Issues on notation and concept of entanglement

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Discussion Overview

The discussion revolves around the notation and conceptual understanding of entanglement, particularly in relation to the singlet state of entangled particles. Participants explore the implications of measurement outcomes versus wavefunctions, the interpretation of entangled states, and the effects of measurement angles on the results. The conversation touches on theoretical and conceptual aspects of quantum mechanics, including the challenges posed by popular media representations of entanglement.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants express concern that popular media oversimplifies entanglement by suggesting that if one particle is measured as spin-up, the other must be spin-down, without addressing measurement angles.
  • There is a discussion about whether the singlet state notation describes measurement outcomes or wavefunctions, with some arguing it represents both.
  • Participants note that if Alice and Bob's measurement angles are not aligned, the outcomes are not definitively correlated, as Bob may measure either spin-up or spin-down.
  • Some argue that the quantum state provides probabilities for measurement outcomes but does not imply that particles have definite properties prior to measurement.
  • There is a distinction made between statements that assert actual properties of particles versus those that describe expected outcomes based on measurements.
  • One participant highlights the ambiguity in interpreting the mathematical formalism of entanglement, questioning whether it pertains to measurement outcomes or ontological states.
  • Concerns are raised about the implications of spacelike separation of measurements and the notion of instant interaction, with references to the Bell theorem and differing interpretations among experts.

Areas of Agreement / Disagreement

Participants express a range of views, with no clear consensus on the interpretation of entanglement or the implications of measurement angles. Some agree on the probabilistic nature of outcomes, while others emphasize the ambiguity in the interpretation of the mathematical formalism.

Contextual Notes

The discussion reveals limitations in understanding the implications of measurement angles and the nature of entangled states. Participants acknowledge that the singlet state notation is more general than specific measurement scenarios, but there is uncertainty about how to interpret this generality in relation to actual measurements.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in understanding the nuances of entanglement, measurement theory, and the implications of different interpretations of quantum states.

  • #31
What do you have to prove? If all operators representing local observables (which inculdes the Hamilton density of the theory) commute at space-like separation of their arguments there cannot be any faster-than-light influence between events. That's why one envokes this "microcausality" property in the first place, implying the existence of antimatter, the spin-statistics relation, and CPT symmetry, all of which are in accordance with (very accurate) observations.
 
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  • #32
vanhees71 said:
What do you have to prove? If all operators representing local observables (which inculdes the Hamilton density of the theory) commute at space-like separation of their arguments there cannot be any faster-than-light influence between events.
I do not understand this argument. You have:

P1. all operators representing local observables commute at space-like separation.
P2. The measurement at A caused B.

Where is the contradiction?
 
  • #33
If local relativistic QFT describes the experiment, then P2 is excluded due to P1.
 
  • #34
vanhees71 said:
If local relativistic QFT describes the experiment, then P2 is excluded due to P1.
You assert that, you did not prove it. What is the relationship between commutativity and causation?
 
  • #35
I still don't understand what you need to prove.
 
  • #36
AndreiB said:
You assert that, you did not prove it.

Isn't that discussed in almost every textbook on QFT? Peskin & Shroeder for example, somewher in the first few chapter.
 
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  • #37
vanhees71 said:
I still don't understand what you need to prove.
P1 speaks about commutativity, P2 about causation. In order to arrive at a contradiction you need to reformulate P1 so that it also speaks about causation, or reformulate P2 so that it speaks about commutativity. You did not do that.

As far as I understand commutativity means that the order of measurements do not matter (statistically, since the theory is not deterministic). Why is this incompatible with A causing B or B causing A?
 
  • #38
weirdoguy said:
Isn't that discussed in almost every textbook on QFT? Peskin & Shroeder for example, somewher in the first few chapter.
Can you provide a reference?
 
  • #39
Just check a good textbook on relativistic QFT. The most lucid treatment of all these fundamental issues is in Weinberg, Quantum Theory of Fields, vol. 1.
 
  • #40
vanhees71 said:
Just check a good textbook on relativistic QFT. The most lucid treatment of all these fundamental issues is in Weinberg, Quantum Theory of Fields, vol. 1.
Can you provide a relevant quote? I do not have that book.
 
  • #41
martinbn said:
If you consider interaction without a mediator, which cannot be detected in principle, you are adopting a very strong form of antirealism.
No I'm not. If I consider something that cannot be detected, it means that I believe that things exist even when we don't measure them, which is the exact opposite of antirealism.
 
  • #42
Demystifier said:
No I'm not. If I consider something that cannot be detected, it means that I believe that things exist even when we don't measure them, which is the exact opposite of antirealism.
But you said that the mediator does not exist. As to the action it is not that you believe that it exist even when you cannot meausre it. It cannot be detected even if you do measurements of any sort.
 
  • #44
martinbn said:
But you said that the mediator does not exist. As to the action it is not that you believe that it exist even when you cannot meausre it. It cannot be detected even if you do measurements of any sort.
So what? In Newtonian gravity planets exist, even though the mediator doesn't. In Bohmian mechanics particle positions exist, even though the mediator doesn't.
 
  • #45
AndreiB said:
Can you provide a relevant quote? I do not have that book.
Here is the relevant part of Weinberg. Whether it confirms the claim of @vanhees71 or not, decide by yourself.

weinberg-I-198.jpeg
 
  • #46
Demystifier said:
So what? In Newtonian gravity planets exist, even though the mediator doesn't. In Bohmian mechanics particle positions exist, even though the mediator doesn't.
It is not the same. In the Newtonian gravity if Alice does something, Bob can detect the influence on his system. In QM you cannot. In your preferred interpretation you put realism in the particle trajectories and posit undetectable action with nonexistent mediator.
 
  • #47
Demystifier said:
Here is the relevant part of Weinberg. Whether it confirms the claim of @vanhees71 or not, decide by yourself.
Thanks! Do you know what Weinberg means by "a measurement at point x should not be able to interfere with a measurement at point y"? What would an interference look like?
 
  • #48
martinbn said:
you put realism in the particle trajectories
Exactly, and that's why it's called realism, not antirealism.
 
  • #49
AndreiB said:
Thanks! Do you know what Weinberg means by "a measurement at point x should not be able to interfere with a measurement at point y"? What would an interference look like?
He doesn't mean interference of probability amplitudes. He means interference in the sense of mutual influence.

It really means the following. Suppose that two quantum observables, A and B, commute. Furthermore, suppose that Alice measured A, that Bob knows that Alice measured it, but that he does not know the result of her measurement. Then, from this knowledge, Bob cannot conclude anything new about the probabilities of measurement outcomes of B.
 
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  • #50
Demystifier said:
Exactly, and that's why it's called realism, not antirealism.
Of course, that is the standard terminology. But you also need nonexistant things. So you are just shifting where the antirealism will be. Some kind of Heisenberg cut for antirealism. To me your interpratation is equaliy unpalitable because it has antirealistic elements as well.
 
  • #51
Demystifier said:
It really means the following. Suppose that two quantum observables, A and B, commute. Furthermore, suppose that Alice measured A, that Bob knows that Alice measured it, but that he does not know the result of her measurement. Then, from this knowledge, Bob cannot conclude anything new about the probabilities of measurement outcomes of B.
This seems compatible with A causing B, right?
 
  • #52
No, it's not necessarily compatible with A causing B. An event at B can be causally influenced by A only if the event at B is in some future lightcome of an event at A. This holds for all special-relativistic dynamical models including standard local relativistic QFT.
 
  • #53
vanhees71 said:
An event at B can be causally influenced by A only if the event at B is in some future lightcome of an event at A.
How does this follow from what Weinberg says? There is no talk there about lightcones.
 
  • #54
AndreiB said:
This seems compatible with A causing B, right?
It depends on what one means by "causing", but in the sense you mean it I would agree. Of course, adherents of orthodox QM by "causing" mean something else.
 
  • #55
martinbn said:
But you also need nonexistant things.
Which ones? I don't need mediator.
 
  • #56
Demystifier said:
It depends on what one means by "causing", but in the sense you mean it I would agree. Of course, adherents of orthodox QM by "causing" mean something else.
By causing I mean that the spin at B is instantly forced to take the opposite value of A.
 
  • #57
AndreiB said:
By causing I mean that the spin at B is instantly forced to take the opposite value of A.
Yes, in that sense I agree.
 
  • #58
Even if you agree with that, the cause is not a faster-than-light interaction, at least not within a local relativistic QFT, but it's due to the correlation described by entanglement.
 
  • #59
Demystifier said:
Which ones? I don't need mediator.
And CI doesn't need values for observables that have not been measured. It is exactly the same. You also need something (the action) that is there, but no way you can tell even in principle, it is like it isn't there.
 
  • #60
martinbn said:
You also need something (the action) that is there
Define "action"!
 
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