Question about entanglement and relative causality

[Loptyur]

Hello everyone !

I am new on this forum and I am here because, while I was learning quantum mechanics, I have noticed something strange.
Indeed, if we take a pair of entangled particules, we know the measures of these two particules are correlated. But if the interval between these measures is spacelike, we cannot say which one is the first (there exists a reference frame with a particular order but there is also a reference frame with the opposite order). But in this case, the first measure establish the second one. Let's call A and B the two measures. If in some reference system we have A then B, so A implies B. But in some other reference system, we have A before B, so that B implies A. This way, can we state that causality is relative to the reference frame. We must note that it does not create any retrocausality paradox, thanks to the no-communication theorem.

Is there a problem in my reasoning ?
Is it acceptable to say that absolute causality does not exist in our world ?
Or maybe is the interpretation (the one I use here) false ? This situation is trivial with the Everett interpretation.

Thank you for filling in the gaps in my understanding of QM !

 

[PeterDonis]

the first measure establish the second one

No, that is not correct. The measurements commute--that is, their results do not depend on which one occurs first. (This has to be the case because, as you point out, the time ordering of the measurements--which one occurs first--is frame-dependent, and no actual physical result can depend on anything that is frame-dependent.) So you cannot say that either measurement "establishes" the other. All you can say is that their results are correlated in the way the entangled wave function predicts.

This way, can we state that causality is relative to the reference frame.

No, we can't, because we can't say that either measurement result causes the other. See above.

maybe is the interpretation (the one I use here) false ?

It's not clear what interpretation of QM you think you're using. But your reasoning is false as noted above.

 

[PeroK]

It's better to think of an entangled system of two particles. The particles are not independent. A measurement of either particle is a measurement of the system.

There is no causality, because the particles are part of the same system.

 

[Dale]

A then B, so A implies B. But in some other reference system, we have A before B, so that B implies A. This way, can we state that causality is relative to the reference frame.

Neither causes the other.

 

[Nugatory]

Is it acceptable to say that absolute causality does not exist in our world ?

I cannot prove that that claim is wrong, but that doesn’t mean that I have to accept it. Causality is such a useful organizing principle and so essential to my understanding of the world around us that I’m not giving it up so easily.

Cause and effect relationships are by definition asymmetrical; the relationship between spacelike-separated measurements of entangled pairs is symmetrical. That and the no-communication theorem are enough to convince me that whatever is going on isn’t a causal relationship.

Of course this invites the question, what is really going on here? And as is frustratingly often the case, QM refuses to answer that question.

 

[gentzen]

10.2.1 Causality​

Causality is an extremely important postulate for quantum theory which nevertheless has an extremely simple interpretation:

If the output of a process is discarded, it may as well have never happened.​

10.4 Historical notes and references​

[...]
Causality, although it plays a very central role in this book, was the last one to enter the picture. Its importance became clear from the information theoretic axiomatization of Chiribella et al. (2010, 2011).

Chiribella, G., D’Ariano, G. M., and Perinotti, P. 2010. Probabilistic theories with purification. Physical Review A, 81(6), 062348.
Chiribella, G., D’Ariano, G. M., and Perinotti, P. 2011. Informational derivation of quantum theory. Physical Review A, 84(1), 012311.

From
Coecke B, Kissinger A. Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press; 2017.