A question about quantum entanglement

[BadgerBadger92]

How do a pair of particles via entanglement “know” what the other particle is doing? Any help is appreciated.

 

[jeffn1]

There is no consciousness here (I would argue). The entangled particle are correlated.

I am curious about other peoples theories of how they remain correlated even when separated by billions of miles. Most of what I have read just says, they act "as one particle". But, this is not satisfying to me because typically part of one particle is proximate to the other part of the "same particle" (locality).

One thought I came up with (but, perhaps others have too) is the entangled particles retain their relationship to their underlying quantum field. As a result, they remain correlated even when separated by billions of miles.

But, if there is research into this that throws additional light, I am interested too.

 

[FactChecker]

"I think I can safely say that nobody understands quantum mechanics."
"in mathematics you don't understand things. You just get used to them.”
-- Richard Feynman

Mathematically, they are one entity. If you are given that $x^2 = 1$, then you know that there are two solutions, $1$ and $-1$. When you are told that one solution is $x_1 = -1$, you know instantly that the other solution, $x_2$, is $x_2=-1$. And the value of either $x_1$ or $x_2$ are not determined until the other is.
That is not one causing the other, and it is not a case of a "hidden variable". Simply, knowing one tells you what the other is.

 

[bhobba]

'In mathematics, you don't understand things. You just get used to them.'

Which he got from his good friend John von Neumann

The exact context and wording were 'Young man, in mathematics, you don’t understand things. You just get used to them.' John von Neumann, to Felix Smith

In answer to the original question, in Quantum Field Theory, two particles are a two-particle excitation of the field, not two single-particle excitations (which is a special case of a two-particle excitation).

Thanks
Bill

 

[jeffn1]

'In mathematics, you don't understand things. You just get used to them.'

Which he got from his good friend John von Neumann

The exact context and wording were 'Young man, in mathematics, you don’t understand things. You just get used to them.' John von Neumann, to Felix Smith

In answer to the original question, in Quantum Field Theory, two particles are a two-particle excitation of the field, not two single-particle excitations (which is a special case of a two-particle excitation).

Thanks
Bill

Bill, any additional thoughts or articles on how quantum fields may explain (non-local) entanglement would be much appreciated.

I tend to suspect this is the case. But, I have not found much literature explaining non-local entanglement by referring to QFT.

To me (non physicist enthusiast in this area), it seemed to make sense, since quantum fields are considered infinite (or about as close to infinite as we can consider in the physical universe we inhabit).

 

[bhobba]

It's a bit pricey, but the following does that and much more:

https://www.amazon.com.au/Fields-Their-Quanta-Quantum-Foundations-ebook/dp/B0DLNLLG7Y

Thanks
Bill

 

[PeterDonis]

Moderator's note: Thread moved to the QM interpretations subforum.

 

[PeterDonis]

How do a pair of particles via entanglement “know” what the other particle is doing?

Different QM interpretations give different (and incompatible) answers to this question.

 

[PeterDonis]

One thought I came up with (but, perhaps others have too) is the entangled particles retain their relationship to their underlying quantum field.

Please do not venture into personal speculation.

 

[PeterDonis]

how quantum fields may explain (non-local) entanglement

Because quantum fields are fundamentally non-local objects. Which many would say is not really an explanation, just a restatement of the problem.

This is really a QM interpretation question, and as I commented in post #8, different intepretations give different and incompatible answers.

 

[PeterDonis]

I have not found much literature explaining non-local entanglement by referring to QFT.

That's because QFT adds nothing useful to the treatment of entanglement, as far as making predictions goes, that's not already contained in the math of non-relativistic QM, and QFT mathematically is a lot more complicated.

The QM interpretation literature in general does not seem to pay any real attention to QFT, but uses non-relativistic QM as its framework. That's probably because most physicists working in the field believe that non-relativistic QM is a valid approximation to QFT for all known experiments in which entanglement is significant.

@bhobba has given references in other threads that show that that belief about approximation is not as simple as it looks. But it doesn't seem like the literature on QM interpretations and foundations has picked up on that.

 

[Roberto Pavani]

Just a small note: von Neumann was actually very interested in the foundations of QM (collapse postulate, hidden variables proof, etc.). His quote was more about developing intuition through practice, not about giving up on understanding.

 

[Peter Morgan]

For a field theory, there are, in the first instance, no particles to be entangled. The idea that each record of an event in a detector must be caused by a particle is sufficiently problematic that it ought not to be axiom #1 for QM (as a Hilbert space~a 'system', largely unchanged since von Neumann). Axiomatic forms of QFT make no such assumption, and there is a tradition of 'algebraic QM' for which the same is true.
Discussions of Bell inequalities all too often begin 'consider two particles', but Bell's article "The theory of local beables" began a tradition of field theoretical discussions, to which I contributed in JPhysA 2006, "Bell inequalities for random fields" (or on arXiv). My more recent discussions focus more on the nontrivial algebraic structure than can be found there (as in §7.2 of my AnnPhys 2020, "An algebraic approach to Koopman classical mechanics" (arXiv)), however it is still unclear to me exactly how field theoretic and algebraic considerations can best be melded.
My most recent attempt at a mixture of intuitive and formal discussion of what happens in an experiment that violates the Bell inequalities (specifically Gregor Weihs's Thesis experiment in the mid-90s) can be found in a video entry for a recent competition, "Explaining Quantum Field Theory as a Dataset&Signal Analysis formalism #CORE1" (starting at 1:21:29, for a little less than 20 minutes, slides 28-35). I believe it is essential to consider the internal degrees of freedom of the Electro-Optic modulators that enforce the detailed choice of polarization, not only the experimenters' binary choice of one of two orientations, which is natural in a field theoretic discussion but never enters into discussions of particles as causes of a violation of Bell inequalities.

I will offer below two slides from that talk for consideration. For the first slide, I emphasize in what I say that there are two reasons I particularly like Gregor's schematic of his experiment: 1) he says that the central source is a 'pump', so that instead of 'shoveling particles into the apparatus' I imagine Gregor modulating the noisy vacuum of the EM field elaborately enough that the experiment exhibits a violation of a Bell inequality; and 2) he presents explicitly what is stored in the experiment's datasets, which are exactly as one finds in the real data as I obtained them from him almost 20 years ago and for which I present a more explicit analysis than can be found elsewhere about such experiments, from the ground up, so to speak.
If we think in terms of particles, there are some aspects that fit so badly that the analogy is a mess, whereas I think a much better fit can be presented in a field theoretic discussion, which is why I have gone so far sideways from your initial question, @BadgerBadger92

[The complete slide set can be found here for a quick look instead of watching the video. A field theoretic discussion of QM/QFT is different enough from a discussion in terms of particles that it takes me 3h26m20s to give even a very incomplete account of how I think the pieces fit together.]
I apologize if my attempt here to thread between published work and more recent unpublished ideas has fallen too far on the wrong side.

 

[jeffn1]

I think I am saying the same thing Bhoppa is saying (and, I suspect, the book he linked). He said QFT treats two entangled particles as a single particle.

Since quantum fields are non-local (infinite, it is often said), the correlations within the two-particle structure remain even if they are billions of miles apart.

It follows that the two entangled particles have the same relationship to their underlying quantum field even if they are separated by billions of miles. This is basically saying the same thing.

This sounds to me like QFT nicely explains quantum entanglement, or least the "weird" part of quantum entanglement (non-locality).

 

[Peter Morgan]

I think I am saying the same thing Bhoppa is saying (and, I suspect, the book he linked). He said QFT treats two entangled particles as a single particle.

Since quantum fields are non-local (infinite, it is often said), the two correlations within the two-particle structure remain even if they are billions of miles apart.

It follows that the two entangled particles have the same relationship to their underlying quantum field even if they are separated by billions of miles. This is basically saying the same thing.

This sounds to me like QFT nicely explains quantum entanglement. (Or at least the reference to the non-local quantum field).

Art Hobson's "Fields and Their Quanta: Making Sense of Quantum Foundations" and his previous work, going back decades, has always seemed a little strange to me insofar as he advocates strongly for field theory but also talks a lot about particles. Although it can be helpful in elementary cases to talk about how particles (as localized systems) cause events, I find it's also helpful to back away from the assumption that events have simple causes a little more than he does. I think of a field theory as essentially introducing an infinity of incoming causes for every recorded event: which we can reasonably think is a massive overkill but which we can also think of as a natural consequence of saying "more than one" (if we subscribe to the saying "once is never, twice is always"). In field theory we sum over an infinite number of paths to obtain the S-matrix entries for each outcome for a given state preparation.
Measurements in quantum field theory are local in the sense of microcausality, so that we can collect data in multiple places that are space-like separated without considering measurement incompatibility, but recorded measurement outcomes are nonlocal in the sense that we can engineer correlations between those outcomes that are nontrivial at arbitrarily large space-like separation. Engineering such correlations at larger space-like separation does not have the same costs as at smaller space-like separation, however. We have to provide millions of miles of fiber optics, for example, with dispersion and absorption increasingly difficult to accommodate, or introduce increasingly elaborate corrections as free-space propagation is increasingly degraded by dust et cetera. Entropy rules eventually.
That said, discussing particle pairs instead of a pair of single particles can be made to work. The formalism for compound systems in terms of tensor products of Hilbert spaces works well, otherwise we would have moved on decades ago, but it requires even more elaboration when we have to introduce particle creation and annihilation to model more detailed effects. One guiding light for me is that when Feynman was not saying that “nobody really understands quantum mechanics,” he was, in contrast, saying, “The physicist needs a facility in looking at problems from several points of view” (I've lifted that from my article here.) I take that to heart when I say that when we can think in terms of particles without too many difficulties arising, we can and should do it, but when difficulties multiply, it can be worthwhile to take a step back into a field theoretic or more empiricist mindset.

 

[bhobba]

when Feynman was not saying that “nobody really understands quantum mechanics,” he was, in contrast, saying, “The physicist needs a facility in looking at problems from several points of view” (I've lifted that from my article here.) I take that to heart when I say that when we can think in terms of particles without too many difficulties arising, we can and should do it, but when difficulties multiply, it can be worthwhile to take a step back into a field theoretic or more empiricist mindset.

Regarding Feynman's view of QM, just before he died, he attended a seminar by his friend (and the guy in the office next door), Gell-Mann, on Gell-Mann's decoherent histories approach. At the end, Feynman stood up, and everyone thought they were going to witness a ding-dong between the two greats. Instead, he said I agree with everything that was said, and left. So I think it's safe to say that was his final view of quantum foundations.

It has been discussed on this forum the difference between Many Worlds and Decoherent Histories. The bottom line was that MW, as presented by David Wallace in his book, The Emergent Multiverse, is, except for some semantic subtleties, basically the same as Decoherent Histories. That book also incorporates QFT in the interpretation. I would say for the advanced reader it is the best source I know of the modern view of QM.

Art Hobson's book is not the final word; some have issues with it. However, as a starting point for understanding QFT, it is the best source I know and a great place to start after a first course in QM, serving as a bridge into QFT for later study. The thing to realise is that ordinary QM does not require an interpretation, because it is wrong. It is only an approximation to QFT. This has been known for many years now, even at the dawn of QM, because it predicts stationary states for the hydrogen atom, so it can not account for spontaneous emission, as explained in one of my favourite papers I am referencing a lot lately:
https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3211&context=physics_facpub

Thanks
Bill

 

[PeterDonis]

He said QFT treats two entangled particles as a single particle.

No, that's not what he said. He said they are a two-particle excitation of a quantum field. That's not the same as a one-particle excitation of a quantum field.

Also, there are many kinds of excitations of quantum fields that do not have a "particle" interpretation at all. QFT does not treat "particles" as fundamental objects.

It follows that the two entangled particles have the same relationship to their underlying quantum field even if they are separated by billions of miles. This is basically saying the same thing.

No, it's not. "Particles" are not things separate from quantum fields that have "relationships" to them. They are particular kinds of excitations of quantum fields. The quantum fields are the only "things" that are there.

This sounds to me like QFT nicely explains quantum entanglement, or least the "weird" part of quantum entanglement (non-locality).

It doesn't "explain" non-locality; it just says non-locality is a property of quantum fields. You still have to accept that quantum fields are fundamentally non-local objects (just like wave functions are in non-relativistic QM); there's no underlying "explanation" for the non-locality, it's just a brute fact.