beero1000
Veteran Member
Maybe I'm not expressing what I'm wanting to express.If there are two ants walking at opposite ends of a rubber band holding a steady pace and the rubber band is stretched, one might conclude that the perceived speeds have increased while the actual speeds have not. I got that. The problem is that the formula for calculating their relativistic speed isn't supposed to account for the difference.
It is a prediction of general relativity, not special relativity. Specifically, the FLRW metric.
I'm not saying an object is exceeding the speed of light through space. I'm saying an object is exceeding the speed of light.
Let's go to the Wild West where two gunfighters stand back to back and begin walking away from each other and they each take off at 95% the speed of light. Neither one is exceeding the speed of light relative to the ground, but if the ground itself between them begin to stretch causing their respective distances from one another to substantially increase, then although it will still be the case that neither is traveling greater than the speed of light relative to the ground (that's still at .95c), if the ground stretching is substantial enough, then calculating their speeds relative to each other (not the ground) should yield a speed that yields an answer greater than c.
No, I think I was answering what you wanted to ask. It's just a not-so-obvious thing to really understand without going into the details of the math.
Special relativity is, well, a special case of general relativity. Specifically, it's the one where spacetime is Minkowski space, which is flat and static. In that kind of spacetime, we can have the simple notions of speed (distance and time) that can be measured without having to worry about space warping and expanding. You can imagine special relativity as being relativity on a very small 'patch' of spacetime like a map would would be of your neighborhood, whereas general relativity handles curvature like a globe - you don't have to worry too much about curvature as long as the patch you're studying is small enough, but you do have to start dealing with the curvature once that stops being the case.
In general relativity, we allow for spacetime to curve and expand and so the idea of 'speed' needs to be formalized as either 'speed through space' or 'speed between objects'. We normally think of those two as equivalent, but they no longer are if spacetime can expand and curve. Physically, the intuitive definition for speed matches the 'speed through space' idea i.e. it's what your speedometer would read. The 'speed between objects' idea becomes much further removed from your standard idea of 'speed' when space can bend and grow and would be like measuring your velocity by constantly finding the change in your distance from the sun. It's actually worse than that though, maybe it would be more like measuring your distance from shore on a boat by measuring distance along the surface of the choppy ocean. As the waves move, you can imagine your 'distance' along the water's surface would change which would give a 'velocity' even if the boat was (locally) stationary. That's the difference.
The speed of light restriction still holds for general relativity, but the restriction is on the more intuitive 'speed through space' notion. If you try to measure 'speed between objects', and factor in the expansion of the universe, there is no restriction to speeds faster than c. In fact, if you do that then even light doesn't move at c anymore.