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What is the speed at which an entangled particles match change of state/spin? Is it instantaneous?
“Does the state change of entangled electrons occur instantaneously or at the speed of light? I.e, if two electrons are entangled and you measure the state of one electron, will the other electron change to a corresponding state instantaneously?” Built into this question is the presumption that a measurement on one electron will “change” the other. The measurement on one electron will certainly tell you something about the other … but change it? There’s a basic problem here in that, in special relativity, there is no concept of “first” when we talk about the order in which space-like separated events occur. “Space-like separated” mean the events are so far separated in space, and are so close in time, that you would have to travel faster than light to be at both. In some frames of reference, one of the events happens at an earlier time; in other frames of reference, the other event happens at an earlier time. So, when you ask, does the first measurement change the results of the second—well, there is no such thing as the “first” measurement. If I’ve convinced you that, instead, that the measurement results on widely separated correlated electrons are predetermined—well, that’s not happening either. The bottom line is that no one can answer your question(s) because no one understands exactly what's going on—that is, why correlated quantum states (which are actually separated parts of the same initial quantum state) behave as t do. There’s a good experiment that demonstrates the behavior (Bell’s Test), but there’s no experiment that sheds light on what's happening under the hood. No one said that the Book of Physics is a finished volume.
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As for this being the Big Bang—well, it is, but it's also not. In the beginning, the quantum states were not actually separated (which is why we are not in what we call the Big Bang); but, at some point in time, they were separated—so the beginning of the test is before the measurement, but it's also after the measurement (which means that the results are determined by the results of both processes). The fact that we call this a Big Bang doesn’t make it a Big Bang. So, as far as the Big Bang is concerned —at least, to your mind—this is still a matter of interpretation. There’s another related question which could be put to you: How much time does it take an electron to reach two positions? This is more in-depth than the one above, and has nothing to do with the question.