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

[PeterDonis]

Relativity of simultaneity still plays a role though, right?

QFT generally does not even use inertial frames and the accompanying concepts like relativity of simultaneity. It tends to use a formalism in which everything is written in invariant form, i.e., without requiring any choice of frame at all. It uses invariant concepts like spacelike separation of events, but not frame-dependent ones like simultaneity.

 

[DrChinese]

Of course I don't know of any Bell test experiment that concludes differently, because, as I've already agreed, there isn't one.

I'm just pointing out that, for the case in which the measurement events are not spacelike separated, the property that the order of the measurements does not affect the results is not a general property of any QM experiment whatever; it is only a property of the particular class of experiments that we are calling "Bell tests".

I'm with you on this all the way.

I sort of thought from the title of the thread that we were speaking of Bell as the background. It is something of a special case where time ordering of events is not a factor to the statistical predictions, and neither is reference frame (at least in traditional spin versions).

 

[DrChinese]

I have been going through some literature on Bell tests but I haven't heard that question before, about whether or not causality applies in physics.

A subject better discussed in the Quantum Interpretations subforum. You will find that this subject stirs up some very strong opinions. After all, QM only makes statistical predictions. And there is no currently known theoretical angle to making a specific prediction in a single instance. (Ignoring interpretations...)

 

[Lynch101]

A subject better discussed in the Quantum Interpretations subforum. You will find that this subject stirs up some very strong opinions. After all, QM only makes statistical predictions. And there is no currently known theoretical angle to making a specific prediction in a single instance. (Ignoring interpretations...)

hahaha thanks Dr. I'll check that out for sure!

 

[vanhees71]

Oh, perfect. I'll do that. Thank you!
As in, QFT doesn't share the determinism of classic relativity?

Relativity of simultaneity still plays a role though, right? Presumably that is a characteristic feature of Minkowski spacetime?

QFT as any quantum theory is not deterministic but probabilistic. It's still causal though by construction.

The difference between classical and quantum descriptions of reality are all in the notion of what's called a "state". In classical physics you have determinism, and the exact knowledge about the state of the system at one time implies the knowledge about the values of all possible observables you can measure on this system at this time and, due to the equations of motion, also for all later times. On the fundamental level you have a very strong version of determinism and causality, i.e., it's sufficient to now the state exactly at one time, and then you know, through solving the equations of motion, the state exactly at any later time (causality), and to know the exact state of the system implies that all possible observable quantities have well-defined values (determinism).

In QT the notion of "state" is different. You still have causality (even in the strong form of locality in time), i.e., knowing the exact state of a system at one time through the equations of motion implies to know the exact state of the system at any later time too.

Knowing the exact state, however, does not imply that all observables take determined values. The only thing you know when knowing the exact quantum state are probabilities for the outcome of measurements of any observable of the system.

In relativistic physics causality means that an event can only be causally connected to another event if they are time-like (or light-like) separated. This is incorporated in all realistic QFTs in terms of the microcausality condition, which means that the Hamilton-density operator has to commute with all local observables at space-like distances of their mutual arguments. This ensures Poincare invariance, causality, and unitarity of the S-matrix as well as the linked-cluster principle. In this sense this type of local relativistic QFTs incorporates the causality structure of (special-)relativistic spacetime, and that's why there is no discrepancy between inseparability (described by entanglement of far-distant parts of quantum systems in Bell experiments) and relativistic causality, and that's also verified in a whole plethora of very accurate and fascinating Bell-test experiments.

 

[PeterDonis]

You keep confusing simultaneity with "relativity of simultaneity"

No, you keep confusing frame-dependent concepts with frame-independent ones. I have already said that both "simultaneity" and "relativity of simultaneity" are frame-dependent concepts in relativity.

You have just earned yourself a thread ban since this subthread is a hijack and is adding no value to the primary discussion.

 

[Lynch101]

The purpose of starting this thread was to try to understand how QFT incorporated relativity (or the relativity of simultaneity - RoS). To my mind there seemed to be conflict, but that's because I was working on the mistaken assumption that relativity or RoS necessitated the Block Universe. I started a different thread on that particular question and I can see that the BU is not the only possible interpretation of relativity.

That discussion has left me with a slightly different question about Bell tests, QFT, and the Block Universe. Would the BU - not RoS - be in conflict with Bell tests?p.s. I'm keen to avoid another discussion on the BU, I'm just left with this residual question.

 

[PeterDonis]

Would the BU - not RoS - be in conflict with Bell tests?

This is an interpretation question and belongs in the interpretations forum. Please start a separate thread there.

 

[Lynch101]

This is an interpretation question and belongs in the interpretations forum. Please start a separate thread there.

perfect. Will do. Thanks Peter.

 

[bhobba]

The point is that "now" at some other location has no physical significance.

I think I know what you mean. But just a question - what about slow clock transport to the other location?

Thanks
Bill

 

[PeterDonis]

what about slow clock transport to the other location?

You don't even need to do that; just transport a clock to the other location any old way, and after it arrives there, Einstein synchronize it with a clock at your location.

The point is that even after you've done all that, the definition of "now" you obtain (events at the two locations with the same readings on the two clocks) only tells you about how you synchronized the clocks. It doesn't tell you anything about the laws of physics or the causal relationships between events (other than that the two "now" events have to be spacelike separated).

 

[bhobba]

I was under the impression that QFT fully incorporated Special Relativity, no?

It certainly does. But pedagogically best to learn standard QM first. The principal of locality in QFT is analogous to the so called cluster decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

You might like to think about Bell using that principle and see what conclusion you reach - hint if correlated systems must be removed from the principle for it to make sense what does that say about Bell?

Thanks
Bill

 

[Lynch101]

The point is that "now" at some other location has no physical significance. To take my favourite example (you may have heard it before!).

Bhobba's comment above reminded me of this and it is something I struggle to interpret.

I understand the idea that we cannot know what events are happening "now" at some other location, but we can know that there must be some events happening "now" at some other location. I guess, I wonder what "no physcial significance" means in that context.

Sometimes people conclude that, such a statement amounts to solipsism but I don't event think it would matter if it was solipsistic. If it was solipsistic, then the issue remains unchanged. Instead of talking about "somewhere else" in an external Universe, we would be talking about "somewhere else" in the Universe [which is the mental projection in someone's mind].

 

[Nugatory]

... but we can know that there must be some events happening "now" at some other location.

That statement is true only if we have defined “now” to mean “has been assigned, on the basis of some arbitrarily chosen convention, a time coordinate less then the time coordinate of where are”; and with that definition of "now", there can be no physical significance to saying that a remote event has happened "now".

You are free to propose and use some other definition of "now", one that does allow us to "know that there are events happening 'now' at some other location". However:
1) It's unnecessary. There are things that we can say about remote events that do have physical significance. These are sufficient to explain everything that we've ever experienced without resort to solipsism, and do not require any stronger concept of "now".
2) You'll also have to describe how that definition can be applied, at least in principle, to spacelike-separated measurements. That's a necessary but not sufficient condition to have the physically meaningful definition that's the whole point of the exercise.

Most often people first encounter these issues in special relativity or when they see non-relativistic treatments of entangled particles. That can be confusing because everything is wrapped up in observers and reference frames and relativity of simultaneity - it's easy to feel as if this all some sort of sleight-of-hand designed to obscure the simple concept that either something has happened or it hasn't. Relativistic quantum field theory sweeps all of this away with a single statement: "Spacelike-separated observables commute", and that's the one-line summary and tl;dr for a thread that has the words "simultaneity", "QFT", and "Bell's theorem" in the title.

 

[Lynch101]

That statement is true only if we have defined “now” to mean “has been assigned, on the basis of some arbitrarily chosen convention, a time coordinate less then the time coordinate of where are”; and with that definition of "now", there can be no physical significance to saying that a remote event has happened "now".

You are free to propose and use some other definition of "now", one that does allow us to "know that there are events happening 'now' at some other location". However:
1) It's unnecessary. There are things that we can say about remote events that do have physical significance. These are sufficient to explain everything that we've ever experienced without resort to solipsism, and do not require any stronger concept of "now".

2) You'll also have to describe how that definition can be applied, at least in principle, to spacelike-separated measurements. That's a necessary but not sufficient condition to have the physically meaningful definition that's the whole point of the exercise.

Most often people first encounter these issues in special relativity or when they see non-relativistic treatments of entangled particles. That can be confusing because everything is wrapped up in observers and reference frames and relativity of simultaneity - it's easy to feel as if this all some sort of sleight-of-hand designed to obscure the simple concept that either something has happened or it hasn't. Relativistic quantum field theory sweeps all of this away with a single statement: "Spacelike-separated observables commute", and that's the one-line summary and tl;dr for a thread that has the words "simultaneity", "QFT", and "Bell's theorem" in the title.

Thanks Nugatory. I also first encountered this when I started to learn about special relativity and it was something that jarred for quite a while and obviously still does. Not to the extent that I would question the validity of it just that it feels like there must be something I'm missing - which obviously there is. To me it makes senes to ask the question, what is happening "now" in a distant region of the Universe, even if the answer is "we can't know, but there must be something".

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"?

 

[DrChinese]

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"?

What I believe they WILL agree with me on is the following statement:

No local hidden variable theory can explain Bell test results. Said another way: QFT is not a local hidden variable theory.

 

[Lynch101]

What I believe they WILL agree with me on is the following statement, which is no way in conflict with theirs:

No local hidden variable theory can explain Bell test results. Said another way: QFT is not a local hidden variable theory.

Thank you Dr.Chinese. I am familiar with that much, the idea that Bell's theorem rules out local hidden variables.

Is it to the idea of hidden variables that their statement, about the commutation of spacelike-separated variables ,refers?

 

[PeterDonis]

Is it to the idea of hidden variables that their statement, about the commutation of spacelike-separated variables ,refers?

No. The statement that spacelike separated measurements commute is a mathematical fact about QFT. It has nothing to do with any hidden variable theory.

 

[PeterDonis]

What I believe they WILL agree with me on is the following statement

Yes.

 

[Lynch101]

No. The statement that spacelike separated measurements commute is a mathematical fact about QFT. It has nothing to do with any hidden variable theory.

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

 

[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.