It seems to me that the Relativists might reply to this as follows. You
have no right to define the initial conditions for a given observer,
then the subsequent movement for another observer who is moving with
accelerated velocity. If you thus define your initial conditions
relatively to the latter, the moving body at the moment when it is
released is not free for this observer, but falls in a gravitational
field. It is therefore not surprising that the motion produced seems to
him accelerated and dissymmetrical. The principle of causality is not
wrong for either observer.
One might also give a different definition of the privileged system,
saying: it is that relatively to which light travels in a straight
line in an isotropic medium. But in that case the rays from the stars
travel in a spiral for an observer fixed on a turning earth, and the
Newtonians would infer from this that the earth turns relatively to
their privileged space. Einsteinians will reply that the space in which
the rays travel is not isotropic, and that they are diverted from the
straight line in it by the turning gravitational field which causes the
centrifugal force of the earth’s rotation. They will always find an
escape which will leave the principle of causality intact.
It seems difficult, therefore, to give unanswerable proof of the
existence of the privileged system when we start from the principle of
causality. Each party retains its position.
* * * * *
On the other hand, there is evidential value, a keen and convincing
penetration, in the second part of the criticism which M. Painlevé
directs against the principles of Einstein’s theory.
Let us sum up the argument of the distinguished geometrician. You,
he says to the Einsteinians, deny all privilege to any system of
reference whatever. But when you want to deduce, by calculation, the
law of gravity from your general equations, you cannot do it, and
you really do not do it, except by introducing scarcely disguised
Newtonian hypotheses and privileged axes of reference. You only reach
the result of your calculation by sharply separating time and space as
Newton does, and by referring your gravitating moving objects to purely
Newtonian privileged axes, in the case of which certain conditions of
symmetry are realised.
To this fine and profound criticism which M. Painlevé raises may be
added that of Wiechert, who has pointed out various other hypotheses
introduced by Einstein in the course of his calculations.
In a word, Einstein seems not to have kept entirely clear of the
Newtonian premises which he repudiates. He has not the disdain for them
that one would suppose, and he does not hesitate to have recourse to
them occasionally for the purpose of helping out his calculations. That
is rather to pay a little reverence to the idols you have burned.
Public-domain text, read in full here on John Shaqi.
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