- #1

Micheth

- 79

- 2

Perhaps someone here can provide a different perspective that will make it click for me, i don't know...

The way I model the problem is thus:

A

C

B

there being 2 inertial frames, one for A&B, and another for C.

A & B, at complete rest with respect to each other, and separated by an arbitrary long distance (let it be many light years), are sending light beams to each other, effectively constituting a light clock.

We may let A/B be the reference frame, with C approaching them at a fixed speed (no acceleration).

At the moment when C transects the light beams being transmitted between A and B, it must necessarily lie on the virtual line between them, since the light beams are never anywhere outside of that line.

Indeed, if A/B wished to send a signal (using the same light beam) that would reach C, then they would need to calculate the appropriate time prior to C's transection of that line, and emit the beam accordingly in advance.

(B would not even be necessary, but just for reference.)

Now, this may be where I'm mixed up but it certainly seems as if the following must be true if we now let C be the reference frame (considered to be at rest).

Now, in this case, for the signal to reach C, A would not emit the signal beforehand, but at the point where C lies on the virtual line between A and B (as calculated by A&B).

That beam would travel along that virtual line that existed between A and B at the moment A emitted the signal, eventually reaching C at some later time after A and B have moved onward (to the right).

Therefore, it seems C transected a line that is no longer between A and B, which contradicts what seemed to happen if we consider A/B at rest...

(Obviously C would "see" A and B along the light beam's line, merely because of the time it took their light to get to him, but knowing the speed of light, he would know A and B are actually beyond that point by now).

Stated slightly differently, to me it seems that in A/B rest frame, A/B could in fact receive a reply signal from C (C reflects the light beam (replies) at the instant it transects line A-B), whereas in the C rest frame, A/B could never intercept a reply (reflection) from C.

This of course renders the light clock analogy (ala SR) completely unintelligible anymore :-(

The only thing I can try to muster is that if you consider yourself at rest and the other frame moving, then somehow that frame imparts lateral momentum to emitted light beams but that can't be right I think.

(I think, I dunno.)