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I am failing to understand how, if entanglement does not violate relativity, then reality can still be not super deterministic.

For the purposes of this question, let’s assume that the many worlds theory is false. Let’s also assume that there is no non local deterministic theory that explains QM, such as bohmian mechanics, since it explicitly violates relativity and posits non local influences between entangled particles.

The “standard” interpretation now says that there are “non local” correlations but without relativity being violated, and thus all influences are local. But if all influences are local, then how is this any different from superdeterminism where you posit hidden variables that predict both the measurement outcomes and measurement choices in such a way that they always result in the correlations predicted by QM, without any faster than light influences?

Unless you deny an objective reality (which seems to be against the very foundations of the scientific method), it seems that there is no way out except superdeterminism. This answer here also details why denying reality still does not save locality. And yet, superdeterminism is considered wildly implausible, but “relativistic” explanations of entanglement are not considered implausible. What’s really the difference? Without non local interactions between particles, it seems very “conspiratorial” for particles to still be correlated to each other even if they were separated by light years, the same way it seems conspiratorial in superdeterminism.

Syed
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I am failing to understand how, if entanglement does not violate relativity, then reality can still be not super deterministic.

What happens when particles are entangled is that they gain a non-local correlation (as you note in the question). This doesn't violate relativity, not because of superdeterminism or because of anything else, but just because no information is communicated during entanglement breaking.

When you break entanglement with a measurement, the results are 100% correlated, but no local observer can know this without directly observing the state of the distant particle, which always happens slower than light. Hence, no FTL communication.

No matter the Hamiltonian, no matter anything, you cannot know that there is a correlation (i.e. you cannot know if you even successfully got the entangled particle to the distant observer) without asking the distant observer what they saw when they measure their particle. The correlation only exists once both particles' measurements are collected in one place. Before that, neither party knows that the correlation exists because they only have half the data.

In fact, since entanglement occurs locally between particles (or, in exotic cases, mediated by other particles), you can't get the entangled particles apart from each other faster than light, so even if you somehow could transfer information through them FTL, you still wouldn't technically be sending anything along spacelike curves.

Therefore, on at least three different levels, causality and thus relativity are not violated.

(Note that at no point I invoked relativity as an explanation for no-signalling in this answer.)

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