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Translated (1980) from Recherches critiques sur l'Électrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13,   p. 145, 1908.


Annales 145 (Oeuvres 317)

      Electric and electrodynamic phenomena have acquired in the course of these last years more and more importance. They include Optics, the laws of radiation and the innumerable molecular phenomena associated with the presence of charged centers, ions and electrons. Finally, with the notion of electromagnetic mass, Mechanics itself seems obliged to become a chapter of General Electrodynamics. In the form given to it by H. A. Lorentz, Maxwell's theory would thus become the turning point towards a new conception of nature, where the laws of electrodynamics, considered as primary, would contain the laws of motion as special cases and would play the fundamental role in the physical theories which, until now, have belonged to Mechanics.
      Under these circumstances, it is plainly desirable to have a rigorous criticism of the foundations of this theory, to give it the degree of clarity and precision that Mechanics itself reached only recently after much controversy. It is in order to ask which hypotheses are essential and can be deduced from observations, which others are logically useless or can be discarded without experience ceasing to be adequately represented, and finally, which are those which can be, and should be (Oeuvres 318) rejected; a question which is asked principally in regard to absolute motion.

Annales 146

      In the first part of his Lessons on Electricity and Optics(1) Poincaré devoted some classic pages to the criticism of the more or less distinctive theories of Maxwell himself and of Hertz; therefore I will concern myself only with the form that the theory took in the hands of Lorentz, a form that presents well known advantages. Some of his results can easily be extended to the other theories. Here again, I only have to recall or to complete the ideas put forward by Poincaré and more importantly by Lorentz who was well aware of the different aspects under which his theory could be interpreted.
      In general, I set aside the phenomena of molecular order, dependent on the corpuscular theory of electricity: this fruitful concept is evidently independent, in large part, of ideas that we can develop about the mode of action of electric charges on one another via the ether medium, which are more specifically the object of electrodynamic equations.
      The result of these researches has not been favorable to the existing theories. The discussions about the difficulties that they raise show that the difficulties have a common origin intimately linked to the concept of ether, which is the basis of all these theories. We will see specifically that:
      l° From a strictly logical point of view, the electric and magnetic forces, which, in appearance, play in the theory a role so fundamental are notions that we can eliminate entirely; they only contain in reality the relations of space and time: we thus return to the old elementary actions, with this sole difference that they are no longer instantaneous.

      (1) H. POINCARÉ, Electricite et Optique: La lumiere et las theories electrodynamiques; 2nd ed, Paris 1901.

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      2° The theory [1] permits an infinite number of solutions, each satisfying all the conditions, but incompatible with experience and even leading for example to perpetual motion. To remove these solutions we must admit by hypothesis formulae for retarded potentials. These formulae introduce irreversibility in electrodynamics (Oeuvres 319) whereas the general equations permit reversibility. I show that, contrary to accepted ideas, that they can't be deduced from a proper specialization of the initial state. They constitute a new hypothesis, making useless the partial differential equations. To clarify this hypothesis it is necessary to distinguish the elementary actions; it is to renounce Maxwell's fundamental idea of rejecting them.
      3° The notion of localization of energy in the ether is vague and allows many simple solutions.
      4° The Impossibility, described by Maxwell, to reduce gravitation to the same notions. That the negative energy involved would correspond to an unstable system, shows that these ideas do not have general applicability to the forces of nature.
      5° Action and reaction are not equal, and this inequality, in the manner in which it is deduced from the introduction of absolute velocities, is contrary to experience.
      6° Kaufmann's experiments on the electric and magnetic deviability of beta rays of radium don't prove that the mass of electrons is entirely of electromagnetic origin, and dependent on their absolute velocity, because on the first hand, nothing obliges us to believe, as in Lorentz's theory, that the forces are linear functions of velocity, (this may be true at small velocities), and that, on the other hand, one of Trouton and Noble's experiments shows that the expression of electromagnetic momentum

[1] Maxwell-Lorentz.

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as a function of velocity from which Abraham has deduced the one of electromagnetic mass is certainly inexact.
      7° The theory of Maxwell and of Lorentz starts from a system of absolute coordinates, that is to say, independent of all motions of matter. In order to be in agreement with experimental results, which have always, in Optics and Electrodynamics, as well as in Mechanics, confirmed the principle of relative motions, we are obliged, then, to eliminate this absolute system by hypotheses of little credibility, thus eliminating the notion of solid bodies, and the concept of the invariability of ponderable masses. It will be necessary also, to change the principles of Kinematics, to consider the rule of the velocity parallelogram just as a first approximation, valid at small speeds, (Oeuvres 320) and to make time and simultaneity completely relative notions.
      It would be regrettable, for the economy of our thinking if we had to live with all the complications listed above. I think, that instead of Kinematics, it will be the ether hypothesis, and with it, the representation of phenomena by partial differential equations, that must be abandoned. The necessity to explain why bodies do not meet any resistance from the ether as they pass through it, and the fact that they do not modify its state, and many other considerations, have created a simple physical space out of Fresnel's mechanical ether, perfectly penetrable by matter, a system of absolute coordinates. The ether is now only a mathematical abstraction and its elimination would only be the final phase of a long evolution.
      This conclusion, as I set it forth, is not at all involved with a return to actions at a distance. Nevertheless, it indeed collides head-on with many currently accepted ideas, and I am the first to admit that a hypothesis which has rendered such great services to Science can't be condemned for the

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sole reason that it presently raises some seemingly inextricable difficulties. We should always hope for future solutions of these difficulties, or accept the idea that they are inherently a part of things, and independent of our models. This is, fortunately, not the case. This is what I have sought to demonstrate in the Second Part of this work, but the theory which I will present does not pretend to be a satisfactory and definite solution to a problem so difficult. Its primary purpose is to show how large is the unknown part which, in spite of recent advances, still exists in this domain, and in what measure, [it's] much smaller than we would be tempted to believe. Experimental evidence may be considered as confirmation of Maxwell and Lorentz's theory, even when we adopt, as I will do, the remarkable ideas of this latter savant on the atomic constitution of electricity, the nature of conduction current and of dielectrics, in a nutshell, the theory of electrons. These researches will show that it is not necessary to introduce absolute motion and thus to upset Kinematics and the notion of time; relative velocities alone will suffice. There will be no use of notions subject to criticism such as polarization, the electric vector the magnetic (Oeuvres 321) force, etc., but only the notions of time, space, and electric charges, these latter only playing, like the masses in Mechanics, the role of coefficients conveniently chosen and invariable for a given ion or electron. In a certain sense it is a mechanical theory of electricity. But I have not believed it advisable to bring in the more or less complicated latent mechanisms which play such an important role in Maxwell's theory-. Those hypotheses are unnecessary, and,. one must say, barely satisfactory. It suffices, indeed, to recall that ponderable bodies

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must pass through these complicated mechanisms without disturbing them and without feeling sensible action, even when their speed reaches that of celestial bodies. Impenetrability, in particular, doesn't exist in the mechanical [ether] theories, and this is the one point which isn't always sufficiently placed in evidence. Experience has shown that actions are not instantaneous; also it hasn't revealed any trace of a medium which could exist in materially empty space. I therefore felt I could restrict myself to give to the law of propagation of these actions, a very simple kinematic interpretation borrowed from the emanative theory of light and satisfying the principle of relativity of motion. Fictitious particles are constantly emitted in all directions by electric charges; they keep on moving indefinitely in straight lines with constant speed, even through material bodies. The action under gone by a charge depends uniquely on the disposition, velocity, etc., of these particles in its immediate surroundings. The particles are therefore simply a concrete representation of kinematic and geometric data. These hypotheses are sufficient for the purely critical objective that I suggest to reach here. They permit study in detail of the law of elementary actions between electrons in motion and show in particular, that this law, almost entirely unknown for great speeds, requires, even at small speeds, an indeterminate parameter K, which is not without analogy with the one that Helmholtz has introduced in his theory.
      I need to specify the temporary scope of these hypotheses. Indeed, when the particles (or, if we like, the actions or energies) emitted by an electrified body reach another electric charge and modify its motion, the principle (Oeuvres 322) of action and reaction demands that they undergo on their part, a deviation, or a change, and it is very remarkable that

Annales 151

Fizeau's experiment on the entrainment of waves, like certain other facts of Optics, is not compatible with the hypothesis admitted here, and demands such a reaction. It's the opposite that happens in the ether hypothesis, as Poincaré so presented it. Hertz's theory, which satisfies the principle of action and reaction, is incompatible with Fizeau's experiment, Lorentz's theory, which doesn't satisfy it, explains the experiment perfectly. But Poincaré has shown that in giving a momentum to the radiant energy, everything falls into place; therefore this hypothesis is natural if this energy is projected instead of being propagated. It is precisely this that permits safeguarding this principle in the new model that I propose. We can even foresee the possibility of obtaining, by these principles, the electrodynamic terms that depend on velocity and acceleration, using only the consideration of propagation [projection?], a problem that Gauss posed in his well known letter to W. Weber, and that Maxwell's theory didn't solve because it introduces to these terms a special quantity, the vector potential.
      I will return to these questions later. The remarks which precede are sufficient to explain why I didn't address optics in this criticism.
      In many respects, the new theory will therefore bring the reader back to some older classical ideas, which seemed destined to be forgotten. The interpretation of certain experiments will necessarily be modified. In particular, perhaps part of or the whole of mass will be electromagnetic in origin, but it will be constant and won't depend on an absolute velocity. It is the forces, and not the mass, that changes. Kaufmann's experiments also permit this new viewpoint.
      The new formulae are applicable to gravitation;

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they permit abolishment of, at least in great part, the most apparent divergence which exists at this time between calculation and experiment regarding the perihelion motion of Mercury.
      The theory of electrons has constituted a first partial return from Maxwell's ideas to others much older, and for those who consider as indispensable a new evolution in (Oeuvres 323) the same sense, Lorentz's hypotheses, which have been so fruitful, will maintain their importance, and the mathematical form that he gave them will continue in many cases to be the most elegant and the most practical.


Copyright © 1980, 2000 Robert S. Fritzius
Installed February 24, 2000

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