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Translated (1980) from Recherches
critiques sur l'Électrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13, p. 145, 1908.
INTRODUCTION
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.
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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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147
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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148
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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149
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
Annales
150
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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152
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.
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