Thus the principle of causality (like causes, like effects) is always verified, and never found at fault. It is therefore an empirical truth, but in addition to this it imposes itself on our mind with irresistible force. It even imposes itself upon animals. “The scalded cat avoids hot water,” is proof enough. In any case, not science only but the whole life of man and animals is based upon it.
It is a consequence of the principle that if the initial conditions of a movement present a symmetry, this will appear again in the movement. M. Paul Painlevé insisted strongly on this in the course of the recent discussion of Relativism at the Academy of Sciences. The principle of inertia in particular follows from this statement: a body left to itself far from any material mass will, by reason of symmetry, remain at rest or travel in a straight line.
It will certainly follow a straight line for a given observer (or for observers moving with uniform velocities relatively to the first). The Newtonians say that the space of these observers is privileged.
On the other hand, for another observer who is, relatively to them, moving at an accelerated velocity, the path of the moving body will be a parabola, and will no longer be symmetrical. Therefore the space of this new observer is not privileged space.
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.