Are you asking if particles exist in gravity?

SpaceTime is defined by 'space' in where we find matter and radiation.

Space as such is 'curved' depending on 'gravity'. Where 'gravity' is stronger particles might 'bend their path' and blue, or red, shift, as defined by some 'inertial observer'.

You might want to define stretches between galaxies as 'flat', just as you when looking very closely at a sphere might find it to be 'flat' too. Neither of those is any proof of 'space' existing without gravity though. Although there is a state wherein you can define 'space' as being 'flat', called a geodesic, it is related to a very special type of relative motion we call 'uniform motion'. The best way to see that motion is using radiation, a photon, as we then don't have to discuss any mass, as it is defined from main stream physics as being mass less.

It depends also on what you think give us a 3D space. You might define it as gravity. Then the next question becomes in what way gravity comes to be? If you define it as 'radiating' from primary mass and accelerations, and to that add that it takes a 'time' 'c' to 'propagate, you might assume that the space between galaxies could be seen as flat. But that would then also mean that we no longer can talk about space as 3D except in those cases where gravity has come to reach. That would make a galactic space trip rather tricky, like traveling a one dimensional string.

On the other hand you can postulate that space is 'gravity', meaning that a 'one dimensional' space can not be. That one better fits the universe we see, and in that one any particle will be defined by the point it is created in, in some 4D position relative you. That 'potential' you discuss would then be observer dependent.

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The observer dependence is in which way you observe it, being at rest with it, or as defined by not being 'at rest', like standing on a planet observing it/them getting created in space. In a geodesic there is no gravity to be observed, excepting the gravity you and your ships invariant mass create locally.

And that is the wonder of a 'uniform motion'. That, and the fact that all 'uniform motions' are the same in a 'black room scenario' making it impossible for you to differ them through experiments. Which to me is a proof that our definitions of 'motion' are slightly lacking, to me it seems as we haven't really described it as it should be described.

That one is discussable though, as what I do here is to define 'gravity' as equivalent to 'energy'. If we assume that 'space warps' around a particle, then that 'warping' should be there no matter your motion, uniform or accelerating. When it comes to 'energy', as in 'potential', my statement is correct though, as you being at rest with that particle will find it of a less energy than when accelerating. Maybe this one is possible to use for a argument that 'gravity' isn't observer dependent, it's a tricky one as you still will find it to be observer dependent locally, but not between frames of reference. But energy will always be observer dependent, differing between frames of reference, as to compared locally. So 'energy' and 'gravity' can not be the exact equivalent, as I see it now.

Which, if my reasoning is correct? Should mean that there is no such thing as a 'potential gravity'. You can only find a 'same gravity' as compared between 'frames of reference' and locally. That as I then would expect that particle to 'warp space', just as good with you in that geodesic, as when watching it from that planet. Which leaves us the question of how 'gravity' can disappear in that geodesic. If you define it so then a 'free fall' is the best description leaving you at rest with the overall 'gravity' surrounding you, even though your, and the particles, invariant 'rest mass' still will influence the space near you.

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That's also why it is simplest to discuss this from 'photons propagating', as we then can leave out 'rest mass'. So in my universe space now is defined by gravity(s metric), and gravity can't be 'potential'. Although the 'energy' expressed is dynamically changing, with invariant 'rest masses relative motion' and accelerations.

If this now makes sense

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Da*n, I will need to think about this one some more. It's easier when you think of it in form of energy, gravity is tricky. Still, a lot of the confusion comes from comparing between 'frames of reference'. Defined locally all particles will have one 'energy' and one 'gravity', defined between frames it seems to me that 'gravity' still will hold, but 'energy' will change depending on motion.

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Assume that you accelerate one kg. That acceleration will according to Einsteins equivalence principle now 'frame drag' the space surrounding it, and warp it. If you were on it and felt one gravity act on you constantly, would the 'warping of that space' be the same at all times? That can't be true, showing us that even though the gravity is equivalent to earth, the warping of space is not. Then assume that you accelerate this way for a week (one G) closing your engines each day to 'coast' uniformly. What happens with that warping surrounding your rocket as you do that? Will the relative 'speed' you build up between each time you coast make a difference?

As far as I can see it won't. The only 'gravity' you will find coasting, no matter your 'speed' is the one created from your own, and the ships, mass.

And that one will mean that although the invariant 'rest mass' might warp 'space' the same, no matter if you observe it locally, or not (frames of reference), the 'mass', and 'gravity', created by your acceleration can not be the same as a invariant 'rest mass'. Also it tells us that a uniform motion is the place where your 'rest mass' is easiest to define, as it won't differ, no matter your 'relative speed'.