At the present time, different opinions are being held about the
fundamental equations of Electro-dynamics for moving bodies. The
Hertzian[9] forms must be given up, for it has appeared that they are
contrary to many experimental results.
In 1895 H. A. Lorentz[10] published his theory of optical and electrical
phenomena in moving bodies; this theory was based upon the atomistic
conception (vorstellung) of electricity, and on account of its great
success appears to have justified the bold hypotheses, by which it has
been ushered into existence. In his theory, Lorentz proceeds from
certain equations, which must hold at every point of “Äther”; then by
forming the average values over “Physically infinitely small” regions,
which however contain large numbers of electrons, the equations for
electro-magnetic processes in moving bodies can be successfully built
up.
In particular, Lorentz’s theory gives a good account of the
non-existence of relative motion of the earth and the luminiferous
“Äther”; it shows that this fact is intimately connected with the
covariance of the original equation, when certain simultaneous
transformations of the space and time co-ordinates are effected; these
transformations have therefore obtained from H. Poincare[11] the name of
Lorentz-transformations. The covariance of these fundamental equations,
when subjected to the Lorentz-transformation is a purely mathematical
fact _i.e._ not based on any physical considerations; I will call this
the Theorem of Relativity; this theorem rests essentially on the form of
the differential equations for the propagation of waves with the
velocity of light.
Now without _recognizing_ any hypothesis about the connection between
“Äther” and matter, we can expect these mathematically evident theorems
to have their consequences so far extended—that thereby even those laws
of ponderable media which are yet unknown may anyhow possess this
covariance when subjected to a Lorentz-transformation; by saying this,
we do not indeed express an opinion, but rather a conviction,—and this
conviction I may be permitted to call the Postulate of Relativity. The
position of affairs here is almost the same as when the Principle of
Conservation of Energy was postulated in cases, where the corresponding
forms of energy were unknown.
Now if hereafter, we succeed in maintaining this covariance as a
definite connection between pure and simple observable phenomena in
moving bodies, the definite connection may be styled ‘the Principle of
Relativity.’
These differentiations seem to me to be necessary for enabling us to
characterise the present day position of the electro-dynamics for moving
bodies.
H. A. Lorentz[12] has found out the “Relativity theorem” and has created
the Relativity-postulate as a hypothesis that electrons and matter
suffer contractions in consequence of their motion according to a
certain law.
A. Einstein[13] has brought out the point very clearly, that this
postulate is not an artificial hypothesis but is rather a new way of
comprehending the time-concept which is forced upon us by observation of
natural phenomena.
The Principle of Relativity has not yet been formulated for
electro-dynamics of moving bodies in the sense characterized by me. In
the present essay, while formulating this principle, I shall obtain the
fundamental equations for moving bodies in a sense which is uniquely
determined by this principle.
But it will be shown that none of the forms hitherto assumed for these
equations can exactly fit in with this principle.[14]
We would at first expect that the fundamental equations which are
assumed by Lorentz for moving bodies would correspond to the Relativity
Principle. But it will be shown that this is not the case for the
general equations which Lorentz has for any possible, and also for
magnetic bodies; but this is approximately the case (if neglect the
square of the velocity of matter in comparison to the velocity of light)
for those equations which Lorentz hereafter infers for non-magnetic
bodies. But this latter accordance with the Relativity Principle is due
to the fact that the condition of non-magnetisation has been formulated
in a way not corresponding to the Relativity Principle; therefore the
accordance is due to the fortuitous compensation of two contradictions
to the Relativity-Postulate. But meanwhile enunciation of the Principle
in a rigid manner does not signify any contradiction to the hypotheses
of Lorentz’s molecular theory, but it shall become clear that the
assumption of the contraction of the electron in Lorentz’s theory must
be introduced at an earlier stage than Lorentz has actually done.
In an appendix, I have gone into discussion of the position of Classical
Mechanics with respect to the Relativity Postulate. Any easily
perceivable modification of mechanics for satisfying the requirements of
the Relativity theory would hardly afford any noticeable difference in
observable processes; but would lead to very surprising consequences. By
laying down the Relativity-Postulate from the outset, sufficient means
have been created for deducing henceforth the complete series of Laws of
Mechanics from the principle of conservation of Energy alone (the form
of the Energy being given in explicit forms).