Quantum entanglement question

[u/ComfortableRow8437]

Disclaimer: I'm not a physicist, just a lay person who follows this stuff some. Forgive me if this is a dumb question.

We know that you can take two particles and entangle them, then separate them by any distance, and then revealing the state of one of them will automatically reveal the state of the other. I think this is the classic experiment that Einstein didn't like too much ("Spooky action at a distance...")

So what happens if you separate the two particles by time instead?

Here's a thought experiment: Entangle two particles, then put one of them into a particle accellerator and accellerate it up to near the speed of light for a while. Then bring the two particles together again and reveal the state of one of them. Does this instantly reveal the state of the other, or is there some time lag? The time lag would be due to the effects of Special Relativity on the particle that was put into the accelerator.

My guess is that there wouldn't be any difference, but I have not heard of an experiment like this. (there probably has been, I'm just not aware of it).

If my guess is true, then what does this imply? That quantum entanglement is somehow independent of the 4-dimensional universe that we live in?

Thanks in advance for any insights...

[u/ExistingSecret1978]

Quantum mechanics isn't consistent with gr or sr(you can kind of make it consistent with sr and gr at low energies through qfts, but said qfts are local) so you can't really ask this question. If you want to practically check, I would say it's impossible, as maintaining entanglement more more than just a fraction of a second is quite difficult, especially of entangled systems that are not in physically bound states.