Does causality become relative in spacelike-separated entanglement measurements?

[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.

 

[Matterwave]

Relativity gives casual structure based on light cones. One must be quite careful in assigning "reality" to global planes of simultaneity based on "frames of reference".

What I mean is the points A and B in spacetime are spacelike separated. This space like separation is an invariant geometrical fact and is preserved in all frames of reference.

Any frame of reference will say "A and B are spacelike separated" and there's not necessarily a fact of the matter that one came before another or not. There is *no causal relation* between A and B in SR.

If you insist that a plane of simultaneity is real and global (i.e. it's not an artifact of your chosen coordinate system) then you immediately run into the Andromeda paradox.

My take away (and this might not be universally agreed upon) from my understanding of SR and GR is that what is "real" within those theories are the coordinate-independent geometrical facts. And there, the only thing we can say about A and B are that they are causally disconnected.

Maybe the following quote helps:

That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity.

— David Mermin, It's About Time

So I would say, the precise statement can be made: entanglement allows correlations in space like separated events. Those correlations are stronger than can be explained by any local hidden variable theory (Bell's theorem).

Statements such as A precedes B in frame K or B precedes A in frame K' are imprecise at best and at worst are pure artifacts of holding on too tightly to the reality of coordinate systems (such is my view).

 

[jeffn1]

I found this thread when I was considering whether there is something more than correlations to entangled particles.
I think we know when we measure/detect the spin of a local particle, we then immediately know what the spin will be of the nonlocal (e.g., a galaxy away!) entangled particle.
We also know that nothing is seen to happen to the nonlocal entangled particle when the local particle is measured/detected. (We only confirm the spin when the nonlocal particle is measured/detected).
And we know that information cannot be sent faster than the speed of light even with regard to entangled particles. This point has been discussed a lot.
But, it does some like the measurement/detection of the local entangled particle does "affect" the nonlocal particle.
"But for" the measurement/detection of the local particle, it seems to me the spin of the nonlocal particle would not necessary be the opposite of the local particle.
In this way, entangled particles seem different than the proverbial pair of gloves, where we "know" the other (nonlocal) glove is left-handed if the local glove is right-handed.
It seems like the local act of "detection/measurement" does "affect" the nonlocal particle.
Further, it does seem that the effect on the nonlocal particle is (nearly?) instantaneous, so the measurement/detection of the nonlocal particle immediately affects the spin of the nonlocal particle faster than the speed of light.
(I have read concepts about how the "light cone" plays a part in this. I am still trying to get a better understanding of that.)

 

[PeterDonis]

when we measure/detect the spin of a local particle, we then immediately know what the spin will be of the nonlocal (e.g., a galaxy away!) entangled particle.

Only if we measure both spins in the same direction. (And even that ignores the difficulty of how we can ensure that we are measuring them in the same direction when they are a galaxy apart.)

If we measure the spins in different directions, then knowing one result only gives us probabilities for possible results on the other.

it does some like the measurement/detection of the local entangled particle does "affect" the nonlocal particle.

In the sense that a local hidden variable model, where each particle just carries "hidden variables" that were set at the source, is ruled out, yes, since such a model cannot produce violations of the Bell inequalities, but we know experimentally (and of course from the theoretical predictions of QM) that the Bell inequalities are violated in reality.

it does seem that the effect on the nonlocal particle is (nearly?) instantaneous

This is highly interpretation dependent, and should be discussed in a separate thread in the interpretations subforum if you want to go into it further.

 

[jeffn1]

Thank you!

 

[jeffn1]

If it is okay, I would like to start this topic in the interpretation subforum to read the comments of the board members.

Also, while I am at it, thank you for this board. I feel fortunate to be able to "peek in" at physicists really working out (through experiments, etc.) how physics works at its most fundamental level (as far as we are in the process of figuring it out).

 

[PeroK]

If it is okay, I would like to start this topic in the interpretation subforum to read the comments of the board members.

Also, while I am at it, thank you for this board. I feel fortunate to be able to "peek in" at physicists really working out (through experiments, etc.) how physics works at its most fundamental level (as far as we are in the process of figuring it out).

There are two responses to QM and quantum entanglement in particular. The first is to try to fit QM into an a priori view of physics, where QM appears to do the impossible.

The other is to assume that QM is telling us something new, that we never thought possible. And to accept that the workings of the universe are harder to conceive than we would like.

 

[jeffn1]

FWIW, I tend to subscribe to Art Hobson's view (although, as I understand it there are details to be worked out): Quantum Fields are nonlocal (and, apparently, not subject to the limits of GR). It is pretty amazing. Local hidden variables seem to have been ruled out and Many Worlds is simply too fantastical for me if there are other options (sorry, not trying to trigger arguments, just my opinion for what its worth (not too much)).

(Maybe not just Art Hobson's view (e.g., Bohmian mechanics? Still a work in progress.....)).