*Jan Lacki, Uni Genève*

I have recently considered the theoretical activity of Arthur Schidlof, who ended up his career as first professor of mathematical physics at the University of Geneva in the early 1930s. Schidlof is a remarkable character to study, as a witness and practitioner of the new physics born out of the revolutions of the quanta and relativity, but also as one of the early theoretical physicists institutionalized in the western part of Switzerland ^{1}. When examining Schidlof’s trajectory and achievements, one cannot help comparing him to another Swiss physicist of highest caliber, Schidlof’s contemporary Walter Ritz. Both are representatives of the theoretical physics taking their autonomous stance inside the academic institutions, mirroring the general European trend of the times. On the personal side, both met a tragic end, Schidlof dying unexpectedly just when he succeeded to make recognize the value of theoretical physics in Geneva, and even more so Ritz who died of tuberculosis at the age of thirty-one, leaving everybody mourning such a young albeit already fully accomplished theoretician. But there are also telling differences: Schidlof, who originated from Austria, spent all his career in Geneva, while Swiss native Ritz left early Switzerland after his studies at the ETH Zürich. Moreover, and especially so, on many intellectual points, they were at odds: while Schidlof recognized early the promises of the new relativity and quanta physics, Ritz remained faithful to the classical scheme that he preferred to reform from inside sometimes with surprising boldness. Thus, in a sense, while Schidlof illustrates the physics community taking divorce with 19^{th} century physics, Ritz’s efforts are exemplary of what could be tried, to what extent, and at what price just to avoid Planck’s and Einstein’s messages. Indeed, in his activity, Ritz persisted to build classical models of the atom and confronted Einstein over relativity and more generally over the foundations of electrodynamics.

Today, the necessity of the departure from the classical scheme operated by quantum theory and relativity appears, with hindsight, as evident. But there were at the time brilliant minds who thought differently. Driven by the same dissatisfaction with received schemes, they chose a different road, in a sense equally revolutionary, so it is fair to say that they too broke with 19^{th} century classicism. Ritz stands high among them.

In the sequel, I want to examine more closely some aspects of Ritz physics, first as a tribute to his short career ^{2}, but also to illustrate the situation of theoretical physics at the beginning of the 20^{th} century, and to contrast the classical and revolutionary stands over the new challenges. It is an interesting exercise to go back to the issues as they presented at the time of Ritz and judge by ourselves, if only to appreciate better the intuition of those who decided to break with the classical scheme ^{3}.

Let me first recall some basic facts from Ritz’ biography ^{4}. He was born in Sion (VS) in 1878, son of a renowned painter. He entered the Zürich polytechnic ETH in 1897 and after three years left for Göttingen to obtain his Ph.D. working on series spectra under the guidance of the prominent Voldemar Voigt. In company of his friend Paul Ehrenfest, he went next to Leyden to benefit from Lorentz’s lectures. Ritz moved then to Bonn and then to Paris to work on infra-red spectra in Aimé Cotton’s laboratory. This was to be followed by a series of stays in various European physics centers, intertwined with visits in sanatoria where Ritz was trying to fight his worsening tuberculosis. When he lost hope for recovery, Ritz decided in 1906 to definitely invest his remaining forces into intense research and came back to Germany, first Tübingen and then Göttingen in 1908. There, he had just time to complete the requirements for his *habilitation*, as well as to publish his unorthodox views on electrodynamics of moving bodies. He died in July 1909 leaving a vivid impression among the best world physicists and a definite trace in history.

Let’s examine now how Ritz coped with the challenges offered by physics of his time. In his short theoretical activity, Ritz got involved with two topics then at the very forefront of research, atomic physics and electrodynamics. Let me start with the first.

Since the early days of spectroscopy in the second half of the 19^{th} century, the observed regularities of spectra were challenging the mechanical views on the structure of the atom, and especially so the Balmer formula (1885)

and its generalizations by Rydberg (1888), expressing the frequencies ν of the Hydrogen lines in terms of intriguing integer number expressions ^{5}. In Ritz’s time two approaches to understand spectra could be distinguished. On one hand, one could try to propose an explicit model of the atom where the conjunction of mechanic and electrodynamic principles applied to the postulated motion of charges inside the atom (the electrons) had to account for the frequencies of the spectral lines. On the other hand, one could, following a phenomenological approach, propose an ad hoc formal model (i.e. mostly mathematical) which could account for the observed regularities, but whose features were not meant to depict the “real” architecture of the atom (no descriptive intent). In his dissertation Ritz followed the spirit of the second approach: instead of trying to imagine an effective motion of the intra-atomic charges to explain the spectra (a dead-end for classical physics, as we well know by now), Ritz proposed, following his adviser’s taste, a mathematical model consisting of an involved partial differential equation for deformations w of a “vibrating square” of side *2a* carefully chosen so that its spectrum could indeed account for spectral formulas of the Balmer-Rydberg type:

where the parameters ρ and υ are related to Balmer’s *N* with *N* = π^{-2}a^{2}υρ^{-1/2}. By varying the boundary conditions, Ritz could actually obtain with the help of a sophisticated mathematical analysis even more general spectral formulas obtaining an unprecedented match with the known series ^{6}. Not being strictly bound, by the very essence of this approach, to the physical principles accepted at his times, Ritz could hence avoid, or at least delay the realization that the latter were incompatible with the observed phenomena and required a deep revision if one pursued to obtain a real physical model of the atom and not simply a mathematical simulacrum. Still, this mathematical-phenomenological approach constrained Ritz to some ad-hoc assumptions and high-brewed formal acrobatics to meet the requirements of phenomenology ^{7}. In a sense while fully conscious that his model was just a formal model, Ritz multiplied attempts at making it plausibly "physical", for instance by deriving his equation out of a variational principle.

It is then maybe no surprise that from 1907 on Ritz turned to a different, more realistically intended strategy. Instead of a purely formal model for the only sake of reproducing the spectral frequencies, Ritz imagined this time an atom governed by a magnetic mechanism ^{8}. His key idea was inspired by the result that in a magnetic field *H* a charge q rotates with the frequency proportional to the value of the field. It was then enough to imagine processes generating magnetic fields proportional to the Balmer-Rydberg ones, i.e. *H* ∝ 1/n^{2} - 1/m^{2} to obtain agreement. Ritz considered over time various magnetic devices to achieve such values, eventually favoring a configuration resulting from the presence of two magnetic poles in a special geometric configuration ^{9}. We do not need to examine them in detail; suffice it to say that although Ritz did not take his magnetic models at face value, he was still trying with their help to get closer to the atomic realia. An important byproduct of this investigations was that Ritz, pondering on his double-pole model, got convinced that all of the atomic spectral frequencies had to be expressed in terms of differences of "terms" (each term resulting from the influence of one pole) that could be combined in any way. The resulting combination principle (1908) is what makes him still remembered in physics textbooks.

In the short span of his life, Ritz found also time to propose his own views on the problems faced then by electrodynamics. In his last months, he even confronted his conceptions with Einstein’s, and their exchange is very instructive to anyone willing to penetrate deeply in the roots of our present physics. Let’s first shortly review the situation concerning electrodynamics, and especially the electrodynamics of moving bodies as understood in Ritz’s times. This was then a pressing theoretical issue giving rise to a heated debate among the tenors of world physics. It should first be reminded that the now so-familiar picture of charges interacting through e. m. fields goes back only to the very end of the 19^{th} century: although Maxwell’s theory was proposed in the early 1870s, it took many revisions, completions and theoretical efforts to arrive at our present electrodynamics ^{10}. In fact, Maxwell’s and his British fellows’ views had first to be accepted on the continent where the more traditional theories based on action-at-distance Coulomb-modified forces between charges were dominant: among them the avatars of Wilhelm Weber’s theory with its velocity and acceleration-dependent force were known best. Maxwell’s original theory comported as well, according to our present views, some oddities: in particular, it was purely "field-theoretic": charges were interpreted as special features of field configurations, and all electromagnetic phenomena amounted to (mechanical) disturbances of the ether. After Heinrich Hertz’s discovery of electromagnetic waves (1888), Maxwell’s views were vindicated and became prevalent on the continent as well but it took the most impressive theoretical work of Hendrik Lorentz to accommodate the physics of charges, in particular of the recently discovered electron (1897), with the Maxwellian ethereal fields. The resulting framework, called at the time the "electron theory", was making possible a most ambitious reconstruction of optical and electromagnetic phenomena on the basis of electrical charges interacting through electromagnetic processes in the ether. At the very turn of the century, an even more ambitious program was proposed: according to this so-called "electromagnetic worldview", all of physics was to be reduced to electrodynamics by interpreting the inertial mass as a mere effect of electromagnetic self-interaction of the charges forming matter.

In spite of his successes, Lorentz’ theory was not immune to criticism: As Henri Poincaré lucidly pointed out, Lorentz approach to the problem of formulating the field equations in frames moving with respect to the ether, and in particular his well-known expedients to explain the lack of effects resulting from such motions were, least to say, most contrived ^{11}. Although Poincaré was himself insisting on the validity of what he called the "relativity principle" according to which such effects were to be understood as *principally* unobservable, he, as most others at various degrees, was still adhering to the ether as a distinguished frame. This is when Einstein entered the stage proposing a radically different view on the problem. As we all know, he solved the riddle by postulating the constancy of the speed of light in all inertial frames which led him then to non-galilean kinematics, giving thus birth to relativity theory. It is maybe less known that Einstein’s views did not prevail from the start: besides being, at varying degree, considered as a mere, albeit elegant, rephrasing of Lorentz’ theory, they had to confront alternative theories based on radically different principles. Among these, and in the framework of the electromagnetic worldview, Max Abraham’s theory of the rigid spherical electron was the most considered. Yet, all the approaches were sharing a common core feature: since the revival and vindication of the wave theory of light by Fresnel in the second decade of 19^{th} century, the field approaches to electrodynamics were all conceiving the speed of propagation of electrodynamic phenomena as solely determined by the ethereal medium and independent of the velocity of the emitting source. This is however just what Ritz challenged in his approach to electrodynamics. Let’s see why.

Because of his familiarity with Göttingen physics and the benefit of Lorentz’s lectures, Ritz was very well acquainted with the contemporary electrodynamics and their foundational problems ^{12}. Almost in the last months of his life, he still found the force to launch a massive attack against the received views which were making of the Maxwell-Lorentz theory (and its various "interpretations" including Einstein’s) the unquestionable framework where to think of electromagnetic processes. In a substantial memoir, Ritz meticulously reviewed and criticized the foundations of electrodynamics of his time, revealing what he thought were its insufficiencies or even inconsistencies ^{13}. His aim, that he made explicit in the second part of his memoir, was a radical departure from the received views, where the field explanation of electromagnetic processes was flatly given up in favor of a theory postulating, *as its foundation*, a retarded force between charges.

To understand such a drastic move, one has first to examine some of Ritz’s criticisms of Maxwell-Lorentz theory. To start with, Ritz observed that in Maxwell-Lorentz electrodynamics, when examining the interaction between two moving charges, one had first to compute the field generated by one charge and then apply the resulting Lorentz force on the second. However, after all the steps required, the resulting formula is for an effective force depending solely on the positions and velocities of the charges (with appropriate retardation) where all reference to the intermediate field is gone. Ritz considered this as a clear indication that the Maxwell-Lorentz field was just a mathematical expedient enabling an elegant formulation of the computations but deprived of *physical reality*. While agreeing on the possible presentational advantages of the field formulation, Ritz insisted that the true physical reality of electromagnetic processes had to be viewed as consisting of two-body forces that one should postulate right *from the start*.

Another point that raised Ritz’s criticism was the justification of the use of retarded potentials. Relying on a most sophisticated analysis of the field equations, Ritz argued that the choice of retarded potentials was in no way derivable from the basic equations alone and had to be introduced ad hoc, showing the insufficiency of the theory. Indeed Ritz was dismissing Lorentz justification of the retarded potentials in terms of choice of appropriate boundary conditions supposedly justified by physical considerations: for him, such conditions were not always warranted. Worse, he showed that other choices were was leading to advanced solutions which were unacceptable because they depended absurdly on future configurations of sources (charge and current densities).

Ritz expressed his dissatisfaction with Maxwell-Lorentz electrodynamics using still other arguments such as those related to the ambiguity in the definition of the e. m. energy density present in the ether and also to the difficulty to secure the action-reaction principle between the latter and matter. I shall not report them here. Suffice it to say that to Ritz eyes, all these problems were symptomatic of the basic insufficiency of the field formulation which, while possibly computationally a handy fiction, had to be given up as far as foundations and true physical description were concerned. Rejecting the fields together with the ether, Ritz sketched instead, in a radical move, an alternative theory where charges were postulated *ab initio* to interact through a retarded force. The latter was conceptually shaped using as guideline the picture of charges *emitting light particles at constant speed*, responsible for the interaction. Since the velocity of these particles depended on that of the emitting charge, Ritz could preserve Galilean kinematics in opposition to Einstein who preferred to keep the equations of field electrodynamics and introduce instead relativized kinematics and relativistic transformations. By a careful tuning of his force expression (but also some ad hoc assumptions) Ritz could account for most of the phenomenology known then ^{14}.

The emissionist stance of Ritz theory should not be considered as indicating that Ritz was trying to rehabilitate for real the Newtonian corpuscular view on electromagnetic processes ^{15}. His writings show that he was just using emission theory as a framework where to think an alternative to the received electrodynamics of his time. Even if his theory was still in a preliminary stage, Ritz was convinced that it showed that alternative ways of thinking of electrodynamic processes were possible and well worth investigating. Ritz confronted his views with Einstein sometimes in 1909 with the ensuing result that none convinced the other ^{16}. In a resulting paper signed by both, they made their disagreement definitive ^{17}. One of the major points of their dispute was the issue of the retarded potentials. For Einstein, both retarded and advanced solutions to the field equations were, under specific conditions, acceptable and actually useful. For Ritz, only the retarded expressions were to be used ^{18}. This strong conviction had deep consequences on Ritz’s views of other physics problems of his time. For instance, he considered that the failure of electrodynamics to explain the black-body radiation, leading to the Rayleigh-Jeans law and the resulting ultraviolet catastrophe as shown by Lorentz, was due to the latter’s error ^{19}. Indeed, Lorentz used in his analysis of the electromagnetic modes inside the cavity where he examined the thermal equilibrium radiation, retarded as well as advanced solutions; to Ritz, this was precisely the source of the difficulty: if only retarded solutions were used, he speculated, the correct black-body law could be derived, making useless Planck’s quanta and hence showing their irreality. This might just be the reason why Ritz never seemed to consider quanta seriously, at least not to the extent to include them in his atomic models ^{20}.

Ritz had no time to make his theory more elaborate. He died complaining that no one, even in Göttingen, was granting his views sufficient care. His emissionist views were submitted to heavy criticism and experimental tests were later realized to show their inanity. Today, with considerable hindsight, we know the end of the story and how Einstein and Planck’s views shaped our contemporary physics. While few would today contest the reality of quanta or turn their back on field theory of elementary processes, it is interesting to know that the criticisms against Ritz’s conceptions were shown, since then, often wanting, if not simply incorrect. It is fair to say that if Ritz’s emission theory is false, it cannot be as easily dismissed as it was thought in Ritz’s times ^{21}. Be it as it may, Ritz remains in the history of physics as an admirable figure, with a highly original theoretical turn of mind and an impressive command of mathematical methods, making him one of the emblematic theoreticians of his time. In retrospect, if he refused to adhere to the ongoing physics revolutions, he was highly aware of what kind of fundamental problems were at stake, and already this lucidity ranks him among the best.

**References**

*OWR:* Walter Ritz, *Gesammelte Werke*. Walther Ritz, *Oeuvres*. Paris, 1911.

Carazza, Bruno and Robotti, Nadia, 2002, "Explaining Atomic Spectra within Classical Physics: 1897-1913", *Annals of Science*, vol. 59 (2002), 299 - 320.

Darrigol, Olivier, 2000, *Electrodynamics from Ampère to Einstein*, Oxford, 2000.

Forman, Paul, 1975, "Ritz, Walter," in *Dictionnary of Scientific Biographies*, New York, 1975, vol. 11, 475 - 481.

Fox, John, 1962 "Experimental evidence for the second postulate of special relativity", *American Journal of Physics*, vol. 30 (1962), 297 - 300.

Fox, John, 1965 "Evidence against emission theories", *American Journal of Physics*, vol. 33 (1965), 1 - 17.

Fritzius, Robert S., 1990, "The Ritz-Einstein Agreement to Disagree", *Physics Essays*, vol. 3 (1990), 371 - 374.

Heilbron, John, 1964, *A history of the problem of atomic structure from the discovery of the electron to the beginning of quantum mechanics*. PhD diss., UC-Berkeley, 1964.

Martinez, Alberto, 2004, "Ritz, Einstein, and the emission hypothesis", *Physics in Perspective*, vol. 6 (2004), 4 - 28.

Ritz, Walter

1903 "Zur Theorie der Serienspektren", *Annalen der Physik*, vol. 12 (1903), 264. Also in *OWR*, 1 – 77.

1907a "Sur l'origine des spectres en série", *Comptes rendus des séances de l’Académie des Sciences de Paris (CR)*, vol. 144 (1907), 834. Also in *OWR*, 91-94.

1907b "Sur l'origine des spectres en série", *CR*, vol. 145 (1907), 178. Also in *OWR*, 95-97.

1908a "Magnetische Atomfelder und Serienspektren“, *Annalen der Physik*, vol. 25 (1908), 660. Also in *OWR*, 98-136.

1908d "Recherches critiques sur l'électrodynamique générale", *Annales de chimie et de physique*, vol. 13 (1908), 145. Also in *OWR*, 317-426.

1908e "Recherches critiques sur les théories électrodynamiques de Cl. Maxwell et de H.-A. Lorentz", *Archives des sciences physiques et naturelles*, vol. 26 (1908), 209. Also in *OWR*, 427-446.

1908f, "Du rôle de l'éther en physique", *Rivista di scienza: Scientia*, vol. 3 (1908), 209, also in *OWR*, 447-461.

1909d "Über die Grundlagen der Elektrodynamik und die Theorie der schwarzen Strahlung", *Physikalische Zeitschrift*, vol. 9 (1908), 903. Also in *OWR*, 493-502.

Ritz, Walter, and Einstein, Albert, 1909, "Zum gegenwärtigen Stand des Strahlungsproblems", *Physikalische Zeitschrift*, vol. 10 (1909), 323.

Weiss, Pierre, 1911, "Préface," in *OWR*, 7 - 22.

^{1} See the May 2011 issue of the *SPS Communications*, p. 48.^{2} In 2009 an international meeting took place in Sion to commemorate Ritz’s untimely death and his contributions to physics and its mathematical methods. A mention of this meeting appeared in the November 2009 issue of the *SPS Communications*. The proceedings are to appear shortly (in *Vallesia*, fall 2011). In the sequel, I shall refer to the material presented then by the speakers. One can find all the papers of Ritz in the collected works, hereafter *OWR*, published by the Swiss Physical Society of which Ritz was member since its beginning in 1908.^{3} For a concise survey of (theoretical) physics in Ritz’s times, see my contribution to the Ritz 2009 meeting.^{4} For more detailed accounts see Forman 1975; Weiss 1911.^{5} On a sketch of the history of spectroscopy and the challenges it offered see my contribution to the Ritz 2009 meeting, *op. cit.*; On early atomic models, see Heilbron 1964, also Carazza and Robotti 2002 for the classical attempts.^{6} Ritz 1903. Ritz’s superior command of mathematics helped him all over his career and is definitely one of his hallmarks.^{7} For instance, simple expressions for the frequencies, as in the Balmer-Rydberg case, and not for their squares as would naturally result from a usual theory of vibrations; see Olivier Darrigol’s contribution to the 2009 Ritz meeting, *op. cit.*^{8} Ritz 1907ab.^{9} *Ibid*, also Ritz 1908a.^{10} The interested reader should refer for details to Olivier Darrigol’s impressive account of the development of electrodynamics in Darrigol 2000.^{11} Lorentz used space and time transformations and some approximations to show that the moving frame description (which he first obtained using "classical" Galilean transformations from the ether-fixed frame) was similar to the ether-fixed one. More precisely, he could prove that to order v/c the equations were the same as those of the ether frame, and hence to this order no e. m. effect could reveal the motion with respect to the ether. The next order (v/c)² obliged him, to explain the negative result of the Michelson-Morley experiments, to postulate what we today call the "Lorentz-Fitzgerald" contraction.^{12} One of his Göttingen senior colleagues was no other than Max Abraham.^{13} Ritz 1908 d, see also 1908 ef.^{14} Because of lack of space I refrain to report here the expression of this force which, to be properly understood requires too many kinematical preliminaries; see Ritz original discussion and Darrigols’ account in the Ritz 2009 meeting proceedings, *op. cit.*^{15} In his memoir, Ritz writes that he introduces the particles for the sake of giving a simple kinematical interpretation of the laws of propagation of e. m. action; see Ritz 1908d in *OWR*, p. 321, also p. 371 where he dubs the particles as evidently "fictitious". For this reason, one should even less look for any connection between Ritz’s light particles and Einstein’s light quanta: Ritz did not consider quanta seriously (see later).^{16} See Fritzius 1990 and Martinez 2004.^{17} Ritz and Einstein 1909.^{18} The whole business is conceptually and mathematically quite tricky and deserves a careful examination. See for instance the detailed discussion in Darrigol’s contribution to the Ritz 2009 meeting, *op. cit.*^{19} See Ritz 1909d, and the reference there to Lorentz’s result.^{20} See my contribution to Ritz’s 2009 meeting, *op. cit.*^{21} See Fox 1962 and 1965, also the detailed account in Darrigol’s contribution to the Ritz 2009 meeting, *op. cit.*, and Martinez 2004.

*[Released: September 2011]*