Undergrad Murray Gell-Mann on Entanglement

[ddd123]

Perhaps you are extending the discussion to other remarks by Gell-Mann outside of the quote in the OP. That's fine, but what I'm talking about is that quote. Some hold that you need nonlocal influences, I'm saying that to have nonlocal influences you first have to think the system is "made of parts" that could be the subject and object of those influences, but the mathematics does not say the system is made of parts, it says the system is holistic. That's all true independent of spatial separation, I just don't think spatial separation has anything to do with EPR physics, it only has to do with the awkward picture of insisting that a system must be comprised of distinct parts which must then propagate influences between them. What I mean by holism is the rejection of that awkward picture, a picture that does not even dovetail with the very mathematics of a Bell state.

I already said this in my own words earlier, so we agree on everything, which is funny since we're disagreeing now.

 

[Ken G]

I already said this in my own words earlier, so we agree on everything, which is funny since we're disagreeing now.

I suspect we are actually agreeing, you just don't like distinguishing nonlocal from holistic. I think that if that distinction is not made, people end up thinking the surprise of EPR is about spatial separation, whereas I say it is the same surprise as the PEP: that systems don't always act like they are made of separate parts. That's very surprising, even in a helium atom with no spatial separation! So let's keep focused on that more general surprise, and not get so hung up on spatial issues that don't even enter into the correlations in an EPR experiment. What we know is that Einstein was wrong: he thought we'd need new physics because he thought spacelike separation would matter to the outcome. We now know it doesn't-- so let's stop pretending that spacelike separation is still the issue here, when we know it isn't-- the issue is how systems act like they are not comprised of separate pieces, like information in the pages of a book, they act like the information is in the system as a whole (or more likely, in the mind of the scientist).

 

[ddd123]

I'm not convinced that space-like separation doesn't matter, do you think Aspect's experiments were kind of useless then?

 

[ddd123]

Let me put it in this way: it's not true that if there's no spatial separation then holism is as remarkable, at the level of the concept being convincing. When you prove that holism still holds even under spatial separation it's just then that the concept becomes utterly convincing, even if in the strict sense it's not its primary aspect.

 

[Ken G]

I'm not convinced that space-like separation doesn't matter, do you think Aspect's experiments were kind of useless then?

Are you referring to experiments that showed spacelike separation doesn't matter, or to experiments that show it does? To me, experiments that show spacelike separation doesn't matter should be telling us it is a red herring to the physics. It's certainly not useless to know it is a red herring to the physics, but now that we know it's a red herring to the physics, let's stop focusing on it like it was the thing that matters. Had there been experiments that showed it did matter, then we would need entirely new physics, like Einstein thought!

 

[Ken G]

Let me put it in this way: it's not true that if there's no spatial separation then holism is as remarkable, at the level of the concept being convincing. When you prove that holism still holds even under spatial separation it's just then that the concept becomes utterly convincing, even if in the strict sense it's not its primary aspect.

That's certainly the way a lot of people think-- like Einstein did. But I'm suggesting that it's simply not true that we'd all be fine if spacelike separation changed the result, but we have a crisis because it doesn't. It's just the opposite-- QM says the separation won't matter, so we have a philosophical puzzle that is easily resolved: retrain our intuition! But had it actually been true that spacelike separation mattered, now that would have been a scientific crisis, because not only would it mean QM is wrong, it would be much worse: we'd have to figure out what on Earth those local influences rattling around in the light cone could possibly be, since none of us have ever even dreamed of an influence that can propagate from one particle to another when you simply do a measurement!

 

[ddd123]

If there's so much difficulty in retraining our intuition, it's useless being overtly cautious about avoiding misunderstandings so to reject the (historical?) significance of the term nonlocality. People are going to misunderstand anyway.

 

[zonde]

the issue is how systems act like they are not comprised of separate pieces

Approach that systems are comprised of separate pieces has been very successful. I would say that systems in general act like they are comprised of separate pieces except maybe under some very specific conditions for some specific property of systems. I would say that without approach that systems in general act like they are comprised of separate pieces there would'n be any science in the first place.
So your philosophical approach attacks it's own foundations IMO.

 

[Ken G]

Approach that systems are comprised of separate pieces has been very successful. I would say that systems in general act like they are comprised of separate pieces except maybe under some very specific conditions for some specific property of systems.

Certainly, over the years scientific thinking has offered us a wide array of information management schemes that have been highly successful in their proper domain of application. It has also taught us not to take these information management schemes too seriously, and to be ready to let go of them when they start to get in the way.

I would say that without approach that systems in general act like they are comprised of separate pieces there would'n be any science in the first place.
So your philosophical approach attacks it's own foundations IMO.

That doesn't follow. Surely we can say that if measuring devices didn't act classically, we wouldn't have science as we know it either-- but that does not require that everything must act classically, simply because we need to count on our instruments to. I realize that Bohmians seek interpretations that do indeed allow everything to act classically, and that's a valid mission if that is their priority, but we need not accept that just because a given mindset has allowed science to flourish in the past, we are therefore disallowed from leaving that mindset to allow it to continue to flourish in the future. There is no part of the scientific method that says "everything must act classically and as if it were comprised of parts simply because we count on our instruments to act that way, and our instruments are how we study everything else."

 

[zonde]

Certainly, over the years scientific thinking has offered us a wide array of information management schemes that have been highly successful in their proper domain of application. It has also taught us not to take these information management schemes too seriously, and to be ready to let go of them when they start to get in the way.
That doesn't follow. Surely we can say that if measuring devices didn't act classically, we wouldn't have science as we know it either-- but that does not require that everything must act classically, simply because we need to count on our instruments to. I realize that Bohmians seek interpretations that do indeed allow everything to act classically, and that's a valid mission if that is their priority, but we must also accept that just because a given mindset has allowed science to flourish in the past, we therefore cannot leave that mindset to allow it to continue to flourish going forward.

Ok, you can replace classical approach with something else after you have shown that within that new approach old reasoning works as well (FAPP).
Any idea how you are going to do that with your holistic approach? What would be starting point for your approach? What you are going to take as given?

 

[Ken G]

The mathematical form of the Bell state. It's holistic, regardless of whether or not there is any spatial separation involved. What is interesting about the Bell state, and its ability to violate the Bell inequality, has nothing whatever to do with spatial separation, and the latter only appears because of the prejudices of the scientist-- it just isn't what is interesting about the formalism of the mathematical structure of a Bell state.

Let me put it another way. It seems to me a lot of people are in effect saying that it would be fine to have the things a Bell state can do as long as they are not spatially separated, but it becomes a crisis when they are. But the whole point of the Bell state is that it cannot be broken down into pieces, and the whole concept of spatial separation already requires that mode of thinking. So the crisis was already there! A far worse crisis would have occurred if spatial separation had mattered, then we'd have no idea what was going on.

 

[ddd123]

I find that actually supports the implication of nonlocality. Since spatial aspects don't matter wrt internal structure of the system. The fact that we cannot invoke the common cause principle in a situation where we 100% would've done that if we weren't forced to do otherwise, which is was zonde was referring to I think.

 

[Ken G]

Something isn't "nonlocal" if it has nothing to do with spatial issues because it isn't strictly made of parts. It is "nonlocal" if it has to do with spatial issues, and is strictly made of parts, but doesn't respect the speed of light. One does need a word for that. That's the distinction I am making with "holistic", which has nothing to do with spatial issues, it has to do with treating a system as if it was not strictly made of parts that could be at different places in the first place.

 

[ddd123]

It has to do with spatial issues because it violates our expectation of being able to factor events to their spatial neighborhood. Long-distance correlations without a perfectly clear cause (and instead a black-box of MEI) for me mean non-locality due to the system being holistic, but not due to action at a distance.

I'm afraid we could go on forever.

 

[Ken G]

The point being, we can only have that intuition in the first place if we regard the system as being made of pieces, that could have local environments to factor. If you do not regard a system as being made of pieces like that, but rather as some kind of Bell state, the spatial intuition is never necessarily invoked. Most places that define nonlocality will call it essentially action at a distance between parts of a system. That's what I'm saying needs to be disambiguated from Bell states, which have nothing to do with that. No matter what words you personally choose to distinguish those things, nevertheless, a distinction needs to be made. I'm using "holistic" versus "nonlocal influences", and pointing out that what Gell-Mann is objecting to is the action at a distance part, not the holistic part.

 

[ddd123]

It's not clear to me if Gell-Mann agrees with holism though, because I don't know decoherent histories.

 

[Ken G]

I don't know his feelings on that either, I am only commenting on his quote, and defending it only insofar as it is saying to be skeptical of nonlocal influences being something relevant to an analysis of Bell states. The reason being, the properties of a Bell state have nothing to do with spatial issues and nothing to do with action at a distance, and exhibit the same behavior whether inside or outside the light cone of some measurement. We simply need to get our own prejudices, which you call "expectations", out of the way and see what matters-- and what doesn't.

 

[ddd123]

Well it's hard to call the common cause principle a prejudice lol.

 

[Ken G]

The prejudice I refer to is not the common cause principle, it is the idea that the common cause principle has anything to do with parts of a system. A common cause can just as easily be holistic, so rejection of parts, and the locations of parts, and the influences between parts, is 100% independent of a common cause principle. The preparation of the Bell state can simply be the common cause.

 

[Simon Phoenix]

Do you disagree with this statement: "Before Alice's measurement the state is |hh⟩+|vv⟩|hh⟩+|vv⟩|hh \rangle + |vv \rangle, and after the measurement the state collapses to |hh⟩|hh⟩|hh \rangle if Alice measures her photon to be horizontal"?

Yes, I disagree with this statement. Correct is: If A's photon passes the h-polarization filter she associates the state hh⟩hh⟩hh \rangle to the two photons. However, her measurement has no instantaneous influence on B's photon, i.e., there must not be a collapse if the interpretation should be consistent with the very construction of QED as a local relativistic QFT, and you don't need it!

Would I be right in thinking that the source of the disagreement here is in that troublesome word 'collapse'?

Let's consider an entanglement-swapping scenario in which Alice has spin-1/2 particles (1,2) prepared in a maximally entangled state, and Bob has spin-1/2 particles (3,4) also prepared in a maximally entangled state. So one thing we can say for definite is that particles (1,4) are not entangled.

Alice sends particle 2 to Clive and Bob sends particle 3 to Clive.

Clive makes a Bell measurement on particles (2,3).

There is no doubt whatsoever that whether we think about it in terms of 'collapse' or not that after the Bell measurement of Clive, the particles (1,4) are now entangled - at least that would be the traditional view based on the axioms.

Of course, without the supplementary information about Clive's actual measurement result, Alice and Bob can't do much with this since (without this supplementary information) they would have to assign a mixture of Bell states to their particles (1,4).

But aren't we justified in saying that (1,4) are really entangled - even though we might not know which particular entangled state we have (without further information about Clive's result)? The knowledge of Clive's result doesn't really alter the fact that the particles (1,4) are entangled now - it just allows us to assign a specific entangled state. It's very tempting to make a statement, based on this, that the particles (1,4) are now actually in a particular entangled quantum state.

In other words there is a definite physical difference in particles (1,4) before and after Clive's measurement (before : no entanglement, after : entanglement)

So we could describe Clive's measurement as effecting a 'collapse' onto a particular entangled state - even though this way of thinking is at odds with the explicitly local construction of QFT - and, as far as the prediction of subsequent experimental results is concerned, there would be no inconsistency or error in so doing.

Let's go one step further and suppose that Clive sends the information about his result on to Alice and Bob. When they receive this update - they can now assign a more appropriate state (a specific pure entangled state). So as soon as they receive this information their state assignation has 'collapsed' from mixed to pure - but nothing has changed, only their knowledge.

But, isn't this whole disagreement about 'collapse' and what it means all a bit academic? There are no predicted incorrect experimental consequences (as far as I'm aware) from adopting a traditional 'collapse' picture - just as there are no predicted incorrect experimental consequences from rejecting this view and doing things without explicitly thinking of collapse in this fashion.

 

[atyy]

But, isn't this whole disagreement about 'collapse' and what it means all a bit academic? There are no predicted incorrect experimental consequences (as far as I'm aware) from adopting a traditional 'collapse' picture - just as there are no predicted incorrect experimental consequences from rejecting this view and doing things without explicitly thinking of collapse in this fashion.

Yes, that's why it's a conceptual error to reject collapse on grounds of locality. Collapse is consistent with locality.

 

[vanhees71]

Ad #140:

Note that only Clive knows that particles 1 and 4 are entangled (it's called "entanglement swapping"). This makes the scheme consistent with relativistic QFT (implying the linked-cluster theorem).

I do not use the word collapse for the very reason you see in this thread. NB: The interactions in relativistic QFT are never instantaneous, which includes the interactions of the measured system with the measurement device. To the contrary, all you can say are transition probability rates (S-matrix elements), which describe the transition from an asymptotic free initial to an asymptotic free final state. What to make of the transient state, the theory is silent. So I disagree very strongly with any statement telling a physical process connected with measurement is instantaneous. The collapse assumption usually implies such instantaneous transitions, but that's the very point where this assumption contradicts the very foundations of the theory (relativistic QFT) that it pretends to interpret. Why should I adapt an inconsistent interpretation that I don't need.

 

[vanhees71]

Yes, that's why it's a conceptual error to reject collapse on grounds of locality. Collapse is consistent with locality.

But if there is no need for the collapse assumption (which indeed is inconsistent with the locality of interactions between the measured system and the measurement apparatus!) I better don't use it, because it provides all these problems. An interpretation should be as minimal and consistent as possible, although it's only the "soft part" of the theory!

 

[Demystifier]

But if there is no need for the collapse assumption (which indeed is inconsistent with the locality of interactions between the measured system and the measurement apparatus!) I better don't use it

But you use the update, which is what atyy really means by "collapse".

So you and atyy agree on physics and on interpretation. You only disagree on the language. Atyy refuses to call it "update", and you refuse to translate his "collapse" as "update".

If fights over correct interpretation are not much relevant to physics, fights over correct language are even less relevant to physics.

 

[Simon Phoenix]

This makes the scheme consistent with relativistic QFT

As it must be :-)

The question I suppose I was really getting at is whether we view entanglement as a physical property of things or not.

In the 'collapse' picture we would say that Clive's measurement projects (instantaneously) particles 1 and 4 into an entangled state.

But you would say, I think, that this is inconsistent with QFT (and quite reasonably so too).

The issue I have is that if we're going to view entanglement as having at least some objective physical character - then when, in QFT, would we say that particles 1 and 4 actually become entangled?

Of course, Alice and Bob don't know this until Clive tells them - so no violation of locality etc. But are we justified in saying that the particles are in an entangled state - or is this a meaningless question? Do the particles become 'entangled' only when Alice and Bob receive the supplementary information, or is entanglement an objective physical property?

I don't think there's any great sin in thinking in terms of 'collapse' in the traditional way - after all no experimental contradictions will ensue - but I accept that this is a somewhat uncomfortable perspective for an explicitly local theory. I tend not to worry too much about interpretations (except on forums where it's great to get the ideas of others) and just view 'collapse' (i.e. projective measurements) as a convenient tool.

 

[vanhees71]

But you use the update, which is what atyy really means by "collapse".

So you and atyy agree on physics and on interpretation. You only disagree on the language. Atyy refuses to call it "update", and you refuse to translate his "collapse" as "update".

If fights over correct interpretation are not much relevant to physics, fights over correct language are even less relevant to physics.

Here I disagree again. Correct language is mandatory for all science. You cannot do science without a concise expression of the meaning of words.

 

[ddd123]

The prejudice I refer to is not the common cause principle, it is the idea that the common cause principle has anything to do with parts of a system. A common cause can just as easily be holistic, so rejection of parts, and the locations of parts, and the influences between parts, is 100% independent of a common cause principle. The preparation of the Bell state can simply be the common cause.

Anyway there is a line of research that shows a different link between entanglement and spatial issues: http://www.nature.com/news/the-quantum-source-of-space-time-1.18797 .

Unfortunately I don't understand a single word of it.

 

[Demystifier]

Here I disagree again. Correct language is mandatory for all science. You cannot do science without a concise expression of the meaning of words.

Fair enough! But do you agree with me that the dispute between you and atyy is not about physics, and not about interpretation, but only about language?

 

[vanhees71]

As it must be :-)

The question I suppose I was really getting at is whether we view entanglement as a physical property of things or not.

Sure, since it leads to observable consequences (as the violation of Bell's inequality).

In the 'collapse' picture we would say that Clive's measurement projects (instantaneously) particles 1 and 4 into an entangled state.

But you would say, I think, that this is inconsistent with QFT (and quite reasonably so too).

The issue I have is that if we're going to view entanglement as having at least some objective physical character - then when, in QFT, would we say that particles 1 and 4 actually become entangled?

I say that the projection describes the update of the state by Clive in the sense of a v. Neumann filter measurement. States refer to ensembles, and filtering out part of the ensemble is a preparation procedure. To evaluate what this means for the far-distantly registered particles 2 and 3 you have to use the corresponding measurement protocol. The observers of particles 2 and 3 alone cannot notice that anything changed, because they have no means to apply the filter. For that they need Clive's results. You can choose the corresponding ensemble a posteriori, and you can have things like the quantum eraser of which-way information which restores an interference pattern for such a partial ensemble. Nowhere in all these ensembles is it necessary to assume any instantaneous interaction at a distance, faster-than-light signal propagation (or even retrocausal inferences) and the like esoterics. That's for the science fiction market but not for science!

Of course, Alice and Bob don't know this until Clive tells them - so no violation of locality etc. But are we justified in saying that the particles are in an entangled state - or is this a meaningless question? Do the particles become 'entangled' only when Alice and Bob receive the supplementary information, or is entanglement an objective physical property?

Sure, the particles are in an entangled state, and usually they are entangled in the very beginning when they are created in a local interaction (like parametric down conversion where a laser em. wave leads to the production of two polarization-entangled photons). Also in your case of entanglement swaping you need the two entangled particle pairs, and then the correlations are there due to this preparation procedure and also the entangledment of particles (1,4) for the corresponding partial ensemble chosen due to Clive's measurements are finally caused by the initial entanglement of the two entangled pairs you begin with. Thus indeed you can have strong correlations (stronger than any correlations possible within any deterministic local hidden-variable model) of far distant parts of a quantum system without violating relativistic causality.

I don't think there's any great sin in thinking in terms of 'collapse' in the traditional way - after all no experimental contradictions will ensue - but I accept that this is a somewhat uncomfortable perspective for an explicitly local theory. I tend not to worry too much about interpretations (except on forums where it's great to get the ideas of others) and just view 'collapse' (i.e. projective measurements) as a convenient tool.

As long as you take it as heuristic, it's fine.

 

[stevendaryl]

Let's go one step further and suppose that Clive sends the information about his result on to Alice and Bob. When they receive this update - they can now assign a more appropriate state (a specific pure entangled state). So as soon as they receive this information their state assignation has 'collapsed' from mixed to pure - but nothing has changed, only their knowledge.

Well, sort of. A feature of quantum density matrices that complicates figuring out what is only a matter of knowledge is the non-uniqueness of writing a density matrix as a mixed state. The "improper" mixed state that you get by tracing over irrelevant components of a composite pure state is identical to the "proper" mixed state that you get by collapse (when you don't know which state it has collapsed into). So the weird nonlocality of the quantum mechanics of entangled particles has the effect of turning one kind of mixed state into another, where they both have the same density matrix.

So Alice initial computes a density matrix for her subsystem, \rho. This can be written in many different ways as a mixed state; for example, it can be written as: \sum_\alpha p_\alpha |\alpha\rangle \langle \alpha| or as \sum_\beta p_j |j\rangle \langle j|, where |\alpha\rangle and |j\rangle are two different bases. If Alice later finds out that Clive has performed a measurement collapsing her system to pure state |k\rangle (one of the states of the basis |j\rangle), Alice can retroactively view this as an update to her knowledge:

p_j \Rightarrow \delta^k_j

If instead, she finds out that Clive has collapsed her state into pure state |\beta\rangle (one of the states of the basis |\alpha\rangle, she can also retroactively view this as an update to her knowledge:

p_\alpha \Rightarrow \delta^\beta_\alpha

So it seems to me that it is the ambiguity of writing a density matrix as a mixture, together with the existence of two kinds of mixed states (proper and improper), that makes it where Alice can always retroactively view wave function collapse as ordinary updating of knowledge based on new information. She can always retroactively view collapse as an analogy to Bertelmann's Socks (Bell's example of classical "collapse" that doesn't involve any superluminal interactions).