There is also a possibility of defining a 'potential energy' from different uniform motions, depending on your choice of referent for a speed, also on your choice of 'who is moving' relative who. I'm not happy about potential energy, from that point of view, as it only will make sense from considering a defined system in its whole. You could say it represent a sort of symmetry perhaps? But 'energy' as in releasing new radiation in a collision exist, and is definably there in a experiment, whereas its potential energy only exist theoretically, until colliding.

Then again, what about 'bending space' as you get up to a relativistic speed, is that a result of 'energy', or is it a result of a geometry? And if light has the possibility of distorting the space it propagates in, would it be possible to measure?

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Although, using matter solely, ignoring a speed, you can define a energy to it, but that's not a potential one, it's the energy released from its rest mass. Or you can turn that one around stating that everything we measure on is in some way in 'motion', even quantum mechanically, as the only way you can define a position is by measuring. Before that you have a probability of position, but no final guarantee, although I'm slightly unsure on that one as I can imagine a experiment repeated using 'identical setups' giving us a same result, position wise. As lights speed in a vacuum for example. It's a tricky universe.

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There is a third point confounding it to me, and that is frames of reference, making all SpaceTime positions a locally defined property, although able to (Lorentz) transform into each other. So what are the 'energy' defined for a patch of space positionally? The space may be contracted from one observer accelerating (for simplicity) relative one uniformly moving. Both descriptions are locally true, according to how I read relativity, and experimentally defined. And the only way you can experiment is 'locally' as I see it. All other descriptions leaves what we measure directly, instead introducing theoretical frameworks transforming one SpaceTime position to another, but, directly measured, A and B will measure on two different 'patches', joined through a Lorentz transformation.

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Assuming that Casimir effect is a result of the 'vacuum energy' it should then give us a different result depending on your acceleration/'speed', as you could be considered to be 'shrinking' a set amount of 'energy', and so volume (or area) of 'space' locally measured. If we define it as existing a set amount of energy, existing inside a 'closed universe'. That one I think might be testable? But I've also made some presumptions that are crucial to such a test. That there indeed is a 'vacuum energy' existing, that the Casimir effect is a result of vacuum energy, expressed in waves fitting, or not fitting, between plates creating a 'pressure'. I've also seen it defined as a result of matter. And yeah, 'compressing a vacuum' is a tricky one

not making much sense, does it? And as you and the plates are of restmass you might get a result consistent with the assumption I make, without that vacuum locally having changed any 'properties' what so ever.

but not really, if it is a result of matter, and assuming that it could differ, then you will see a difference between defining that 'equivalent speed', relative a uniform motion, or getting to it under a acceleration, all as I think for the moment

But if it indeed is possible to compress a 'vacuum' energy-wise, then, and only possibly (still a acceleration and restmass involved), it might make no difference for the energy difference?

Or you won't see a thing differing it? Which then, to me, and assuming a defined volume of space to contain a defined amount of (vacuum)energy, means that A and B:s local definitions of a area/volume doesn't matter for that definition. which becomes a hard nut to crack from a idea of a seamlessly same common (closed) space in where we all co-exist, to me at least. Because how do you define a energy to a volume, if it is observer dependent?

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We can indeed simplify it, by defining Lorentz contractions to exist relative different uniform speeds too. Accepting this, one will find it simpler to define. And can one really expect the Casimir effect to differ, relative 'different' relative (uniform) motions? I don't expect it too.

So?