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what would be the difference between the idea of being at point A and moving toward B in space-time; and being at point A and not moving and B not moving but the space-time between them moving and warping out of the way?
what would be the difference between the idea of being at point A and moving toward B in space-time; and being at point A and not moving and B not moving but the space-time between them moving and warping out of the way?
Particles have wordlines in spacetime and cross events which are points. In a curved spacetime worldlines can cross even if at some point the lines were parallel to each other.what would be the difference between the idea of being at point A and moving toward B in space-time; and being at point A and not moving and B not moving but the space-time between them moving and warping out of the way?
Didn't you just answer it yourself while asking the question? In the second case, space-time is curved. I assume that's not what you wanted to hear, since you said so yourself. What sort of answer are you looking for?
The difference is that is scenario 1, the subject would have the epxreince of moving from A to B, whereas in scenario 2, the subject would ahve the experience of not moving while the two points would move to coincide.
It would be easy to tell the difference merely by observing external reference points, such as distant stars.
Particles have wordlines in spacetime and cross events which are points. In a curved spacetime worldlines can cross even if at some point the lines were parallel to each other.
But spacetime itself is fixed, it does not change.
I guess you can say that it changes the meaning of velocity. Consider e.g. the case of galaxies moving away from each other due to the expansion of the universe. I'm quoting myself from another thread:would the idea change the way the motion, or lack thereof, of particles, is conceived;
This speed is something very different from the speed an object has in a local inertial frame. That's why it can be >c.When we say that galaxy A and galaxy B are moving apart with speed v, it really means that "the proper distance between A and B along the shortest possible path in the hypersurface of constant time coordinate changes by v units of length for each unit of time that we change the time coordinate".