for_more_ken said:
Special Relativity predicts that the two clocks at b and d will tick at the same rates and remain to be in synchronization during a process where a transmission wave front is sent from point b when b passes point a, is then reflected from a mirror at point d and returned to point b. In this process Special Relativity predicts that a timestamp by clock d when the wave front reaches point d will be half way between a timestamp by clock b when the transmission is sent and a timestamp at point b when the reflection from the mirror at d is received at b.
It does, if we make several additional assumptions:
1) We are ignoring the effects of gravity from both the Earth and the sun; that is, we're effectively doing the experiment in empty space.
2) We are ignoring that "moving along the Earth's orbital path" implies moving on a curved path; that is we're assuming straight-line motion. It takes fully six months for the Earth to change its direction by 180 degrees, so straight-line is a pretty good approximation when the clocks are separated by only a few light-seconds.
3) We synchronized the clocks so that they both read zero at the same time according to an observer who is at rest relative to the clocks. (It also works if the synchronization is done by an observer moving perpendicular to the line between the two clocks, although in this case the synchronization procedure is more complicated without contributing any additional insight into the physics involved).
Without these assumptions, the clocks won't in general be synchronized. But even with these assumptions, so that the clocks are synchronized...
My first question is: "Do these timestamps obey and prove the validity of the Principle of Relativity". That is, will a transmission from point b to a mirror at point d and back to point b when at rest have a "one-way" send response time component that is equal to the "one-way" receive response time component?
Yes, the timestamps will come out that way.
This result results "obeys" the principle of relativity and the postulate that the one-way speed of light is equal to the round-trip speed. However, it does not "prove" anything. Our synchronization procedure will necessarily have assumed these postulates (depending on the details, the assumption may be well-hidden, but it's there) so all we've shown is that when we assume something is true we can get results consistent with that assumption.
My second question is: will such "one-way" send transmission response time component always be equal to the "one-way" receive transmission response time component regardless of the orientation of PLbd (e.g. may PLbd also be aligned with and overlay the velocity vector (v))?
Yes, provided that the clocks are synchronized as in #3 above. The easiest way to see this is to analyze the problem in a frame in which the two clocks are at rest; now the possibility that someone else is moving in some direction at some speed is clearly irrelevant to the behavior of the clocks.
