To me, this was why the statement that "B would see the objects growing further apart while A would see them getting closer together", if FTL was allowed, was not a very satisfying answer.
So given what you've described, that means that forces applied to bodies need to have a time component equal in magnitude to the spatial components. Forces must always exist along that 45° line. The limit of the force required to continue to rotate that spacetime velocity out of the time component and into the spatial components goes to infinity as the vector approaches that 45° line.
The fact that forces are unidirectional is the unexplained part. If they weren't, then we could rotate that vector further, and start traveling backwards in time. Then wouldn't B expect to see the objects moving apart, while A sees them moving closer together?
To me, the impossibility of the disparity in observations is a consequence of, dependant on, no-FTL, not an explanation thereof.
Addendum: I don't understand why you said 45° instead of 90°. I thought objects traveling at the speed of light would experience infinite time dilation, and thus be observed as having 0 passage of time.
> Addendum: I don't understand why you said 45° instead of 90°. I thought objects traveling at the speed of light would experience infinite time dilation, and thus be observed as having 0 passage of time.
Think about what the diagram shows: Every (s[pace], t[ime]) coordinate pair on the spacetime diagram shows an observation of a particle. So in natural units, a photon's wordline is given by s=t or s=-t (traveling in one or the other direction). If you draw that, it's a 45° line. It also gives you the light cone of the observer at (0, 0).
A horizontal wordline would be something moving at infinite speed, not the speed of light, as it is observed at every place at the same time.
So given what you've described, that means that forces applied to bodies need to have a time component equal in magnitude to the spatial components. Forces must always exist along that 45° line. The limit of the force required to continue to rotate that spacetime velocity out of the time component and into the spatial components goes to infinity as the vector approaches that 45° line.
The fact that forces are unidirectional is the unexplained part. If they weren't, then we could rotate that vector further, and start traveling backwards in time. Then wouldn't B expect to see the objects moving apart, while A sees them moving closer together?
To me, the impossibility of the disparity in observations is a consequence of, dependant on, no-FTL, not an explanation thereof.
Addendum: I don't understand why you said 45° instead of 90°. I thought objects traveling at the speed of light would experience infinite time dilation, and thus be observed as having 0 passage of time.