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According to relativity, a future event X in one inertial frame lies in the present of another inertial frame, assume for example that the event is the decay of a radioactive atom, doesn't this imply that whatever laws of physics we use to describe such decay must be deterministic? After all, if the decay already happened in the other frame, then it means that the result of this event must already be decided before I measure the atom, but doesn't this contradict quanutm mechanics?

EDIT: By "deterministic" I don't mean that the future state of the particle can be determined with certainty, I mean the fact that the quantum state of the particle cannot fully determine the dynamics of the particle

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    $\begingroup$ Where is this different from any discussion of the Bell-type (e.g. Bohm-EPR set up) experiments? $\endgroup$ Commented yesterday
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    $\begingroup$ I don't know, I guess, that's why I asked $\endgroup$ Commented yesterday

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You are drawing the wrong conclusions from the relativity of simultaneity. If event b happens after event a on my world line, and I am at event a, then event b has not yet happened to me. The fact that event b might be in the past of some other event in some other frame of reference is irrelevant, and does not mean that event b has ‘already happened’ when I am at event a.

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  • $\begingroup$ The question "when does event B happen" is frame dependent, so you cannot say absolutely that event B didn't happen when you were at A, different observers will disagree about what you said. Event B didn't happen while you were at A, but it did happen for another observer, so the existence of the event in space-time is fixed isn't it? $\endgroup$ Commented 23 hours ago
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    $\begingroup$ No! The order of events on a world line is not frame dependent. When I am celebrating my 67th birthday I am not celebrating my 68th. That is true in every frame. $\endgroup$ Commented 23 hours ago
  • $\begingroup$ the order is invariant but the particular time at which the two events happen is dependent, right? isn't your 68th birthday a single event in spacetime on which different observers will disagree on when it happens? when you celebrate the 67th birthday, that event didn't yet happen but this is only true in your frame, right? $\endgroup$ Commented 23 hours ago
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    $\begingroup$ No, you are not thinking it through. My 68th birthday happens on my 68th birthday, and always after my 67th, regardless of what frame you adopt. Different observers will say my 68th birthday is simultaneous with other events happening elsewhere, and will allocate different time coordinates to it, but they will all agree it is not taking place on my 67th birthday. $\endgroup$ Commented 22 hours ago
  • $\begingroup$ @Davyz2 Don't forget that if events A & B are timelike separated in one frame then they are timelike separated in every frame, and have the same order in every frame. Frame change can only affect the ordering of events with spacelike separation. See physics.stackexchange.com/a/844818/123208 $\endgroup$ Commented 14 hours ago
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You are correct that it takes careful reasoning to combine indeterminism with relativity. That it can be done is argued here:

Del Santo, N. F.; Gisin: The relativity of indeterminacy. Entropy 23, 1326 (2021) https://doi.org/10.3390/e23101326

This issue is not just about quantum theory. It arises in any indeterministic model. (Classical physics can be either deterministic or indeterministic, depending on how it is formulated).

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After all, if the decay already happened in the other frame, then it means that the result of this event must already be decided before I measure the atom, but doesn't this contradict quantum mechanics?

I am only addressing the last part of your question.

There is nothing in QM that is contradicted by special relativity. It is possible the reverse is true (something in relativity is contradicted by QM), because of well documented experiments demonstrating quantum nonlocality. However that is a matter of interpretation.

And in fact, orthodox QM does not even make a statement about time ordering in entanglement experiments. @TobiasFunke alluded to this in a comment above. In spin measurements on entangled systems, it is only the relative angle settings that contribute to the quantum mechanical predictions. Their distance apart and order are not a factor. See for example:

Violation of Bell's inequality under strict Einstein locality conditions

Further: Delayed Choice versions using swapping explicitly attempt to defy the concept of pure forward in time determinism. You can accept or reject their clear conclusions based on your preferred interpretation, but QM itself is clearly silent. See for example:

Experimental delayed-choice entanglement swapping

So there is nothing to contradict. From another seminal paper on entanglement swapping:

”Therefore, this result indicate that the time ordering of the detection events has no influence on the results and strengthens the argument of A. Peres: this paradox does not arise if the correctness of quantum mechanics is firmly believed.”

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You don't need relativity for this. I don't need relativity to convince myself that the sentence "An asteroid hits the earth in the year 3000" is either true or false (though I don't know which), and that the truth value of this sentence will be the same in the years 3000 and 4000 as it is today. None of that tells me anything about whether the sentence's truth or falsity is deducible from things I can observe today; that is, it tells me nothing about determinism.

Likewise, even if you've got a particle in a box that will decay or not decay tomorrow for purely random reasons, it is either already true that the particle will decay or already false that the particle will decay. Again, no relativity required. And again, no implications for determinism.

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    $\begingroup$ When you say "it is either already true that the particle will decay or already false" what do you mean by that? Isn't the point of quantum mechanics that this fact is completely indeterminate before measuing the particle? How can it be "already" false or true, if the state of the particle is fundamentally not determined? $\endgroup$ Commented yesterday
  • $\begingroup$ @Davyz2: My coffee cup is either red or blue? Which is it? I claim that a) there is a right and a wrong answer to this question, b) you have no way of knowing which answer is right and which answer is wrong, and c) that these facts do not contradict each other. I don't think this bears further discussion. $\endgroup$ Commented yesterday
  • $\begingroup$ If the coffee cup is truly either red or blue, but you have no way of knowing this state, wouldn't this be an explanation in terms of hidden variables of the cup? If you say this, it means that there is an hidden variable (albeit completely unknowable) which determines the future decay of the particle isn's it? But according to quantum mechanics, isn't let's say the spin of the particle fundamentally not defined until the future measurement occurs? $\endgroup$ Commented yesterday
  • $\begingroup$ The problem here would be that the future measurement already occurred in another inertial frame, so how can the first observer say that the spin of the particle is "not defined"? Something is either defined, or not defined after all, and if the laws of physics are invariant they both have to agree on one of these options $\endgroup$ Commented yesterday
  • $\begingroup$ A number of comments deleted. Knock it off, y'all. $\endgroup$ Commented 17 hours ago

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