False assumption. What direction they are moving is irrelevant, only that they move at the same approximate velocities.
Objects share a proper (co-moving) frame if they have the same velocity.
Direction is clearly relevant when dealing with velocities because velocity is a vector of speed and direction.
That’s just it, we can never tell. A could be moving at 1/2 of c and B moving at 1000 mph and you would never know. All your devices say you are stationary. All you know is that A or B is moving at 1/2 of c plus the 1000 mph RELATIVE to the other....
No. all I said was, "if A & B are in relative motion, A is moving at
exactly the same speed relative to B as B is to A". The speed they are moving relative to some other observer is irrelevant. Consider the limit case where A and B share a proper frame; A is moving at 0 mph relative to B, and B is moving at 0 mph relative to A.
Sure he did, use your brain. If B must be transformed into the measurements of A, then the measurements are not the same....
Yet you can't provide any quote, link, or reference to his use of that phrase. The Lorentz transformations simply translate from one inertial frame to another, so you can see what an observer in another inertial frame will observe. Of course observers in different frames will make different measurements, that's SR.
No, just observers moving at the same approximate velocity. Hence all other observers not moving at your velocity have clocks of a different duration and rulers of a different length.
All observers in different inertial frames will make different observations. Only observers sharing a proper frame will make the same observations.
No such frame exists......
You'll have to explain what you mean - all frames are in relative motion.
You must adjust GPS clocks. No third observer is required. Their rate is not the same as yours. They neither measure the same time as you nor the same distance as you, because their velocity is not approximately equal to yours.
Approximate doesn't come into it; unless the velocities are
exactly equal, i.e. they share a frame, observers will make different measurements.
