B Bell's theorem, QFT, and the Relativity of Simultaneity

[PeterDonis]

Does it have something to do with the idea that it doesn't matter in which order Alice or Bob make their measurements?

Go read post #48.

 

[Lynch101]

Go read post #48.

I did, that is what prompted me to ask the question.

the results of two commuting measurements are independent of the order in which they are made.

This is what made me think of two observers in a Bell test, where the order in which they make their measurements doesn't affect the outcome.

Mathematically this means the operators representing the measurements commute in the arithmetical sense, i.e., their product is the same in either order.

I was thinking this is how the above is represented mathematically.

 

[PeterDonis]

I did, that is what prompted me to ask the question.

And this...

the results of two commuting measurements are independent of the order in which they are made.

...didn't give an obvious answer to your question?

At this point, if I didn't think it highly unlikely based on your previous posts (including PMs to me), I would conclude that you were trolling and close this thread.

Please, please, please be more careful about reading posts and thinking things through before you ask questions. I believe you mean well, but you are taking up a lot of other members' time with things that you should be able to figure out for yourself.

 

[Nugatory]

it feels like there must be something I'm missing - which obviously there is.

It's not that you’re missing something, it's something that you’re including: an unnecessary (and as it turns out, incorrect) assumption about how our universe works.

I'm only familiar with the term "commute" in the sense that a x b = b x a. Does it have a different meaning in the context "Spacelike-separated observables commute"?

That’s an example of the more general notion of commutation, which is part of abstract algebra and group theory. Numbers are fairly simple but more complex mathematical objects may have more complex commutation relationships; for example if $A$ and $B$ are square matrices in general $AB\ne BA$.
Much of quantum mechanics involves mathematical objects called operators and the commutation relations between them.

 

[Lynch101]

And this...
...didn't give an obvious answer to your question?

At this point, if I didn't think it highly unlikely based on your previous posts (including PMs to me), I would conclude that you were trolling and close this thread.

Please, please, please be more careful about reading posts and thinking things through before you ask questions. I believe you mean well, but you are taking up a lot of other members' time with things that you should be able to figure out for yourself.

I completely accept that Peter. I guess I'm just overly cautious now because I've jumped to conclusions before about things and there usually turns out to be some nuance that I've missed out on.

 

[Lynch101]

It's not that you’re missing something, it's something that you’re including: an unnecessary (and as it turns out, incorrect) assumption about how our universe works.

I'll have to spend more time on this one I think. Thank you though.

That’s an example of the more general notion of commutation, which is part of abstract algebra and group theory. Numbers are fairly simple but more complex mathematical objects may have more complex commutation relationships; for example if $A$ and $B$ are square matrices in general $AB\ne BA$.
Much of quantum mechanics involves mathematical objects called operators and the commutation relations between them.

Thanks Nugatory. I'm vaguely familiar with the notion of commutation of operators in QM insofar as I've read statements about it in articles and papers but I had never really understood it. It's something I'll try brushing up on.

 

[PeterDonis]

I guess I'm just overly cautious now because I've jumped to conclusions before about things and there usually turns out to be some nuance that I've missed out on.

The correct way to address that is to not jump to conclusions. That means taking more time to think things through, read things multiple times, etc. before asking a follow up question. Only five minutes elapsed between my post #48 and your post #52. Now, based on my feedback, you know that's nowhere near enough time for you to think things over before asking a follow-up question; you need to take a lot more time, if you see something you're not sure about, to think it through first and consider if the answer might already be there in what you're reading, you just haven't seen it yet.

 

[PeterDonis]

Moderator's note: some off topic posts have been deleted, and the thread has been reopened.

 

[Elias1960]

As strange as it sounds, Bell tests can be run in which Alice and Bob run their tests BEFORE entanglement is generated. (The experimental demonstration of this would be better discussed in a separate thread.) So clearly, the order of events has nothing to do with the QM predictions.

On the other hand, it does seem to violate our world view of causality.

This is an example of what I reject as misleading popular explanations of delayed choice, erasure and similar experiment.

These are all standard QM examples, nothing extraordinary happens if one does not formulate all this is a strange, mystical way, and, of course, there is no conflict with causality at all. Why? Because we have a causal deterministic interpretation of QM, namely dBB. And in dBB, classical causality holds. In a relativistic context, it holds only in some preferred frame, but this is classical causality too.

 

[DrChinese]

This is an example of what I reject as misleading popular explanations of delayed choice, erasure and similar experiment.

These are all standard QM examples, nothing extraordinary happens if one does not formulate all this is a strange, mystical way, and, of course, there is no conflict with causality at all. Why? Because we have a causal deterministic interpretation of QM, namely dBB. And in dBB, classical causality holds. In a relativistic context, it holds only in some preferred frame, but this is classical causality too.

There is nothing misleading about this example. You can entangle particles that have never existed in a common light cone AFTER the fact. In fact you can entangle particles that never existed at the same time. And you can do that at a time when neither existed. And yes, this is standard QM and I don't consider it mystical - just a counterexample when some folks try to come up with classical explanations for certain quantum behaviors.

On the other hand, dBB is a viable interpretation of QM that lacks classical causality despite what you say. Obviously, there are FTL effects present which remove what is usually considered the classical element. Not sure why you would claim otherwise. The whole point of dBB is that its non-locality is manifest.

 

[Elias1960]

On the other hand, dBB is a viable interpretation of QM that lacks classical causality despite what you say. Obviously, there are FTL effects present which remove what is usually considered the classical element. Not sure why you would claim otherwise. The whole point of dBB is that its non-locality is manifest.

No. There is no lack of classical causality in dBB. There is no Einstein locality in dBB, but classical causality in a preferred frame.

 

[PeterDonis]

classical causality

What is your definition of "classical causality"?

 

[DrChinese]

No. There is no lack of classical causality in dBB. There is no Einstein locality in dBB, but classical causality in a preferred frame.

When an action here affects an outcome there (and vice versa), that is not "classical causality" in my book since it is quite obviously the "out" needed a la Bell. It is causal/deterministic, as you say, and locality fails. To use Bell's words, it has a "grossly nonlocal structure". I won't even begin to discuss the issue of preferred frames in dBB, as that is entirely different discussion and belongs in a different thread.

At this point we are arguing about the definition of a word ("classical"), and I doubt we gain anything from tripping down that path.

 

[Elias1960]

What is your definition of "classical causality"?

Causality as used in classical, pre-relativistic physics. Where Newtonian mechanics, despite its action at a distance, is nonetheless considered causal. The cause has to precede the effect in Newtonian absolute time. Reichenbach's common cause principle holds.

When an action here affects an outcome there (and vice versa), that is not "classical causality" in my book since it is quite obviously the "out" needed a la Bell. It is causal/deterministic, as you say, and locality fails. To use Bell's words, it has a "grossly nonlocal structure". I won't even begin to discuss the issue of preferred frames in dBB, as that is entirely different discussion and belongs in a different thread.

At this point we are arguing about the definition of a word ("classical"), and I doubt we gain anything from tripping down that path.

The first sentence simply does not make sense to me. I don't see any issue of a preferred frame in dBB, it is quite obvious that if a preferred frame is allowed, dBB can be defined so that it will be causal, deterministic and nonlocal in the absolute time of the preferred frame.

So I don't understand the problems you have with the notion of classical causality, simply because I don't see any different notions of classical causality which could be confused.

 

[PeterDonis]

Causality as used in classical, pre-relativistic physics.

Ok, that makes your position clearer.

I don't see any different notions of classical causality which could be confused.

The term "classical" is often used to include relativity. Those who prefer such usage (which includes me) will certainly have a different notion of "classical causality" from yours, since in relativity causality is limited to within the light cone.