Page:CarmichealPostulates.djvu/9

 But, although the absence of this effect cannot be proved, it is probably impossible to conceive any satisfactory may in which it could be present. Physical intuition is emphatic (and it may be that this is what Tolman intended to say in the passage cited) in asserting that if the direction of the velocity of S has no effect on the observed velocity of light then the absolute value of the velocity of S has no effect on such observed velocity. But this does not constitute a proof. There is in this, however, nothing to invalidate the naturalness of the assumption of such independence of the two velocities; in fact, it would be unscientific to make a different assumption (which would necessarily introduce greater complications) unless we were forced to it by unquestioned experimental fact. Accordingly, we shall make the assumption and shall state it as postulate $$R''$$:

$$R''$$. The velocity of light in free space, measured on an unaccelerated system of reference S by means of units belonging to S, is independent of the absolute value of the velocity of S.

R. The postulate obtained by combining $$R'$$ and $$R$$ will, for convenience, often be referred to as postulate R.''

Now, since unaccelerated velocity is completely determined when the absolute value of the velocity and the direction of the motion are given the truth of the following theorem is an immediate consequence of theorem I. and postulate $$R''$$.

II. The velocity of light in free space, measured on an unaccelerated system of reference S by means of units belonging to S, is independent of the velocity of S(MR).

The second postulate of relativity has usually been stated in a form different from that given above in $$R'$$ and $$R$$ or R''. In fact, the truth of theorem I. has often been taken as part of the assumption in this postulate, notwithstanding that I. can be derived from M and $$R'$$. Now, it is precisely the assumption of I. that has given most difficulty to some persons. It is believed that a part of this difficulty will disappear in view of the fact that I. is here demonstrated by means of M and $$R'$$.

For the sake of convenience in future discussion one of the customary formulations of the second postulate is appended here. It must be remembered, however, that it is not a separate constituent part of our present body of doctrine but is already contained in M and R, in part directly and in part as a necessary consequence of these postulates.

$$\overline{R}$$. The velocity of light in free space, measured on an unaccelerated system of reference S by means of units belonging to S, is independent of the velocity of S and of the unaccelerated velocity of the light-source.

From the very nature of the postulate $$R''$$ it is difficult to obtain direct experimental evidence for or against it. It seems, however, as we have