Acording to quantum mechanics, when you observ…

Acording to quantum mechanics, when you observe one of a pair of entangled particles, the other is instantly in the same state, regardless of the separation of the two. What if one of the entabed particles movee at close to the speed of light, but not the other. The two particles would then be in different "times" with resepct to each other. If you did the observation of one or the other particle, wouldn't that mean that somehow the particles are connected through time as well?

So first off, when you have an entangled pair, when you observe one, the other is instantly in the opposite state, not the same one. Regardless of when or where you break the entanglement, the “breaking” is instantaneous. In relativity, objects are separated in spacetime, so you can separate them through space, time, or a combination of both; it doesn’t matter. The entanglement is still there until it’s broken.

So, the tl;dr version is: sure, they’re connected through time as well.