Undergrad Issues on notation and concept of entanglement

[vanhees71]

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.

 

[AndreiB]

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?

 

[vanhees71]

If local relativistic QFT describes the experiment, then P2 is excluded due to P1.

 

[AndreiB]

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?

 

[vanhees71]

I still don't understand what you need to prove.

 

[weirdoguy]

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.

 

[AndreiB]

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?

 

[AndreiB]

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?

 

[vanhees71]

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.

 

[AndreiB]

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.

 

[Demystifier]

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.

 

[martinbn]

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.

 

[vanhees71]

Here's a very good online resource

https://www.damtp.cam.ac.uk/user/tong/qft.html

 

[Demystifier]

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.

 

[Demystifier]

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.

 

[martinbn]

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.

 

[AndreiB]

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?

 

[Demystifier]

you put realism in the particle trajectories

Exactly, and that's why it's called realism, not antirealism.

 

[Demystifier]

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.

 

[martinbn]

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.

 

[AndreiB]

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?

 

[vanhees71]

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.

 

[AndreiB]

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.

 

[Demystifier]

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.

 

[Demystifier]

But you also need nonexistant things.

Which ones? I don't need mediator.

 

[AndreiB]

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.

 

[Demystifier]

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.

 

[vanhees71]

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.

 

[martinbn]

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.

 

[Demystifier]

You also need something (the action) that is there

Define "action"!