “heavy German writers”:

As Maxwell developed his thoughts in preparation for the draft of “On Faraday’s lines of force”, he communicated to Thomson:

According to one of the modern historians,

Moreover, as Maxwell himself later pointed out referring to Ludwig Lorenz’s paper,

–All that Maxwell could initially oppose to the Ampère–Weber advances was that

However, in another part of the same paper Maxwell offers more profound arguments in favor of creating a new electromagnetic theory. He points out that Ampère–Weber electrodynamics is too mathematized and ignores the important connections between the phenomena; in particular it oversimplifies the relations between static and dynamic electricities:

Further, completing his theory creation on the basis of Lagrangian formalism, in his introduction to “A Dynamical Theory of Electromagnetic Field” (read December 8, 1864), Maxwell gives a sketch of action at a distance theory ending with a phrase:

And, at last, in his “Treatise on Electricity and Magnetism” Maxwell describes the creation of his system of equations in the following way:

At the same time in Hertz’s well-known paper “On the Electromagnetic Waves in Air and their Reflection” (1888) Maxwell’s theory is quoted only at the end after the following reservation

And in Hertz’s introduction to the first collected volume on “Electrical Waves” (1893) it is stated that

And at the end of this paper Hertz explains his methodological standpoint in the following way:

Maxwell’s friend and colleague Hermann Helmholtz had sought from the middle of 1860-s to reach consensus between the major directions in electromagnetic research of the second half of the nineteenth century, namely, Newton’s instantaneous action-at-a-distance concept as used by Weber, and Faraday’s contact action concept. By the time of Helmholtz’s first attempt of reconciliation (1870), the research programmes of Weber and Faraday had successfully incorporated all well-established empirical facts. Hence when trying to arrive at results similar to Maxwell’s without losing the elements of action at a distance, Helmholtz assumed that the electrostatic forces are constantly present as a field in space and that the change in the polarization or the displacement of the charges signaled the change in the electrostatic field (Helmholtz [1870], 1882). Under these assumptions, Helmholtz in his 1870 paper successfully derived generalized equations very similar to those of Maxwell and found that in a limited case they yield equations identical to Maxwell’s. Yet in addition to the ordinary transverse electromagnetic waves, Helmholtz discovered the existence of longitudinal electric waves which turned out to be instantaneous at the Maxwellian limit k \(=\) 0. To check the consequences from his theory in 1879 Helmholtz proposed a prize competition “To establish experimentally a relation between electromagnetic action [Helmholtz’s and not Maxwell’s notion!] and the polarization of dielectrics” and persuaded one of his pupils whose name was Heinrich Hertz to take part.

And finally in 1886–1888, at Karlsruhe, Hertz attempted to establish Helmholtz’s theory and finally the compatibility of the theories of Helmholtz and Maxwell in a new series of experiments. He designed his measurement procedures, taking into account Helmholtz’s ingenious separation of the total electric force into the electrostatic and electrodynamic parts to which different velocities of propagation were ascribed. In his own words

According to Coulomb’s law, the electrostatic component was thought to be proportional to the inverse square of the distance, whereas the electrodynamic part was only proportional to the inverse of the distance. In the usual theory of the Liènard-Wiechert potential it would correspond to decreasing rates of the bound-field, or longitudinal, component and the radiation field, or transverse component, respectively.

Hertz had planned a series of experiments and his efforts appeared to be fruitful. Yet it should be noted that the title of his 1888a paper “On the Finite Velocity of Propagation of Electromagnetic Action” is perhaps misleading nowadays, because the usual Maxwellian electrodynamics does not employ the Helmholtzian “action” terminology, nor does it split the total electric force into electrodynamic and electrostatic parts. But for Hertz’s contemporaries who supported the Helmholtz theory, the underlying meaning of the presented results was clear enough: Hertz’s experiments could qualitatively conclude about the finite propagation of the electromagnetic part, but could say nothing definite about the electrostatic component. Hence at the end of the paper one finds Hertz declaiming:

According to one of the modern action at a distance devotees (Smirnov-Rueda 2001), some of Hertz’s measurements tended towards the instantaneous nature of the electrostatic modes. Yet he was still not convinced of this instantaneity and preferred instead to be cautious:

Faraday’s apparatus of “lines of force” and strains in the field seemed both vague and clumsy to most of his contemporaries, especially when compared with the precise and elegant action-at-a-distance theories (Hunt 2005).

The immediate aim of the present paper is to answer the question “Why did Maxwell’s programme supersede the Ampère–Weber one?” Yet it appears that to answer it one has to take a further step in revealing the inter-theoretical context of Maxwellian electrodynamics genesis and development and to propose a rational reconstruction of the process that takes into account the (A)–(F) arguments. The reconstruction should provide a “theoretically progressive problemshift” relative to other “internal” reconstructions and argue that Maxwellian revolution is a more complex phenomenon than appears from the standpoints of some well-known scientific revolution conceptions (Kuhn 1977; Lakatos 1978).

Previous nineteenth century physics studies have oscillated between two extremes. On the one hand, in the more traditional vein, differences between research traditions were considered to be insignificant and communication unproblematic. On the other hand, in the more recent, post-Kuhnian, studies, differences between traditions are often taken to be so radical that communication is impossible among them.

This study originates from an intermediate picture. According to this, profound differences between the “field” and “action at a distance” research traditions existed at various levels, ranging from ontological commitments to epistemological beliefs. Yet these antagonistic traditions were able to communicate in the creative acts of such men of science as Thomson, Maxwell, Helmholtz, Hertz and Einstein. They communicated in the ways that permitted comparisons, adaptations and even cross-fertilizations of different traditions as well.

The intermediate picture stems from the critique of the insufficiencies of the Kuhnian and Lakatosian conceptions: they lack the mechanisms of the paradigms’ (or scientific research programmes’) interactions (Nugayev 1985a, b). It seems to me that this drawback derives from implicitly accepting from Max Weber a conception of rationality that is too narrow to cover all the stages of the advancement of science (Nugayev 2002). According to Weber, the rationalization of scientific (and, in the general case, of any) activity is an irreversible process of displacement of all other forms of social action—affective, traditional, and value-oriented rational—by goal-oriented rational action.

For instance, it was none other than Thomas Samuel Kuhn in “The Structure of Scientific Revolutions”, reflecting on progress in the history of science, who emphasized repeatedly that progress is made possible by the increasing precision of successive paradigms—by the consistent mathematization of scientific knowledge, expressed in the gradual displacement of qualitivism (in the chemistry of the transition period from Stahl to Lavoisier) by quantitavism. Indeed, from the point of view of theoretical ontologies, successive paradigms are incommensurable. The scientists who adhere to different paradigms “live” in different worlds, separated by irreversible ‘gestalt-switches’. But nonetheless they can be compared in their formal aspects and relations.

Imre Lakatos has proposed as the main criterion for preferring one scientific research programme over another the criterion of an empirically progressive shift in the problems tackled, which is possible as a rule in implementing a mathematically more perfect programme. One of his (and Elie Zahar’s) favorite examples was the victory of Einstein’s programme over Lorentz’s, which culminated in the creation of the extremely mathematized (for those times) general theory of relativity (Zahar 1989). And although, at first glance, the explanation of Lakatos and Zahar has to do with the discovery of new empirical facts that secured the victory of Einstein’s programme, the circumstance that these facts are also explained within competing nonmetric programmes brings to the forefront the chief merit of the general theory of relativity—its ‘mathematical beauty’, its capacity to describe phenomena in a single, coherent, and noncontradictory fashion.

In the Weberian approach all social actions are compared with a certain model or template—goal-oriented action, one of the most obvious examples of which is mathematical calculation. It is presupposed that the subject of social action has a perfectly clear idea of the goal of his actions, and that all his actions differ only in the degree of their adequacy as a means to the goal.

Such an approach is fully justified when we are examining the evolution of a single programme, paradigm, or theme in the history of science. In this case, a common goal of in individuals’ actions really is fixed in a generally accepted paradigm and the meaning of their deeds consists merely in specifying the paradigm in certain theories, which are reminiscent of sketches of a definite ideal or approximation to “perfection”. But the approach is of little or no practical use when it is necessary for us to examine the interaction of several themes, scientific research programmes, or paradigms, as is inevitable during fundamental shifts in the history of science (Nugayev 1999).

Max Weber’s concept of goal-oriented rationality, which covers cases of mathematization and increasing precision, seems to apply to basic paradigm change, but in fact it does not, because this concept presupposes that the goals remain fixed while only the means to them change. This is what happens in what T.S. Kuhn calls ‘normal science’—when constants are measured with increasing accuracy and data are accumulated. To justify paradigm shifts we need another concept of rationality proposed by Jurgen Habermas—rationality aimed at understanding and the coordination of actions—which may be called ‘communicative rationality’. This kind of rationality can account for paradigm shifts in which the new paradigm proves its superiority by reconciling or unifying under it more paradigms than its rival.

The Weberian understanding of social action is too narrow and one-sided (Habermas 1987). Social actions may differ from one another not only in the way they connect goals and means but also in the way they coordinate the subjects of social action; for example, depending on whether social actions are oriented toward success or toward the attainment of understanding. We call a success-oriented action instrumental if we consider it from the point of view of its correspondence to technical rules and assess the effectiveness of its impact on a complex of events and circumstances. On the other hand, we call a success-oriented action strategic if we consider it from the point of view of its correspondence to the rules of rational choice and assess the effectiveness of its influence on the decision of a rational opponent. But we call ‘communicative’ those social actions whose subjects are coordinated not by means of egocentric calculations of success, but by acts aimed at understanding. In communicative actions the agents are initially not oriented toward individual success. They pursue their individual goals subject to the condition that they can coordinate plans for their actions on the basis of definitions of situations that are shared by all (Habermas 1995).

The structure and content of communicative action can be better understood with the aid of the concepts of locutionary, illocutionary, and perlocutionary acts (Austin 1962). By means of locutionary acts the speaker expresses a state of affairs. By means of illocutionary acts the speaker performs an action by saying something; an action such as a promise, an order, or an oath. By means of perlocutionary acts the speaker acts on the listener. Thus the three kinds of act may be characterized in the following way: to say something; to act by saying something; to bring about an effect by talking about something. As a result, communicative action is a more general form of social action that encompasses all the three above-mentioned types.

Thus, communicative action is distinguished from action of all other kinds by its orientation not only toward success but toward achieving mutual understanding among various social subjects. In the particular case, the social subjects are various scientific communities of physicists associated with various paradigms. As Kuhn showed, each paradigm possesses at least three aspects. On the one hand, it is the most general picture (eine Weltanschauung) of a rational arrangement of Nature. On the other hand it is also the matrix of a scientific discipline, which characterizes the totality of the convictions, values, technical means, and so forth that unite specialists into a given scientific community. And only third, a paradigm is a generally recognized model or template for solving puzzles.

Hence the conflict of paradigms is first of all a conflict between various systems of values, various ways of solving puzzles, various ways of measuring and observing phenomena, various practices, and not only between various pictures of the world. The conflict can be eliminated by the genuine communicative action that is distinguished from action of all other kinds by the fact that it serves as a mechanism for the coordination of subjects’ plans of social action. Communicative action is a ‘complex of interactions’, a complex of subjects’ social actions.

To meet the above-mentioned critical comments, a “mature theory-change model” was proposed based on the “communicative rationality” concept (Nugayev 1999a). According to the epistemic model, the origins of scientific revolutions lie not in a clash of fundamental theories with “facts”, but of “old” fundamental theories with each other, leading to contradictions that can only be eliminated in a more sophisticated theory. The key role in theory change is played by the proponents of the old paradigms’ dialogue that leads to intercorrections, interpenetrations and cross-fertilizations of the participants’ views.

The very realization of reductionist and synthetic research programmes is brought about by the clash of mature theories which they are designed to eliminate. Having compared the heuristic potentials of the reductionist and the synthetic programmes, I favor the latter group since it has the following objective advantages (Nugayev 1999b). Firstly, synthetic programmes should provide a greater empirically-progressive shift of problems solved than the reductionist ones. Secondly, only these programmes can rationally explain the use of the so-called crossbred theoretical objects which spring from the coincident theories. For instance, if one considers the structure of two basic modern theories - quantum theory and general relativity - he finds that their global theoretical schemes arose from the unification of the crossbred theoretical ones (Nugayev 1987, 2000).

Every case of the meeting of different programmes leads to a situation when a domain of hybrid models occurs formed by simple conjunctions from the models of different research programmes. However, the hybrid models appear to be self-contradictory; and when this is realized, the crossbreeds from the basic objects of all the cross-theories are constructed. A new mature theory is created due to crossbred domain growth.

This is not to diminish the role of experiments in science. On the contrary, the epistemic model proposed seems to elaborate further the point of view stated in the current literature that both theorists and experimentalists have breaks in their respective traditions, but they are not typically simultaneous (Pickering 1985; Galison 1987). Theory development must have, to some extent, a life of its own (Stepin 2005). The development of two main cultures within science does not mean that the two do not speak to each other.

The epistemic model was illustrated with reference to physics in the early twentieth century, the three “old” theories in this case being Maxwellian electrodynamics, statistical mechanics and thermodynamics (Nugayev 1999a). As a result, the world of “old”, pre-Einsteinian physics appeared to be conceptually and socially fragmented. It had been split on at least 3 research traditions. Traditions organized around different groups of phenomena generated little support for one another. The practitioners of each theoretical tradition acknowledged the existence of the other but went their own separate ways. With the advent of relativity and quantum theory, the conceptual unification of worldviews was accompanied by a social unification of practice.

Thus, it is one of my basic aims to show that the above-mentioned remarks are especially appropriate for the genesis and development of Maxwellian electrodynamics. I’ll try to demonstrate that the Maxwellian programme superseded that of Ampère–Weber because it constantly communicated with it. The Maxwellian programme assimilated some of the propositions of the Ampère–Weber “hard core”, as well as some propositions of the Faraday and Young-Fresnel programmes. But the opposite proposition is not true. The Ampère–Weber programme did not assimilate the propositions of the Maxwellian programme.

Maxwell’s research programme superseded that of Ampère–Weber because it was a “synthetic” one (in the sense that was in more detail disclosed in Nugayev 1999b). It appeared, according to one of Maxwell’s (Kantian) philosophical gurus, one of “successive steps by which we gradually ascend in our speculative views to a higher and higher point of generality” (Whewell 1847, vol. 2, 74). Contrary to Maxwell’s, the Ampère–Weber programme was a reductionist one (see Nugayev 1999b for details) for it tried to reduce all the theoretical ontologies to one and the same ontology of “action at a distance”.

According to Boltzmann’s 1904 lectures, “It is certainly useful to set up Weber’s theory as a warning example for all times that we should always preserve the necessary mental flexibility” (quoted from Buchwald 1994, 261). Boltzmann constantly emphasized the need of a “plurality of approaches”, including both mathematical formalism and picture-based physical theories.

In particular, Maxwell’s programme was not only successful in assimilating the propositions of the Ampère–Weber hard core, combining them with Faraday’s “field” notions, as well as with those of Fresnel-Young optics; it was open for synthesis with other research traditions as well. For instance, as Heinrich Hertz put it,

This “abundance of the relations” was due to the fact that Maxwell put forward as a synthetic principle an idea, that differed radically from that of Ampère–Weber by its flexible and contra-ontological, strictly epistemological, Kantian character.

For Maxwell, ether was not the last building block of physical reality, from which all the fields and charges should be constructed. “Action at a distance”, “incompressible fluid”, “molecular vortices” were “contrived analogies” (Hon and Goldstein 2012) for Maxwell, capable only of directing the researcher to the “right” mathematical relations: “my aim has been to present the mathematical ideas to the mind in an embodied form” (Maxwell [1858/1890] 1952, p. 187). Maxwellian analogy is contrived and is not intended to illustrate anything in nature. Maxwell gave a new meaning to analogy that comes close to modeling in current usage:

Usually the defining feature of all analogies is supposed to be a bidirectional relation between the two domains for which an analogy is established. Neither domain is privileged over the other. Relation holds both ways: one can move from one domain to its analogue and vice versa.

The principle of usual (“physical”) analogy between theories in two different domains that are identical in nature came from William Thomson. But for Maxwell the methodology of analogy was only a tool. Contrary to Thomson, both mathematically identical systems need not exist in nature. In a pair of such systems one of them could be imaginary (“imaginary fluid”), and the other real (“physical”).

From the old-fashioned “presentationalist” point of view all the hydrodynamic models were doomed to failure, in their efforts to describe what could not be described in principle—things in themselves, the “nature” of electrical and magnetic phenomena. By contrast, Maxwell aimed his programme at finding empirically meaningful mathematical relations between the basic objects of electrodynamics, i.e. the creation of a concordant system of electromagnetic field equations.

Hence even Ludwig Boltzmann agreed with Hertz that Maxwell’s concepts of charge and current were “irremediably obscure”. In his lectures he adopted Hertz’s view that electricity was a “thing of thought, serving to picture the integrals of certain equations” (quoted from Buchwald 1994, 258).

However, all the afore-mentioned arguments do not mean that I agree with all the results of Margaret Morrison, Daniel Siegel and Olivier Darrigol. It seems to me that the main insufficiency of their studies is an underestimation of Maxwell’s own methodology, used by himself for his ambitious project of mechanics, electrodynamics and optics unification. In every domain of creativity (including “metaphysics”) Maxwell always took his own way; and he tried to teach his students in the same way too. It is clear from the following passage of his Marischal college speech:

As the author of the “Treatise on Electricity and Magnetism” himself put it in one of his letters, “I find I get fonder of metaphysics and less of calculations continually” (quoted from Campbell and Garnett 1882, 298). One has to remember Gustav Kirchhoff’s comment: “He is a genius, but one has to check his calculations”.

Maxwell’s behavior corresponded to William Whewell’s dictum:

It seems to me that one should take Ludwig Boltzmann’s comments on Maxwell’s works more literally. In his lectures on Maxwell’s theory as well as in his comments on Maxwell’s electromagnetic papers (that he had translated into German), the founder of statistical mechanics had pointed out that many of Maxwell’s works but especially his early electrical papers “were not properly understood”. It can be explained by the fact that these works “written according to the long-term plan” show that their author “was as mastermind in theory of knowledge as he was in the field of theoretical physics” (Boltzmann 1895). Maxwell was a great scientist as well as a great innovator of methodology (Hesse 1973; Achinstein 2010). Maxwell’s methodology, springing out from an intention to find a fruitful compromise between the extremes of Kantian relativism and Scottish “common sense realism”, was a necessary part of his ambitious design of unifying optics and electromagnetism.

Maxwell was not the first to unify optics and electromagnetism. Yet he did not like the way his predecessors had done it. Why? The following quotation helps to find the answer: the theories of action at a distance were too formal and abstract to grasp the connections between the electromagnetic phenomena.

His predecessors were Hans Christian Oersted (1777–1851), Andre-Marie Ampère (1775–1836), Wilhelm Weber (1804–1890), Michael Faraday (1791–1867) and William Thomson (1824–1907). Their names speak for themselves. Yet Maxwell’s Weltanschauung was characterized by an extraordinary high level of philosophical culture. A brilliant student at Edinburgh and Cambridge and a post-graduate at Cambridge, he was enchanted by the profound skepticism of David Hume, George Berkeley and Immanuel Kant in the lectures of Sir William Hamilton on mental philosophy at Edinburgh University.

For instance, in the 03.25.1854 letter Maxwell states that

Hamilton’s lectures, which were a prominent element in the Scottish university curriculum, “interested him greatly”. From the Class of Metaphysics his mind “gained many lasting impressions” (Lewis and Campbell 1882); the lectures of Hamilton made a strong impression on him, in “stimulating the love of speculation to which his mind was prone”.

Sir William Hamilton (1788–1856) was one of the outstanding representatives of Scottish “common sense philosophy”, an heir of Thomas Reid and James Stewart. Yet he stressed Kant’s proposition that all knowledge is relative; so we know nothing about things themselves except by their relationship to other things. He had stimulated a spirit of criticism in his pupils by insisting on the great importance of psychology as opposed to the older metaphysical method.

Hamilton’s “philosophy of the conditioned” surely had a strong Kantian flavor. Like Kant, he held that we can have knowledge only of “the relative manifestations of an existence, which in itself it is our highest wisdom to recognize as beyond the reach of philosophy”. But unlike Kant, he argued for the position of a “natural realism” in the Reidian tradition.

The Reverend Thomas Reid (1710–1796) directed his “An Inquiry into the Human Mind on the Principles of Common Sense” (1764) against Hume and Berkeley. It is here—he argued—that the awful “danger of the idealism” lies—in its reduction of reality to “particular perceptions”, essentially unconnected with each other. The unit of knowledge is not an isolated impression but a judgement; and in such a judgement is contained the reference both to a permanent subject and to a permanent world of thought, and, implied in these, such judgements, for example, as those of existence, substance, cause and effect. Such principles are not derived from sensations, but are “suggested” on occasion of sensation, in such a way as to constitute the necessary conditions of having perceptive experience at all.

The doctrine of relativity of knowledge has seemed to many—including John Stuart Mill—contradictory to his realism. But for Hamilton, the two are held together by a kind of intuitionism that emphasizes certain facts of consciousness that are both primitive and incomprehensible. They are, though constitutive of knowledge, “less forms of cognitions than of beliefs” (quoted from Audi 1999, 360).

The relativism or phenomenalism which Hamilton adopted from Kant and sought to engraft upon Scottish philosophy is absent from the original Scottish doctrine. Thus, denying Hume’s skepticism, Hamilton did his best to find a compromise between Kant’s relativism and Reid’s realism; and it was this that Maxwell set out as a basic tenet of his metaphysical programme on moving from Edinburgh to Cambridge:

The “Copernican revolution” in epistemology that had been initiated by Kant consisted in the idea that the world of usual every-day experience (or Husserl’s “lebenswelt”) had lost its dominating position in interpreting things that can be perceived by our senses. Kant had exchanged the world of common experience for the world of Galilean experimental and mathematical physics based on the idealizations of the “lebenswelt” phenomena. Hence truth became something not spontaneously revealing and disclosing itself but something that can be comprehended only by a special (“scientific”) method.

On the other hand, if truth is comprehended only in experience and we can grasp not “the things by themselves” but just the “phenomena”, it is necessary to reject the opportunity of reaching the absolute truth. Our sensory representation is by no means a representation of things “in themselves”, but only of the way in which they appear to us. Hence the “analogies of experience” are especially important in Kant’s epistemology (Kant [1783], 2002, 146–147).

In “The Critique of Pure Reason” Kant considers an important example:

Thus, even the example of the analogy of experience was taken by Kant from the domain of electromagnetism thus paving the way to Maxwell. The latter had pointed out many times that things we can measure directly, like mechanical force, are merely the outward manifestations of deeper processes, involving entities like electric field strength, which are beyond our power of visualization (see Mahon 2003).

A more detailed exposition of Maxwell’s research programme that he had followed through all his life is given in his truly philosophical works—in a speech “Are There Real Analogies in Nature?” read at the “Apostles” Cambridge club in 1856 (just after the publication of his most profound paper “On Faraday’s Lines of Force”, 1855–1856)—and in his trailblazing paper “Helmholtz” (1877).

The Cambridge speech is not a crude exposition of Kant’s epistemology but a tense discussion of Maxwell with “Kant in himself”. It is not accidental that the very heading of the speech contains a question and not an assertion: “Are There Real Analogies in Nature?”—Maxwell gives no definite and unambiguous answer—in full accordance with Kant’s antinomies that occur to Human Reason as attempts to overstep the Limits of Experience.

Certainly Maxwell’s thinking in terms of Kantian antinomies is not accidental. Following Hamilton’s traditions, Maxwell tries to find his own way between the Scylla of Kantian transcendentalism and the Charybdis of Scottish common sense realism.

That is the first lesson taught by Kantian epistemology—(I) “the principle of relational character of scientific truth”, stating that the relation is the most important thing to know. It should be pointed out that even the examples of the analogies are taken by Maxwell from Kant’s “Prolegomena”. Hence it is not surprising that the second principle—(II) “theory laidenness of observation”—is also extracted from Kant:

The importance of the principle (II) for Maxwell’s methodology cannot be overestimated. In nature all the phenomena are interconnected and merge into one another; all the differences in theoretical approaches are due to the fact that their authors focus on different facets and different levels of the phenomena investigated. Hence a theoretician’s task is to provide the “appropriate ideas” (Whewell’s term) to cover the various domains of experience. But where should he find them?—In experience, from immediate generalizations of the experimental data?—Another piece of Maxwell’s creativity—a part of his 1854 letter—makes it possible to take a glance at his thought laboratory:

Now it is clear where the “appropriate ideas” come from: they are not the slavish copies of things, but are the a priori forms by which a chaos of sensations is “brought to order”. According to Maxwell’s essay “Has everything beautiful in Art its original in Nature?” (Spring of 1854),

At first the “appropriate ideas” are vague and dim; however in the long run they are “grinded out” by knocking them with the “facts” and the other theories. However the theoretician’s task is not only to introduce and polish subtle notions “reflecting” the different facets of the phenomena under consideration, but also to unify the notions in synthesis.

The outlines and the stages of such a synthesis are described in Maxwell’s paper “Hermann Ludwig Ferdinand Helmholtz” that begins as follows:

This passage is not accidental for Maxwell. In other works Maxwell himself emphasized the value of the next principle (III) - “cross-fertilization of the sciences” (Maxwell 1890, vol. 2, 744) evoking the image of bees pollinating flowers (see Harman 2001 for further details).

The typical example of “the daubing of untempered mortar elimination” principle (IV) for Maxwell was

The first paper [1856–1858] is dedicated to elaboration of the “analogies” method borrowed from Kantian epistemology. The method rejects the “ontological” approaches looking for the “essences” of electrical and magnetic phenomena and proclaiming that “in reality” electricity and magnetism are “fields” and not “action at a distance” phenomena, or vice versa. Maxwell’s proposal is to consider Faraday’s lines of force as a kind of tubes filled with ideal incompressible fluid.

It is crucial for a Kantian that this incompressible poison has nothing to do with experimental reality. The constraints on the theory proposed consist in the demand that the mathematical constructs should not contradict each other. In all the other matters the physical analogies method admits an unlimited freedom of imagination. Even the conservation laws can be broken down!

Maxwell stresses the generality of the lines of force approach, for it can account for any kind of force. For instance, it does not exclude the force of action at a distance which varies inversely as the square of the distance, as force of gravity or as observed electric and magnetic phenomena. ”This is a significant remark which is probably intended to undermine possible objections that, in principle, the method excludes the dominant theory based on action at a distance” (Hon and Goldstein, 2023, 243).

And in the other parts of the paper Maxwell exhibits the ways by which the idea of incompressible fluid motion can be applied to the sciences of statical electricity, permanent magnetism, magnetism of induction, and uniform galvanic currents. The core element of his innovations consisted in constituting a language game with a “neutral language” for description and comparison of the consequences from the rival theories. Maxwell’s “neutral language” was not Carnap’s and Reichenbach’s “observation language” springing out from the “protokolsatze” generalizations. Maxwell is aware of the theory-laidenness of the observation data (“experimental laws already established, which have generally been expressed in the language of other hypotheses”—Maxwell [1861–1862/1890] 1952, 162). He clearly understands that every observation always carries the footprints of the theoretical language that helps to describe it. (“The daubing of untempered mortar”, as he will call them later in his “Helmholtz” paper).

In order to compare and to unite in a theoretical scheme lacking contradictions all the results of the different experiments carrying the footprints of different theoretical languages, it is necessary to construct an artificial theoretical language equally distant from the languages of theories under comparison. This language appeared to be the solid state mechanics (with hydrodynamics as its part). Maxwell’s ultimate aim was to rewrite all the known empirical and theoretical laws of electricity and magnetism using the neutral language and then to compare them in order to create a system without contradictions.

The final result of the 1856 paper was a system of equations lacking the “displacement current”. It was not accidental that one of the main drawbacks of the incompressible fluid theory consisted in the latter, apart from some simple cases, being unable to explain interrelations and interactions of electrical and magnetic fields and electric currents, as well as Faraday’s (1845) interconnection between optical and electromagnetic phenomena.

The Maxwellian programme’s ultimate goal was to reveal the connection “between electricity at rest and current electricity”, absent in the Ampère–Weber electrodynamics. Was it reached in 1856?—Certainly not. The connection between the current density j and the charge density \(\uprho \) was lacking in Maxwell’s initial 1856 scheme. It was to appear later, after the introduction of the “displacement current” and the finding out of its consequence—the continuity equation div \(\mathbf{j } + \partial \rho /\partial t = 0.\)

So, in 1861 the publication of Maxwell’s second paper [Maxwell 1861–1862] consisting of four parts begins. Its aim was to rederive the results of the Weber and Neumann theories on the basis of a new mechanical hypothesis containing the vortices of incompressible fluid.

Again and again he has to point out that

The theory started from the investigations of William Thomson, who showed that the connection between magnetism and electricity has the same mathematical form as that between certain parts of phenomena, of which one has a linear and the other a rotatory character. It is important that Thomson introduced the vortices theory in an incompressible fluid while studying Faraday’s experiments on the rotation of the plane of polarized light when transmitted along the lines of magnetic force. So, it was the effort to theoretically reconstruct the Faraday effect that provided the meeting between the theories of magnetism and optics.

In the second Maxwellian theory the magnetic field was represented now by a set of vortices in an incompressible fluid with the axes of rotation coinciding with the direction of magnetic field at a point. But now the neutral language role is played not by tube hydrodynamics but by a theory of stresses in the medium where the necessary relations among the forces are described by mathematicians with the help of entities that now are called tensors. The most general type of a tensor describing the most general type of stress consists of a combination of three principal pressures or tensions, in direction at right angles to each other. The tensor apparatus of solid state mechanics provided the creation of new neutral language “dialect”; it enabled one to calculate the force upon an element of the medium: \({\mathbf{F}} = {\mathbf{F}}_{\mathbf{1}} + {\mathbf{F}}_{\mathbf{2}}+ {\mathbf{F}}_{\mathbf{3} } + {\mathbf{F}}_{\mathbf{4} } + {\mathbf{F}}_{\mathbf{5}}\). The first term \({\mathbf{F}}_{1}\) refers to the force acting on magnetic poles; the second term \({\mathbf{F}}_{\mathbf{2}}\) refers to the action on bodies capable of magnetism by induction; the third \({\mathbf{F}}_{\mathbf{3} }\) and fourth \({\mathbf{F}}_{\mathbf{4}}\) terms refer to the force acting on electric currents; the fifth term \({\mathbf{F}}_{\mathbf{5} }\) refers to the effect of simple pressure that lacks an electromagnetic analogy.

But one of the most intricate problems of the vortices theory that puzzled even Daniel Bernoulli who had invented it in the XVIII-th century (Whittaker 1910) was: how can the rotation be transferred from one vortex to another so that “ vortices in a medium exist side by side, revolving in the same direction about parallel axes”?—The only conception that aided Maxwell in conceiving this kind of motion was that of the vortices being separated by a layer of particles called the “idle wheels”. Was it possible to connect these particles with electricity?

And in the second part of his 1861/1862 paper, “The Theory of Molecular Vortices applied to Electric Currents”, Maxwell comes up to the hardest problem of his research programme: what is “the physical connexion of these vortices with electric currents, while we are still in doubt as to the nature of electricity”. It is at this point where Maxwell has to admit the principal limits of pure mechanical theories and to borrow the elements of action at a distance theory! Or, using our methodological language (Nugayev 1999), we can conclude that Maxwell had to construct the “crossbred theoretical objects” from the languages of both cross-theories that combine the properties of quite different theoretical schemes.

According to Maxwell’s theory, an electric current is represented by the transference of the moveable particles interposed between the neighboring vortices. As a result,

On introducing such abstract objects as “electrical particles” and “electric current representing the motion of such particles” Maxwell had deviated significantly from Faraday’s lines of research. According to Michael Faraday, the electrical charges should be considered as created by the ends of lines of force; they lack an independent substantial existence. Correspondingly, in his genuine research programme the electric current had to be considered not as the motion of real particles but as an “energy axis”.

This is the nub of the British Field Programme: the fields are primary, and the particles are only secondary. Later on Maxwell’s eclecticism was followed and advanced by H.A. Lorentz’s in his dualistic theoretical scheme. Lorentz initiated it in an 1875 paper: “I shall start with instantaneous action at a distance: thus we will be able to found the theory on the most direct interpretation of observed facts” (quoted from Darrigol 2001, 323). So it was not a temporary retreat. Even after 1861 Maxwell introduced the notions of the Ampère–Weber atomism into his theories many times (Darrigol 2001).

Yet the results obtained were apparently insufficient; the theoretical derivation of Coulomb’s law was lacking. This was finally done in the third part of 1861–1862 paper “The Theory of Molecular Vortices applied to Statical Electricity”. It is important that the vortices theory contained too many ad hoc assumptions. And now we come closer to “Maxwell’s miracle”. It appeared that if one transposes the ether properties from optics to electromagnetism in the course of combining Fresnel optics with electromagnetic theory, at least some ad hoc suppositions could be eliminated. Indeed,

The peculiarity had a vital significance for Maxwell’s neutral language game:

Thus, the extrapolation of the molecular vortices theory on the electrostatic domain became possible due to the elasticity of the vortices that enabled the medium to maintain the elasticity waves. As a result,

The introduction of the displacement current was due to Maxwell’s efforts to link the equations relating to electrical current with that of electrostatics, which demanded the Ampère law modification for the sake of the introduction of a new term; the term had to describe the elasticity of the vortices medium. The driving force for the introduction of the displacement current came from Maxwell’s efforts to unify all the main empirical laws belonging not only to electricity and magnetism but to optics as well.

As a result Maxwell obtained his famous system of equations along with the continuity equation describing that electrical particles that transform the rotations from one vortex to another do not appear from nothing and cannot disappear to nowhere. But one could not state any final unification of optics and electromagnetism in 1861. It was possible to speak only of their reconciliation beginning, of the beginning of the “grinding” of rather different theoretical ontologies.

At last in 1864 Maxwell proposed a modified version of his 1861–1862 paper that avoided any special suppositions on the nature of molecular vortices. In his 1864 masterpiece Maxwell derives his equations from the abstract dynamics of Lagrange. The Lagrangian function L is found as the difference between the kinetic and potential energies of a system. From those he was able to derive the basic wave equation of electromagnetism without any special assumptions about molecular vortices or forces between electrical particles. Although the displacement current retained a prominent position in “A Dynamical Theory of Electromagnetic Field”, its role was rather different from the role it played in 1861–1862 paper. It was no longer associated with changes in positions of rolling particles; rather, Maxwell defined it simply as the motion of electricity, that is, in terms of a quantity of charge crossing a designated area.

However, despite Maxwell’s claim to provide deductions from (three) experimental facts, his account still required the postulation of a displacement current, something that could neither be verified by nor deduced from experiment (Morrison 2000; Darrigol 2001).

As a result he sums up the main merits of the 1864 paper in the letter to C. Hockin, September 7th, 1864:

Maxwell’s creativity ends finally with “A Treatise on Electricity and Magnetism” conceived as an encyclopedia of the electrical and magnetic effects. In his “Treatise” Maxwell goes further in purifying his deductions from the model remnants and in strengthening the Lagrangian approach. In the final chapter XX, dedicated to the electromagnetic theory of light, the basic argument in defense of electromagnetic waves is posited:

Yet it is important that in his “Treatise” Maxwell was faced with the same problem as in 1864 paper: the problem of the application of a Lagrangian mathematical formalism to the case of the electromagnetic field. Maxwell himself used a fitting comparison with a belfry. He aimed to develop a Lagrangian formulation of electromagnetism in which the ether mechanism would be the analogue of the mechanism in the belfry, whilst the positions and velocities of the ropes would have their analogues in measurable charge and current distributions serving to determine the electromagnetic energy.

However on twenty pages of his “Treatise’ chapter Maxwell gave a detailed Lagrangian treatment for interacting closed conduction currents only. And when, two chapters later, he came to build on his Lagrangian formulation to formulate the general equations of his electromagnetic theory, he simply added the displacement to the conduction current “by hands” to give the total current (see Chalmers 2001 for details). The step was justified as follows:

But this move by Maxwell in fact undermined the major attraction of his Lagrangian method. The first direct experimental evidence for the existence of displacement currents emerged only with Hertz’s experiments culminating in the production of radio waves in 1888. As always, the Lagrangian formulations were retroactive attempts to accommodate results obtained by other means.

But let me return to Maxwell’s synthetic programme. Eventually Maxwell found that his elastic vortex medium would propagate waves whose velocity, calculated from electromagnetic constants, was that of light. Yet he said nothing about how electromagnetic waves might be generated, nor did he attempt to derive the laws governing reflection and refraction (Sengupta and Tapan 2003). Hence the task of extracting a cogent and empirically sound theory from the “Treatise” and of casting it into a form in which it could command general assent fell to others. Later they were called “the Maxwellians”: George Francis Fitzgerald (1851–1901), Sir Oliver Lodge (1851–1940) and Oliver Heaviside (1850–1925).

Of their advances one should mention those discussed at the Bath meeting where the Maxwellians made it clear that Maxwell’s displacement current was not just a dispensable appendage to the theory, but its keystone: remove it, and the whole theoretical structure would collapse. Without displacement currents, electromagnetic waves could not exist.

Besides that, Oliver Heaviside had found that the ordinary radial electric field of a point charge is compressed along its line of motion by a factor of \(\root 2 \of {1-v^{2}}/c^{2}\). Heaviside’s formula for the field around a moving charge showed (especially for Fitzgerald) that electromagnetic forces would be altered by just the factor involving \(v^{2}/c^{2}\) needed to explain the Michelson and Morley 1881–1889 experiment’s negative results.

But the most important step in the consequent unification of optics and electromagnetism, i.e. in the extrapolation of electrodynamics principles onto optical phenomena, was taken in 1879 by Fitzgerald. He first broached the possibility of combining Maxwell’s theory with James MacCullagh’s. In 1839 MacCullagh had devised a Hamiltonian formulation of wave optics which yielded equations describing the main optical phenomena, including reflection, refraction and double refraction. Fitzgerald, by drawing correspondences between the terms in MacCullagh’s theory and electromagnetic terms, was able, in 1879, to translate MacCullagh’s theory into an electromagnetic theory of light. It should be noted, however, that MacCullagh’s theory suffered from serious mechanical difficulties, pointed out in 1862 by Gabriel Stokes. Stokes showed that MacCullagh’s theory implied attributing elastic properties to the ether which were quite unlike those of any known substances. The merger not only resuscitated MacCullagh’s theory but also extended Maxwell’s own theory in important new directions, yielding as one of its first fruits a prize that had eluded Maxwell himself: an electromagnetic theory of the reflection and refraction of light.

Indeed, in an 1873 review of Fitzgerald’s paper, Maxwell described his own treatment of the Faraday 1845 effect as a “hybrid” in which he had combined his electromagnetic theory of light with elements of an elastic solid theory. He had treated light waves as actual motions of the ether and had traced how these would disturb the spinning of the magnetic vortices in such a way as to cause the plane of polarization of the light to rotate.

In his review Maxwell had found this detour into a “hybrid theory”, in which electrical and mechanical actions were combined, the least satisfactory part of his own explanation of the Faraday effect. And Fitzgerald’s 1879 paper brought out, more clearly than before, the fundamental incompatibility between Maxwell’s theory and an elastic ether. Fitzgerald had shown that Maxwell’s theory was mathematically equivalent to MacCullagh’s, while Stokes had shown in 1862 that MacCullagh’s theory, considered as an elastic solid theory, was untenable.

Thus, in his encyclopedia on the phenomena of electricity and magnetism Maxwell sums up his results. His Copernican deeds consisted in combining arguments for electromagnetic and luminiferous ethers’ identification and constructing the crossbred theory with displacement current that was capable of electromagnetism and optics unification.

Nicolas Copernicus had pioneered in considering the Earth as an ordinary planet orbiting the Sun; hence he had created a crossbred theoretical object capable of extrapolating the mathematical principles from divine phenomena on the mundane ones. On the other hand, through the same crossbred object the physical principles were extrapolated from mundane objects on the skies (Nugayev 2013). Similarly, James Maxwell had constructed a crossbred object—the displacement current - and was able to extrapolate the electromagnetic principles on the optical phenomena, and vice versa. Introducing a kind of “complementarity principle” in the XXIII chapter called “Theories of Action at a Distance”, Maxwell describes the difference between field and corpuscular approaches in the following way:

Thus, we are ignorant of what really is moving between magnets and conductors, but if we decide to describe it we have no other “appropriate” images except “waves” and “particles”. Maxwell’s approach contains the seeds of the modern one. As Richard Feynman has put it,

And the lines of force represent a “crude way of describing field” only. They have some merits since they give a visual representation, yet they have their own drawbacks too. For instance when one talks on E and B lines of force one should not exaggerate the reality of their existence. The lines may disappear when one wants to look at them in another frame of reference.

Due to its Kantian background, the development of Maxwell’s programme would be especially to be fruitful in Germany. And it was. Maxwell’s efforts to find a reasonable compromise between the three research programmes (that of Young-Fresnel, Faraday and Ampère–Weber) were picked up by Hermann Helmholtz in his “On the equations of motion of electricity in conducting media at rest” published in 1870. In Helmholtz’s paradigm charges and currents were considered as the sources of electrical and magnetic fields. It led directly to H.A. Lorentz’s dualistic picture of the field equations and the equations of motion in his 1892–1900 papers. Furthermore it was Hermann Helmholtz who convinced the Berlin Academy of Science to set up a special prize for the experimental confirmation of Maxwell’s theory. And it was Helmholtz’s star pupil - Heinrich Hertz - who got the prize in 1888. From two possible explanations of his experiments (see Smirnov-Rueda, 2010, for details) Hertz had chosen the simplest one:

It seems to me that it was the attempt to justify the rationality of choosing the simplest explanation that forced Heinrich Hertz after 1888 to give up his electromagnetic experiments, fruitful both from heuristic and technological vistas, and to devote the last three years of his short life to his extremely ambitious project of rebuilding classical mechanics. As he put it clear in his “Principles of Mechanics”,

Hertz’s apparent aim was to eliminate the “force” concept. But his more remote aim consisted in reconciling classical mechanics foundations with positivistic Zeitgeist :

It is important that the methodological principles for the rebuilding of classical mechanics were to be found by Hertz in Kantian epistemology; even before he met Helmholtz, Hertz had attended in Dresden a course on Kantian philosophy (Hertz 1899).

But his Kantian background manifested itself not only in the epistemological issues. According to Jed Z. Buchwald, Hertz had, already in 1884, proposed a version of Maxwell’s equations that was free of the ether notion completely.

And, what is more important, quite unlike in Maxwellian field theory, in Hertz’s theoretical scheme the source continued to exist as an entity “in and of itself”. In Hertz’s diagram the material object remains unknown, whereas the inferred field is known. This diagrammatic inversion encapsulates the originality of Hertz’s physics. It was because Hertz ignored the physical character of the object that produced his radiation—“because he boxed it in with a mental quarantine against asking questions against it—he was able to make progress where his British contemporaries had not been able to do so” (Buchwald 1998, 272).

Being a pupil of Helmholtz, Hertz learned to watch for novel interactions between laboratory objects without worrying overmuch about the hidden processes that account for the object’s effect-producing power.

Thus the nature of electromagnetic waves appeared to Hertz as a kind of “thing in itself” that admits a variety of interpretations. A researcher chooses the version that is the simplest one to work with. The most important thing is the equations depicting the relations between the objects under investigation.

And it was Albert Einstein who picked up the problem after Maxwell, Helmholtz, Hertz and Lorentz. In his trailblazing 1905b paper “Zur Elektrodynamik bewegter Körper” he proposed a theory based on the “relativity principle” stating that all the laws of nature should be the same in all inertial frames of reference. It followed from this theory, as Richard Feynman has put it, that electricity and magnetism are not independent entities and should always be considered as a whole, as a single and complete electromagnetic field. Although in the static case the Maxwell equations split into two parts, one for electricity and the other for magnetism without any visible connections between the fields, in nature there is a deep interconnection between the fields that follows from the relativity principle.

In particular, when one considers relative motion of a charged particle and a wire, she gets one and the same result that does not depend on whether she considers the particle’s movement in the wire’s system at rest or in the reference frame of the particle itself. In the first case the force is purely “magnetic” and in the second—it is purely “electric” one.

In his “Zur Elektrodynamik bewegter Körper” Einstein had demonstrated that electrical and magnetic forces are different parts of the same whole—the electromagnetic interaction. The separation of this interaction into the electric and the magnetic components is a conventional one and depends on the system of reference used for the interaction description. Hence “magnetism is a pure relativistic effect” (Feynman). For instance, in the plane electromagnetic wave that moves with a speed of light there is the constant pumping of the magnetic energy into the electric one and vice versa.

However the problem of electrical and magnetic fields’ complementarity appeared to be connected with a deeper one—with the problem of the wave and corpuscular descriptions of the electromagnetic phenomena. Indeed the 1905b relativity paper begins with the description of “deep asymmetry” in the electromagnetic induction description. Experience tells us that the induction current caused in the conductor by the motion of the magnet depends only on the relative motion of the conductor and the magnet. However the Maxwell-Lorentz theory provides us with two qualitatively different descriptions of the effect that mystically lead to one and the same result. In the first case, an electric field with a certain energy density is responsible for the induced current. In the second case, there is no electric field, and the induction current is ascribed to an electromotive force with no corresponding field energy.

In order to understand the reasons for the creation of special relativity it is quite important to take into account that Albert Einstein was by no means the first to note asymmetries in the theoretical representation of the induction phenomenon. In 1885 the asymmetry was described by Oliver Heaviside and independently by a telegraphic engineer Tolver Preston, in 1894—by Herman Föppl, and in 1898—by Wilhelm Wien himself (see Darrigol 2001, 377 for details). Hence the pertinent question is not how Einstein became aware of asymmetries, but what made them so intolerable to him.

Of course, now we have reminiscences of the author of special relativity about his imaginary travels on the light rays at the age of 16 which would lead to the Relativity Principle. But the documents of history of science do not confirm them. On the contrary, Einstein’s first scientific paper written when he was 16 as a letter to his uncle (found and published in “Physikalische Blätter”, August 9, 1971 by Jagdish Mehra) tells us something different. In this paper Einstein takes ether as an ordinary element of physical reality just the same as electric and magnetic fields. The paper was entitled “On the Investigation of the State of the Ether in the Magnetic Field” and was written in 1895, before Einstein entered the Aargau Cantonal School. The main problem of Einstein’s first scientific survey consisted in how “three components of elasticity influence ether wave velocity”.

Even during the second course of Eidgenossiche Technische Hochschule he believed in the existence of ether and intended to investigate the motion of the Earth through ether experimentally. He thought of constructing several measuring devices in connection with it (Feuer 1974). In the Kyoto Lecture he described one of the devices consisting of a system of thermocouples (Ono 1983). Another proposal, based on the interference phenomena, was mentioned in Einstein’s 1901 letter to Marcel Grossman (Kostro 1988).

One knows for sure that Einstein was working on a “capital memoir” on the electrodynamics of moving bodies at the end of 1901. Then he stopped doing that and returned to his memoir only in 1905. What happened during the interval, and why had Einstein, being initially an adherent of the ether, became its strong enemy?

Was it the Relativity Principle, stating relativity of time and space?—Yet the principle was elaborated by Henri Poincaré and it did not prevent the latter from believing in ether as in the medium necessary for electromagnetic disturbances propagation. For instance, in 1902 Henri Poincaré wrote that

I think that the key answer to the questions posed lies in other works of Albert Einstein (see Nugayev 1985b for details). It was Einstein himself who had revealed another asymmetry - of a deeper nature—in another 1905a paper “Über eine die Erzeugung und verwandlung des Lichtes betreffenden hewristischen Lesictpunkt” (“On an heuristical point of view concerning the processes of emission and transformation of light”) that was published in the same journal “Annalen der Physik” but three months before the relativity paper.

Although one often reads the statement that in the 1905a paper Einstein was concerned with an explanation of the photoelectric effect, a study of the paper reveals that this was not the case. The measurements of the effect at that time were not sufficiently accurate to point without any doubt to a violation of classical behavior (Ter Haar 1967). Einstein was worried not so much by the evidence dealing with the photoeffect, and appealed to fluorescence, photoelectricity and photoionization data only as indirect evidence in favor of his thesis. Rather, Einstein was concerned mostly with a contradiction between mechanics and electrodynamics. Hirosige (1976) correctly attributed Einstein’s sensitivity to the inconsistencies between mechanics and electrodynamics to the influence of Ernst Mach, whose writings supposedly freed the special relativity creator from the mechanistic worldview. Einstein could therefore freely juxtapose mechanics, thermodynamics and electrodynamics without reducing one to the others. Of course the theory of relativity arose not from philosophical reflections only, but from Einstein’s own daily considerations about current physical problems and from his concrete physical investigations.

Yet the seeds of Ernst Mach’s influence fell on already prepared Kantian soil (Palmquist 2011). Einstein first read Kant at the age of thirteen and again at the age of sixteen (Howard 1994, 49). Later on Einstein was immersed in Kant again and again. For instance, in 1918 he wrote to Max Born:

And, what is more important, Einstein was exposed to Kantian teachings in the year 1897, when he had enrolled in lectures on Kant’s philosophy by August Stadler, a neo-Kantian of the Marburg school (Einstein 1987, 45–50).

However, the most important Kantian notion for understanding Einstein’s epistemological framework is Kant’s idea of the systematic Unity of Nature (Beller 2000; Morrison 2000). This unity, for Kant, is not an ontological principle at all. It is meaningless to ask whether Mother Nature in fact possesses such a unity or not. The idea of unity has epistemological importance. Systematic unity of nature provides a criterion of the validity for scientific hypothesis that complements the empirical idea of confirmation. From the infinity of different uniformities only those can be regarded as having law-like necessity that can be fitted into a unified, systematized general system.

Correspondingly,

But from the fact that the last quotation belongs to 1949 one should not deduce, as is widely acknowledged, that an urge for unification guided Einstein’s scientific activity from his general relativity creation onwards. Too hastily, the young Einstein is presented in the literature not as a unifier but rather as a follower of the empiricist approach of Ernst Mach.

Yet it was the holistic approach that allowed Einstein as early as 1906 to disregard the results of Kaufmann’s “crucial” experiments that contradicted “the Lorentz-Einstein theory”. As Einstein put it, the rival theories

Thus Einstein’s attraction in his 1905a paper to the subject of the theory of quanta was caused by its unifying possibilities. Hence he begins the paper with the heart of what troubled him most—duality in the foundations of physics that was felt most sharply in Lorentz’s Electron Theory. Look at the beginning of his 1905a paper:

What does this difference consist in?

But this difference can give rise to a situation where

Hence

And in the first part of his 1905a Einstein discloses that the joint application of the mechanical and electrodynamical “theoretical pictures” for the description of black-body radiation leads not only to contradiction with experiment (his paper did not cite the results of Lummer & Pringsheim and Rubens & Curlbaum), but to paradox that cannot be eliminated by usual methods. To demonstrate it Einstein uses gedankenexperiment with both theories. He considers a cavity containing free electromagnetic field, gas molecules and Hertz’s resonators. As a result one can conclude that joint application of mechanics and electrodynamics leads unavoidably to the Raleigh-Jeans law for the energy density of black-body radiation. But

Thus, Einstein pioneered in demonstrating how the cross-contradiction of mechanics and electrodynamics led to the “ultra-violet catastrophe”. The basic result of the 1905a paper consisted in that

Four years later (1909), in Salzburg Einstein made a report at the 81-st meeting of German Natural Scientists and Physicians under the heading “On the Development of our Views on the Nature and Structure of Radiation”; it represented the first effort to analyze his works as a whole. And it was one of the first public reports of the STR author dedicated to explanation of its foundations:

So, they were the foundations of Lorentz’s dualistic programme that were correctly described by the following Einstein’s words:

Thus, the dualism between the wave and corpuscular descriptions that was at the heart of Maxwell’s theory received an adequate treatment only during the first half of the twentieth century. But this is another story.

To sum up, one of the aims of my paper is to answer the question “Why did Maxwell’s programme supersede the Ampère–Weber one?” I think that the Maxwellian programme superseded that of Ampère–Weber because it constantly and fruitfully communicated with it. The Maxwellian programme assimilated some of the propositions of the Ampère–Weber “hard core”, as well as some propositions of the Faraday and Young-Fresnel programmes. But the opposite is not true. The Ampère–Weber programme did not assimilate the propositions of the Maxwellian programme.

Hence, Maxwell’s research programme superseded that of Ampère–Weber because it was a “synthetic” one. Maxwell put forward as a synthetic principle an idea, that radically differed from that of Ampère–Weber by its open, flexible and contra-ontological, strictly epistemological, Kantian character. For Maxwell, ether was not the last building block of physical reality, from which all the charges and fields should be constructed. “Action at a distance”, “incompressible fluid”, “molecular vortices” were contrived analogies for Maxwell, capable only of directing the researcher at the “right” mathematical relations. Contrary to Maxwell’s, the Ampère–Weber programme was a reductionist one for it tried to reduce all the theoretical ontologies to one and the same ontology of “action at a distance”.

Finally progressive scientific change under consideration can be described in terms of Habermas’s communicative rationality encouraging the establishment of mutual understanding between the various scientific communities. Maxwell’s programme constituted a progressive step in respect to its rivals because it constituted a basis of communication and interpenetration between the paradigms of 19th century physics.

It is a pleasure to thank the reviewers for helpful comments.