The Emission Theory of Walter Ritz

In 1908 the young Swiss physicist Walter Ritz wrote a critique of the (then) prevalent theories of electrodynamics, referring primarily to the theory developed by Lorentz, Poincare, and (especially) Einstein, of which he disapproved. The paper was “Recherches critiques sur l'Électrodynamique Générale”, Annales de Chimie et de Physique, Vol. 13,  p. 145, 1908. In the second part of this paper Ritz outlined an idea that he hoped might form the basis of an alternative theory. He died at the age of 31, shortly after this paper appeared, so he did not have the chance to develop the idea. This has led some to romanticize Ritz, imagining that his paper contains a great insight that would obviate the relativistic theories of Lorentz and Einstein, and restore the primacy of Galilean relativity and Newtonian physics… if only Ritz had not tragically died so young.

Before discussing Ritz’s idea, we will briefly review his stated reasons for disapproving of the theory of Lorentz, et al. (It’s interesting that Ritz mostly avoided mentioning his former class mate Einstein by name, even though the main target of Ritz’s criticisms is evidently the aspects of relativity theory that were highlighted by Einstein.) Ritz makes seven main criticisms, the first of which is

l) From a strictly logical point of view, the electric and magnetic forces, which appear to play such a fundamental role in the theory, are notions that we can completely eliminate. They entail only the relations of space and time. We thus return to the old elementary actions, with the sole difference that they are no longer instantaneous.

This is not a novel observation. Ritz is simply pointing out the well-known fact that a field theory can also be formulated as a distant-action theory, provided we understand that the potentials are retarded rather than instantaneous. The Lienard-Wiechert potentials give a workable representation of electromagnetic interactions. In this view, the field variables representing the electric and magnetic forces are just derived variables. Whether we regard the retarded potentials or the field variables as primary is a matter of convention. This, in itself, is not actually a criticism of the theory of Lorentz, et al.  There are, or course, issues involving back reaction that present special challenges to distant-action theories, but Ritz didn’t address these.

2) The theory permits an infinite number of solutions, each satisfying all the conditions, but incompatible with experience and even leading (for example) to perpetual motion. To exclude these [unrealistic] solutions we must hypothesize formulas for retarded potentials. These formulas introduce irreversibility into electrodynamics whereas the general equations exhibit reversibility. I show that, contrary to accepted ideas, they can't be deduced from a proper specialization of the initial state. They constitute a new hypothesis, rendering the partial differential equations useless. To clarify this hypothesis it is necessary to distinguish the elementary actions; thereby renouncing one of Maxwell's fundamental ideas.

This “criticism” was fundamental for Ritz. He had an informal published “debate” with Einstein on this subject in 1909. Ritz’s animating idea was that Maxwell’s equations are temporally symmetrical, i.e., they are compatible with advanced as well as retarded waves, and yet we observe only retarded waves. Ritz argued that this reveals a fundamental flaw in Maxwell’s equations. To remedy this flaw, rather than beginning with Maxwell’s differential equations and then arbitrarily (as Ritz saw it) specializing to the retarded potentials, ignoring the advanced potentials without justification, we should simply take the retarded potential integrals as fundamental, and dispense with Maxwell’s equations. Since we have discussed this elsewhere, we won’t dwell on this point here.

3) The notion of localization of energy in the ether is indeterminate and allows several simple solutions.

This is a criticism of ether theories, but by 1908 the ether was no longer regarded as a meaningful concept, at least not in the context of Einstein’s special relativity (which is the ultimate target of Ritz’s criticism), nor even in Lorentz’s amended theory. Ironically, it was the indeterminate localization of field energy in the traditional accounts of, for example, unipolar induction that led Einstein to formulate special relativity in the first place, precisely to eliminate the indeterminateness that Ritz complains about. (Even more ironic is the fact that the energy of the gravitational field in Einstein’s general relativity is inherently non-localizable.)

4) The impossibility, remarked by Maxwell, of reducing gravitation to the same notions. The negative energy involved would correspond to an unstable system, which shows that these concepts do not have general applicability to the forces of nature.

This criticism turned out, just seven years later, to be spectacularly wrong, since Einstein’s approach to relativity, especially the spacetime metric with the negative signature – the very conceptual basis that Ritz was campaigning against – led to a successful field theory of gravitation. (Later in Ritz’s paper he comments on the hope that his ideas might lead to an explanation for the anomalous precession of Mercury’s orbit – the very thing that was so convincingly accomplished by Einstein’s theory.)

5) Action and reaction are not equal, and this inequality, insofar as it stems from the introduction of absolute velocities, is contrary to experience.

This critique was simply a misunderstanding, although, to be fair, it was a misunderstanding shared by both Lorentz and Poincare. Einstein (followed by von Laue) was the first to clearly recognize the momentum flows associated with the flows of energy in any given frame, and how this ensures the conservation of momentum, i.e., equal action and reaction.

6) Kaufmann's experiments on the electric and magnetic deflection of beta rays of radium do not demonstrate that the mass of electrons is entirely of electromagnetic origin, dependent on their absolute velocity, because on the one hand, there is no obligation to admit, as Lorentz's theory requires, that the forces are linear functions of the speed (this might not be true other than for small speeds), and that, on the other hand, an experiment of Trouton and Noble shows that the expression for electromagnetic momentum as a function of speed from which Abraham deduced the one for electromagnetic mass is certainly inaccurate.

Again Ritz is laboring under a common misunderstanding of that time. Prior to Einstein’s 1905 paper, it was commonly believed that if the effective mass of the test particles in Kaufmann’s experiments exhibited the velocity-dependence consistent with the electromagnetic mass associated with induction, then all the mass must be electromagnetic. Only gradually during the years following Einstein’s 1905 paper did people begin to realize that all forms of energy and mass transform according to the same Lorentz transformations, so Kaufmann’s results do not imply that all mass is electromagnetic in origin (just as Ritz says). This is not a criticism of Einstein’s relativity, it is a confirmation. (Needless to say, pointing out the inaccuracy in Abraham’s competing formulation is also not a criticism of the Lorentz-Einstein theory.)

7) The theory of Maxwell and Lorentz starts from a system of absolute coordinates, that is to say, independent of the movement of matter. To be in agreement with experimental results, which have always, in optics and electrodynamics, as well as in mechanics, confirmed the principle of the relativity of motion, they are obliged, then, to eliminate this absolute system by hypotheses of little credibility, thereby eliminating the notion of a solid body and of the invariability of weighted masses. It will also be necessary to change the principles of kinematics, to consider the rule of the velocity parallelogram as just a first approximation, valid at low speeds, and to make time and simultaneity completely relative notions. It would be regrettable, for the economy of our thought, to admit such complications.

This criticism is based on several misconceptions. Ritz does not identify the “hypotheses of little credibility”, but in any case it is a mistake to think that the viability of the notion of solid [rigid] bodies, or the dependence of the inertia of a body on its energy content, are determined by hypotheses (credible or otherwise). These are empirical facts, as is the fact that inertial coordinate systems are related by Lorentz transformations rather than Galilean transformations. Lorentz invariance has been experimentally established to extremely high precision, and it follows that the relevant kinematics for inertial coordinate systems are those of coordinate systems related by Lorentz transformations, from which relativity of simultaneity follows.

In summary, none of Ritz’s criticisms were well founded, particularly with regard to Einstein’s special relativity. Now we turn to Ritz’s proposed alternative. To begin, he claims to accept several features of Lorentz’s theory, namely “the nature of electricity, the current of conduction, dielectrics, etc., and especially the principle of superposition, which states the complete independence of effects of diverse charges which comprise a system”. (I say he claims to accept these things, because we will find that some of them are actually incompatible with his proposal.) His objective, then, is “to show that we can eliminate absolute motion [from Lorentz’s theory] without ceasing to be in agreement with experiment”. He might have added “and without grasping the fact that, as my former classmate has shown, inertial coordinate systems are related by Lorentz transformations”. Ritz continues by describing the basic kinematic puzzle that faced physicists at the end of the 19^th century:

In the theory of ether, a material point P, at rest in relation to its surroundings, will be able to emit waves of a constant radial speed and which will make at each instant a system of spheres having P as a center. If P is animated by a motion of translation, the spheres, on the contrary, will become eccentric, each keeping its center at P₁ of ether which coincides with P at the instant of emission. According to the principle of relativity, on the contrary, if the motion of translation is uniform, the spheres will have to stay concentric, as at rest, and the center will always be P.

We now know that the solution to this puzzle is to recognize that relatively moving systems of inertial coordinates are related by Lorentz transformations, so the emanating spheres are concentric about the emitting particle in terms of the inertial coordinates in which the particle is at rest, but they are eccentric in terms of relatively moving coordinates. This was the unexpected reconciliation of two seemingly incompatible facets of light, i.e., the independence of light speed from the speed of the source (associated with ether theories), and the invariance and isotropy of light speed relative to the source (associated with emission theories). But Ritz, along with many of his contemporaries, still doesn’t understand this in 1908, so he seeks some other resolution.

There are two ways to represent the phenomena: the one of emission (the light moves) and the one of ether (the light is propagated). The second introduces absolute motion while the first leads to the movement of light in vacuum exactly in accordance with the principle of relativity: the luminous particles expelled in all directions at instant t move with a constant radial speed and form a sphere for which the center is animated with the motion of translation w that had P at the instant of emission. If w is constant, this center will continue therefore to coincide with P. It is this fundamental image only that we will borrow from the theory of emission.

Here Ritz acknowledges that his proposal borrows only this one concept from emission theories, because the remainder of his proposal is certainly not consistent with the concept of an emission theory, at least not in the sense of a ballistic theory in Galilean spacetime. According to any such ballistic theory, the particles of light are emitted from a source at some invariant isotropic speed, but thereafter when encountering other objects the particle of light would either be absorbed and re-emitted (at the invariant speed relative to this object) or else would be altered by interacting with the other object in a relativistic way, conserving momentum, etc. For example, in a Galilean ballistic theory we would expect the speed of a particle of light reflected off a mirror to equal either the invariant speed of emission relative to the mirror, or else the incident speed relative to the mirror, but neither of these is true in Ritz’s proposal. According to Ritz, after emission, “the velocity of the particles remains invariable, even when the particles pass through ponderable bodies or electric charges”, and hence even when reflected off mirrors. This latter stipulation may seem implausible, not to say bizarre, but it is essential to Ritz, because otherwise his conception is immediately falsified by simple first-order phenomena such as the Sagnac effect.

So, according to Ritz, whenever a particle of light is emitted, we must imagine that it moves as if propagating in an ether that fills the entire universe and with a state of motion matching that of the emitting particle at the instant of emission; and thereafter this fictitious ad hoc ether maintains that same state of motion (regardless of the subsequent motions of the emitting particle). The light particle always moves with the invariant speed c relative to the dedicated ether, created (so to speak) at the instant that the light particle was emitted. Thus, Ritz has proposed a hybrid theory, partly based on emission theories, and partly based on ether theory, although it would more properly be called the Many Ethers theory. (Indeed it has some striking similarities with the Many Worlds interpretation of quantum mechanics, spawning a complete universal ether with each emission event. Ritz’s ad hoc ethers are also similar to the "pilot wave" of the de Broglie and Bohm interpretations of quantum mechanics.)

Now, Ritz tells us not to take the “particles of light” too seriously, since he is merely using them as a way of speaking about how the light moves. Also, we’re not to think of an actual mechanistic ether being created with each emission of a particle of light. We are simply asked to believe that each of these fictitious particles of light moves as if it was propagating in its own fictitious ether. At this point the reader won’t be surprised when Ritz says “I will offer for the propagation of electrodynamic actions this new image, but I will not draw all the consequences, in offering here only the work of a critic.”

By the way, Ritz’s theory is sometimes presented (as in Pauli’s 1921 article) in terms of modified formulas for the retarded potentials. Instead of integrating the charge and current on the past light cone at t′ = t – (r/c), they are integrated on the locus at t′ = t – (r/(c+v)), accounting for the posited source-dependence of the speed of light (assuming the potential propagates like a particle of light). However, this does not capture the essence of the theory, because it doesn’t make the crucial distinction between original emission events and secondary interactions. In other words, these formula for the retarded potentials don’t provide any basis for Ritz’s concepts of reflection and refraction, which are essential for inferring any physically observable consequences from the theory. There is no mathematical expression for Ritz’s actual hypothesis, because there is no clear physical meaning to the distinction between “original emissions” and secondary interactions.

Ritz’s basic idea raises many more problems than it solves. First, it makes a fundamental distinction between an original emission event (which creates an eternal and universal guiding ether for the particle of light) and subsequent interactions involving reflection, refraction, etc. Each of these subsequent interactions could be regarded as absorptions and re-emissions. (The fact that we see some objects as red and others as blue – and others as transparent – demonstrates that the reflected or refracted light has interacted with the molecules on the surfaces of those objects, exhibiting the resonant frequencies of those molecules, as if preferentially absorbed and re-emitted.) If there really is no guiding ether, and if Ritz really is concerned to avoid “hypotheses of little credibility”, then there is no rational basis for the assertion that the state of motion of the emitting particle at the instant of emission should continue to govern the motions of the light particle, even after that light particle has interacted with other material particles. Indeed, when neo-Ritzians are confronted with demonstrations of the independence of the speed of light from the speed of the source, they frequently appeal to “extinction”, according to which the particles of light actually do take on a characteristic speed relative to the material they have encountered. However, when challenged to explain how Ritz’s theory can predict any Sagnac effect in a fiber-optic gyroscope, given that the light particles ought to similarly have the invariant speed relative to the fiber optic material through which they are propagating, the Ritzian denies any such extinction effects. Thus the neo-Ritzian is committed to an intellectual shell game: He must both rely upon, and deny the existence of, extinction. It is not a rationally coherent theory.

But this is not the only problem with Ritz’s idea. Pauli’s encyclopedia article comments

It has first to be noted that the emission theories are not consistent with the electron-theoretical explanation of reflection and refraction [recall that Ritz claimed to accept this], for which it is essential that the spherical waves emitted by the dipoles in the body should interfere with the incident wave. If we now think of the body as at rest, and the light source moving relative to it, then according to Ritz the waves emitted by the dipoles will have a velocity (i.e., c) different from that of the incident wave. Interference is therefore not possible. A further important point is that additional, artificial, hypotheses are needed to enable emission theories to explain Fizeau’s experiment, which is so fundamental to the optics of moving media.

The problem is even worse than Pauli says, as can be seen from the phrase “the waves emitted by the dipoles”. If we accept that these are emissions, then a new guiding ether is created with each interaction (e.g., reflection, etc.), and hence light should always propagate at the speed c from its most recent microscopic interaction, and at the speed c through any medium through which it is propagating. As a result, the theory fails to predict any Sagnac effect for a fiber optic gyroscope.

On the other hand, if we accept Ritz’s claim that, subsequent to their “original emission” (however that is distinguished from other interactions of the same localized energy) the particles of light always move at the speed c, as if propagating through their original guiding ether whose state of motion matches that of the original emitting material particle, we arrive at absurd consequences. Consider, for example, two stationary parallel mirrors facing each other, and a source of light (e.g., an excited atom) in between them moving at 0.99c directly toward one of the mirrors, as depicted below.

According to Ritz’s “more credible hypothesis”, the particle of light emitted from the source will move toward the left-hand mirror at 1.99c relative to the mirrors. Then when it is reflected off that mirror it will be moving at 0.01c toward the right-hand mirror. Presumably the energy and momentum of the light particle was absorbed by the left-hand mirror (since we know Ritz is concerned to maintain equal action and reaction, and definite localization of energy, and there is no actual ether here to be assigned any unobservable energy or momentum). Then the light particle strikes the right-hand mirror at 0.01c and recoils at the speed 1.99c. The right-hand mirror must impart the huge amount of energy to the light particle necessary to accelerate it to this speed. What is the source of this energy? And how does the left-hand mirror act to slow down the light particle, while the right-hand mirror acts to speed up the particle? Remember, there is no actual ether (Ritz despises the concept of an ether), so we cannot appeal to the ad hoc ether as the source or carrier of energy or momentum. When the light particle then reaches the left-hand mirror again, it strikes the mirror at 1.99c and recoils at 0.01c, thereby depositing nearly all the energy it gained from the right-hand mirror. And so on. Continuing in this way, the light particle transfers infinite energy from the right-hand mirror to the left-hand mirror. What is the source of this infinite energy, so clearly violating both the first and the second law of thermodynamics? Recall that one of Ritz’s criticisms of (his understanding of) the theory of Lorentz and Einstein was that it would permit a perpetual motion machine, but he was mistaken about that, because special relativity obeys strict energy and momentum conservation. In contrast, the “more credible hypothesis” of Ritz actually does lead to gross violations of energy conservation, and of course the alternating acceleration and deceleration of light particles between identical mirrors is far from credible.

We should also note that, prior to discovering special relativity, Ritz’s former class mate from the Zurich Polytechnic had also entertained the idea of an emission theory, but Einstein later explained that he abandoned this idea because he could see no way for an emission theory to give a coherent account of the wave-like behavior of light, e.g., consistent frequencies, wavelengths, interference effects, and so on. He noted that, in an emission theory, the phase relations of light would be “all mixed up”. In particular, for an accelerating source (which Ritz claimed to accommodate), a trailing wave crest could overtake a leading wave crest, so the frequency of arrival would contain singularities of infinite frequency. Einstein knew this was contrary to experience, and also that the energy of a photon is proportional to the frequency of the light, so a pulse of light with temporally varying frequency in flight is an absurdity, and violates energy conservation. (When describing to Shankland how the phases would be all mixed up, “he waved his hands before his face and laughed, an open hearty laugh at the idea”.)

Despite the theoretical absurdity of Ritz’s proposal, it has received some attention from experimentalists. De Sitter’s observations on binary stars were taken as falsifications of any theory in which the speed of light depends on the state of motion of the source. More specifically, Tomaschek repeated the Michelson and Morley experiment in 1924 using light from the Sun, thinking that this light would, according to Ritz, move at c relative to the rest frame of the Sun. However, the Sun consists of a high-energy plasma, with excited atoms moving at very high speeds in all directions, and each of these excited atoms emits “particles of light”, so the incident light arriving at Earth from microscopic particles on the surface of the Sun would not be expected to have the speed c relative to the macroscopic rest frame of the Sun. (Similar comments apply to tests using light from stars.) Of course, all these observations could be waived off by invoking extinction, but Ritz himself explicitly disavowed any extinction effect, and for good reason, because extinction essentially amounts to saying that (for suitable frequencies) the speed of light changes to c relative to any material that it encounters (assuming it is absorbed and re-emitted, or interacts in some other suitable way), which defeats Ritz’s fundamental premise, on which rests the compatibility with non-zero Sagnac effect, and so on.

Another fundamental problem with Ritz’s proposal is that it treats light in a framework that is completely disconnected from other forms of mass-energy, i.e., with completely different kinematics, by positing that particles of light behave fundamentally differently than material particles. One of Ritz’s criticisms of special relativity was that the composition of velocities of material particles is no longer simply additive, but this non-additivity is an empirical fact about the behavior of material objects, and cannot be evaded simply by positing some peculiar behavior for light. Light is an inertial phenomenon, i.e., we know that light conveys momentum, so in order for any theory of relativity to be valid (as Ritz espoused) it must be characterized by the same inertial coordinate systems as for material objects. Special relativity places all physical entities and processes within a single framework, and notes that inertial coordinate systems are related by Lorentz transformations, which follows as an immediate consequence of the inertia of energy.

Overall, Ritz’s criticisms of the relativistic theories of Lorentz, Poincare, and Einstein were unfounded, based on misconceptions that were still widespread in 1908, and his proposed “more credible” hypothesis for the propagation of fictitious particles of light as if guided by many different fictitious ad hoc ethers was logically incoherent, with physically preposterous consequences.

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