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Oh yes let's talk about my favourite subject ever!
The coolest thing I know of comes from wondering why bent spacetime makes you move at all. The answer is that you always move through time and the bending of spacetime actually turns a bit of time into space and vice versa.
Unnecessary tangent
For a horrible but intuitive explanation of how this works, time is kinda just a direction and bending sorta rotates things so that time looks like it's one of the space directions. Just like turning to the left makes what was your left look like it's straight ahead.This leads to my favourite saying about black holes, once you enter them you can no more escape falling to the singularity than you can escape tomorrow.
I've never heard that take on it before (the idea of turning time into space), but it sounds fascinating. Do you have any links I could follow up on?
Only a few really dry textbooks I'm afraid, it's a subject that's extremely difficult to explain in lay terms as the mathematics is so complicated.
That said if you're feeling masochistic, Schultz's first course in GR is the most approachable that I know.
I really like this PBS Spacetime video, which is at least a little related. Great channel for diving into these subjects further, but in a more casual way than a textbook.
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.
I can escape tomorrow.
Dread it, run from it...
So gravity is some kind of derivative property of entropy? I'm out of my depth here. Did anyone ever define time properly?