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