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§17. – GENERAL REMARKS
WALTER RITZ
Translated (1980) from Recherches
critiques sur l'Ėlectrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13, p. 145, 1908.
Annales 271 (Oeuvres 422)
Between the new formulas and Lorentz’s theory, there is therefore no
presently known contradiction in the domain of observed facts in
electrodynamics. It is evident that from the viewpoint of mathematical elegance
and simplicity, that the advantage will often be on the side of the theories of
Lorentz; but, on the other hand, the latter can not always avoid the use of elementary
forces. We have even seen that their use is indispensable in the theory
of radiation. In these cases there will be equivalence. In fact, no
deduction may be drawn from Lorentz’s equations before the demonstration has
been done, which are often so complicated, that the movement of the Earth
doesn’t noticeably influence the result; here, the advantage is on our side.
One of the most fruitful of Maxwell’s
ideas has been the introduction of displacement currents, which form, along
with conduction currents, a system of continuously closed currents to which
Maxwell applied the known laws of electrodynamics (Neumann’s integral, etc.);
it is thus that he arrived at his equations. The preceding developments show
that this application constitutes a second hypothesis: indeed, we have shown
that from our point of view and even from that of Lorentz, that these laws
apply only to neutral currents, and this last point is, for (Oeuvres 423) Ampere’s laws for example, more important than the
other; Maxwell’s hypothesis
Annales 272
comes back to the
introduction of an elementary law for which all experimental basis is
missing.
Our theory necessitates once again the
distinction of open and closed currents. But if one considers not the
mathematical formulas but the physical realities, one finds that the two orders
of phenomena are quantitatively and qualitatively so different that the
practical utility of their synthesis is not perhaps as great as it seemed at
first glance.
The formula for the action of a mobile
electrified point on another, to which Lorentz theory leads, is very analogous
as Schwarzschild[1] has
remarked, to that of Clausius[2],
which contains absolute speeds as well. The latter arrived at this by
admitting, among other things, that there is no action between a galvanic
current and an electric charge at rest. This is very obviously true for neutral
currents, as we have seen, but could be absolutely false in other cases. This
hypothesis leads, according to Clausius as well as Lorentz, to the introduction
of absolute movement.
We have seen that, in the expression of
the elementary force, a factor k remains indeterminate. This calls to
mind the analogous result of Helmholtz, and likewise formula (25), which is
applicable to elements of neutral current, is identical to those of Helmholtz[3]
and reduces to that of Ampere for k = -1, and to that of F. Neumann,
Maxwell, and Lorentz for k = +1. The couples that are added in
Helmholtz’s theory are lacking, however, and this point is essential. Moreover,
we now know that only in the case where there is no radiation does the energy
remain constant; the relations that the energy equation involves between
the open current’s inductive actions
Annales 273
and their
electrodynamic actions can consequently cease to be satisfied. This is
indeed what happens. For induction phenomena inside bodies at
rest, the equations of Maxwell-Lorentz and those of Helmholtz[4]
become identical if k = 0, as the latter has remarked. In this (Oeuvres 424) case, only the resistance, the electrostatic force and
the accelerations play a role. Lorentz’s formulas are then
identical to ours, which also correspond to k = 0. As to the
consequences relative to stability, requiring k ³ 0, they can only apply to the value of k that
figures in induction phenomena (it is enough, to see it, to suppose the
currents effectively nil). Our formulas therefore always
satisfy, and our parameter k stays entirely undetermined.
It is interesting to notice that, in
bodies at rest, induction phenomena in a closed circuit come only from the
finite propagation speed in our theory. Indeed if we refer to the
developments of section 3, we see that as far as the terms of the second order
are concerned only this finite speed [] introduces accelerations, and it
is these latter which determine the induction phenomena, for the term of the
second order 
which does not come from these developments gives a
nil electromotive force for a closed circuit. We know that, in the hypothesis
for actions at a distance, the induction phenomena have been deduced from []
electrostatic and electrodynamic forces, starting from the energy equation; in
our theory, they are deduced from propagation.
We could determine the k
factor by adopting the theory of metals, proposed by Riecke and Drude,
Annales 274
according to which the speed of electrons in their irregular molecular
movement would be much greater than that of the positive ions, and which
amounts to tens or hundreds kilometers per second. Let
dt' be an element of volume of the metal;
E'dt' be the total charge of the electrons in this
element;
v' be their mean speed.
The body not being
electrified, the action of dt' on a charge e situated in xyz will be by symmetry, considering the irregularities of the
movements, parallel to r, and equation (VI) gives for this
force
Now we have, on the average
(Oeuvres 425) the force is therefore
(54) 
Everything happens as if
the body carried an electric charge 
proportional, like v'², to the absolute temperature, and quite considerable; since this
cannot be, it must be that k is
equal to two.
It is true that, if such an action existed, it would no longer be barely
possible to demonstrate, nor doubtless even to admit, Boltzmann’s theory
relative to the distribution of energy between independent coordinates, on
which is founded the hypothesis of large values of v'. If the molecular speeds of positive and negative ions are,
on the contrary, essentially equal, force (54) would cease to exist, except
perhaps for electro-thermal phenomena.
We have seen that the new
theory represents
Annales 275
hertzian oscillations well. The fictitious particles are thus
periodically distributed in time and space. This distribution in turn
provokes the oscillations of other ions or systems of ions; the combination of
these actions by interference, that is to say, by simple superposition, then
gives rise to the diverse phenomena of reflection, refraction, etc.
When one can consider the
speeds and the amplitude of the accelerations of ions as being infinitely small,
the concordance between Lorentz’s formulas, and mine demonstrated for hertzian
oscillations, continues to exist no matter what the frequency is. With
this restriction, both would represent optical phenomena. But when the speeds
intervene, for example in Fizeau’s experiment on the entrainment of waves, the
agreement ceases; our formulas demand, as do those of Hertz, total entrainment.
I said in the Introduction that one could eliminate the difficulty by admitting
a certain reaction on the part of electric charges caused by the movement of
the [fictitous] particles.
Let us remark in conclusion,
that our law of propagation effortlessly reconciles the phenomenon of
aberration and Michelson’s experiment, which seemed contradictory in the theory
of ether. Indeed, in the second experiment, the light sources being (Oeuvres 426) drawn along in the Earth’s movement,
the speed of their light in relation to the latter has a different value than
that of the speed of light from the stars, which is independent of the Earth’s
movement; the emanative theory of light which gives such a simple explanation
of aberration will subsist in its essential features.
[1] Göttinger Nachrichten, 1903.
[2] Journal für Math. (Crelle), v.82, 1877, p.85.
[3] Wissenschaft. Abhandl., v.I, p.688, Leipzig, 1882.
[4] Loc. cit.,
p.573, equation (3b).