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Yes! About that aspect of turning either into space movement or time movement - everything is constantly moving, either in space or in time. I like to think of anything moving (which is everything) as having to plot itself on a X,Y chart where X is space and Y is time. If you trade all your movement/momentum so that you experience no time (like a photon of light for example), then you’re moving as fast as you possibly can in space. The less of that movement through space, the more you experience the rate of time.
Oh god the case for a photon is super hard to talk about in any meaningful way, photons “see” every point in their journey as happening at the same instant of time and at the same place, null geodesics are nuts.
But yeah, the underlying mathematics that causes this can (kinda) just be pinned on the normalisation of the four velocity, which I think is what you’re describing.
Yes! About that aspect of turning either into space movement or time movement - everything is constantly moving, either in space or in time. I like to think of anything moving (which is everything) as having to plot itself on a X,Y chart where X is space and Y is time. If you trade all your movement/momentum so that you experience no time (like a photon of light for example), then you’re moving as fast as you possibly can in space. The less of that movement through space, the more you experience the rate of time.
Oh god the case for a photon is super hard to talk about in any meaningful way, photons “see” every point in their journey as happening at the same instant of time and at the same place, null geodesics are nuts.
But yeah, the underlying mathematics that causes this can (kinda) just be pinned on the normalisation of the four velocity, which I think is what you’re describing.