In another thread I can see there is some terrible confusion of what "relative velocity" means. I need to clear this up here because no one will understand the discussion on the propagation of light signals. Let's do some examples:
1. If Bob throws a football at 15mph, what is Bob's relative velocity to the football? 15 mph. If Bob is running at 15 mph while throwing the football at 15 mph, what is his relative velocity to the football? 15 mph.
2. If Bob and Harry are playing catch and Bob throws a football to Harry at 15 mph, what is Harry's relative velocity to the football? 15 mph. If Bob is running toward Harry at 15 mph (relative to Harry) while throwing the Football to Harry at 15mph, what is Harry's relative velocity to the football. 30 mph. If Bob is stationary and Harry runs towards him when Bob passes the football at 15 mph, what is Harry's relative velocity to the football. 30 mph.
3. If sound only travelled at 15 mph and Bob yelled at Harry at the same time he was passing him the football and both weren't running, which would Harry catch first, the yell or the football? Both would be simultaneous. If a wind was blowing at 15 mph at Harry's back, he would never hear the yell from Bob. If Bob was running toward Harry and passing the football (no wind this time) at 15 mph, Bob would hear his initial yell the entire trip to Harry.
Bob and his yell would have 0 relative velocity but Bob and his football would have 15 mph relative velocity. Bob's velocity did not push the sound any faster while it did push the football. Sound's velocity is relative to the medium and Bob or Harry's relative velocity to sound must first be calculated from their relative velocity to the medium.
Harry's velocity toward the sound or the football will yield a relative velocity to those of 30 mph. Bob's velocity, throwing sound to a stationary Harry, will not add to Harry's relative velocity to the sound but it will add to Harry's relative velocity to a thrown football.
4. Now let's say the max relative velocity anything could travel was limited to 15 mph. Bob's relative velocity to either a football or to the sound he throws should be unaffected as the velocities do not combine above 15 mph relative velocity. But this doesn't happen in relativity. Bob would not be able to keep up with his yell if he tried to run with it at 15mph. The relative velocity between him and his yell would be 15mph and not zero.
If Bob yelled while running to Harry, his yell would not be pushed towards Harry any faster so the speed limit law would not affect the example above. But if Harry was running towards Bob, who was either running or stationary, Harry's velocity relative to the football or sound could not exceed 15 mph. It could not be 30 mph as in the example above.
These strange results are not totally happening as the result of an arbitrary speed limit but because Bob nor Harry can establish a relative velocity to the electromagnetic medium as the Michelson Morley experiment proved. Yes relativity postulates the relative speed of the football is limited by the arbitrary speed limit the same way as light would be limited by its self-propagation through its electromagnetic medium. But let's leave that aside as this is way outside normal physics. Solid objects are not normally subject to the physics of waves.
These next two paragraphs sounded right at the time but the real story is far more complicated so ignore what I said here:
Let's concentrate on Bob's yell and how it's limited by Bob's and Harry's inability to move in relation to the medium and thereby move in relation to the sound wave. Bob and Harry can still register velocities relative to each other (not in a normal additive way though) but Bob can neither push or catch up to his yell because he can't register a relative velocity to the medium through which the wave propagates. Harry can't get to Bob's yell any faster because he is also incapable of registering a relative velocity to the medium. There's also no wind that can push the medium. Relativity's explanation for this breach in the normal understanding of relative velocity is time and space must bend.
If you can never catch up with a light wave or can't get to it any faster, you might as well be standing still. And this is what you're actually doing in your own frame. Even if you feel the absolute motion of acceleration (or gravity) you're still standing still. I find it far easier to understand we are always going at a combined velocity of c.The faster we're observed to move through space, the slower we're observed to move through time. This is how we preserve causality, get around the max speed limit and reach a light wave faster than if we were standing still.
Edited by ralfcis, 18 December 2019 - 05:16 PM.