Such is often the case with relativity. The main tenets of which have been raked over ad nauseum. Therefore, I will briefly mull over a few things which I have not seen elsewhere and which I find interesting. We will not be overthrowing relativity theory which is by my accounts (and others) on about as solid ground as exists in physics.
[ Actually it is solid in a way reminiscent of the east caisson of the Brooklyn bridge. That rests on sand rather than bedrock because of nitrogen narcosis problems during construction. Similarly, one would like relativity to rest on firm bedrock logic rather than the 'sand' of the Michelson/Morley "experiment" but ... ]
The relevant fact here that is sometimes forgotten is that relativity is a physical theory and not a logical theory (a fine distinction which does not bear up under infinite scrutiny). Thus, the "electrodynamics of moving bodies" is about bodies whose parts are connected by electromagnetic bonds which are affected by velocity. Galilean relativity is a "logical" theory which doesn't pan out at high velocity but would if there were no "speed limit".
If, on the other hand, C moves and AB remains at rest, the distance AB as measured by C is altered as a function of apparent velocity.
We must bear in mind that as of 1957 it has been understood that the actual shortening of an object (via relativity) cannot be seen because of the travel time differences of light coming to an observer from the front and back of the object. In fact, it is beleived that it would appear to be "rotated" and we could at sufficiently high velocity actually see the backside of the object.
Anyway that's the present understanding.
Of course, I don't buy into that either or I wouldn't bother to write about the subject.
What really happens at the visual level is a quick streak of light and nothing else. This is because no integrated object of ponderable size (read here electrodynamics of moving bodies) will ever be accelerated to such high velocities even by natural processes. So the most we could ever see will be something on the size order of a bottle rocket trucking along at near c. And such an object crossing our field of view at say, the distance of Saturn isn't going to be seen very well by any forseeable telescope. And if it streaks past us at 1 mile distance, we won't see anything either because no geometric relativistic effect can be seen 'head on' and the time the object spends near right angles to the observer will be too short to collect any meaningful information. So expect a blast of gamma rays, a streak of light and ... that's it ... no license plate number ... nada.
Would you have time to:
As I said, relativity is a physical rather than a logical theory. So there's this little problem with what two observers see when they pass each other at relativistic velocity.
This matter is misunderstood.
The above statement is not logically consistent with the rest of relativity theory (forget about the visual appearance).In fact, every object has a history of acceleration. And to be consistent with the infamous "twin paradox" (infamous for being rehashed more than any other physics idea), it must be that three possibilities exist.
I wish to add a minor principle to relativity theory. It's supposed to bridge the gap between physics and information theory. It goes like this.
The resolving power of a telescope is independent of its state of motion.Its meaning is that we can't accelerate away from a star, point a telescope at it and, using the redshift phenomena, gleen more information about the star than we would have got if we had remained stationary. Nor should we obtain less. Same, same all same from forward direction as well. If this rule is correct, we should be able to predict some physical effects.
We can't use the blue shift to obtain more info about a star in that direction. So, since blue has greater resolution than red it must be that stars to the front of a speedy observer would appear to "jump away" from the observer as he accelerates so as to make the star subtend a smaller angle. And the stars to the rear must "come closer" to subtend a larger angle.
In fact then, the appearance of the universe to an accelerated observer is sort of "egg-shaped" darkening in the back with the observer at the rear "egg-focus", getting brighter to the forward section eventually just a point of light there.