Maybe you can look at it this way, a Lorentz contraction and a time dilation will always demand at least one other 'frame of reference' to exist. So they can exist in both a acceleration and a uniform motion. And 'gravity' could then be seen as a symmetry to 'energy expended'? But then we have Earths 'gravity', what would that make matter? Matter do not expend energy? It 'binds' energy though.

And that would indeed make a acceleration 'gravity', and so 'energy'. But how does the acceleration 'bind' that energy into 'gravity' locally? Ouch

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So, not 'energy expended' but 'bound energy' in both cases, although a acceleration expend 'energy' to 'bind' it. Heh, and that was a very strange definition

It's like we have two states in this universe describing or coupled to 'gravity'. Accelerations and matter/mass. Then we have our 'uniform motion' that always will describe a state of being 'at rest' relative spaces metric 'gravity', in a geodesic, aka 'free fall'.

And 'motion' becomes truly weird.

I think 'gravity' should be a geometry, to make this work. And it should have to do with the displacements in the four 'directions/dimensions', three spatial together with one temporal, inside that local accelerating frame? But how to relate that to invariant mass. Gravity may be about time dilations and Lorentz contractions, just as uniform motion. But, you will need two 'frames of reference' to prove them, just as you will need it with 'potential energy/momentum' in a uniform motion.

When it comes to 'gravity' itself, you only need one 'frame' to prove it though, as long as it is mass or an acceleration.

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Sorry, I'm talking to myself here

If I assume times arrow to be linked to 'c', as a 'clock', then that 'time' can't change locally. So, how would that create a 'gravity'? The room time geometry will change, but only when comparing frames of reference, same as in a uniform motion. So it still needs two frames of reference to exist, if I define it as a 'geometry'? I can't, or can I? Define it as happening locally?

The question to define here. How big is a 'frame of reference'. How many will I find using 'ideal clocks' inside that accelerating frame? If I define it from 'c', a frame of reference, ideally, should be the same length as it takes light to move one Plank length, that is one Planck time.

(To make this one work we first need to agree on that any 'clock' normally, as on Earth, is a primarily conceptual device, always approximately defined. We know that gravity dilates 'clocks', and the distance of a frame of reference should be a Plank length in my definitions, as that's where our definitions fail, as well as where we define light to 'propagate' the smallest amount. But then you have HUP to consider too, so it could be slightly 'indeterministic' and so of a slightly greater value.)

I better sleep on this one