I Murray Gell-Mann on Entanglement

[Buzz Bloom]

It doesn't sound like the ontology you are picturing to demonstrate that interpretation would exhibit correlations that would violate the Bell inequality.

Hi Ken:

I confess I may well be misunderstanding the issue, but my intended interpretation of the metaphorical experiment is that the probability distribution for the first measurement metaphorically represents the Bell distribution. The distribution for the second measurement "violates" whatever inequalities that might be a consequence of the first distribution.

Regards,
Buzz

 

[Ken G]

The problem is, the second probability doesn't violate the Bell inequality, the measurements you describe would show correlations between outcomes that satisfy the Bell inequality. Remember, the Bell inequality is not a constraint on individual probabilities, it is a constraint on joint probabilities-- the probability of this and this happening together. It's subtler than having one event change the probability of another, that's what happens in "Bertlmann's socks", where if one sock of a pair is left in the dryer, and the other gets in your drawer, and you see you have a left sock in the drawer, you immediately know you have a right sock in the dryer. Probability changes like that don't violate the Bell inequality, so we can imagine that the socks "know their own handedness", if you will. If you have balls that are black or white, and their order is set in the tubes they are being drawn from, then joint probabilities you get from a system like that (say, the chance that if I drew white on pick N I'll draw black on pick N+1, that kind of thing) won't violate the Bell inequality.

 

[Ken G]

It's natural that, since our experiences are of a collapsed and disentangled world, we should be a bit befuddled about why there are superpositions and why there are entanglements. But what I find ironic is that quantum mechanics has long since moved past the question of why are there superpositions, and moved on to how do the superpositions "collapse," yet we still seem stuck on "what enforces the entanglements." We get all these notions of nonlocal effects and so on, all to try to answer how systems can remain entangled when separated. Why haven't we also moved on to the question of how the disentanglement occurs? There's not going to be any nonlocal issues in producing disentanglement, so if we just accept that systems start out entangled, we are not going to have anything difficult to explain. We don't need to explain why the strange correlations are there, we need to explain why we don't usually encounter those correlations, and see them as strange as a result.

 

[ddd123]

Why haven't we also moved on to the question of how the disentanglement occurs?

Isn't that "the measurement problem"?

 

[secur]

Isn't that "the measurement problem"?

Decoherence also addresses how and why disentanglement occurs.

We don't need to explain why the strange correlations are there, we need to explain why we don't usually encounter those correlations, and see them as strange as a result.

We don't "need" to explain the strange correlation; life will go on without it. Nevertheless there is no accepted explanation for the correlation, yet. Quantum theory only defines it - correctly, of course, as shown by experiment. It doesn't address the how or why at all. It's an issue because it requires nonlocal influence, or something equally strange, to implement those correlations. Until that's resolved curiosity demands further explanation.

The reason it's strange is directly addressed by my post in the other thread, https://www.physicsforums.com/threa...tional-in-physics.885480/page-21#post-5578506, except there I use the word "weird" instead.

 

[Zafa Pi]

In this example, for Murray's statement to be true, he would be talking about the reduced density matrix of an observer who only makes a measurement on the other photon.

However, it would be equally right to say that measuring one photon does affect the other photon, since a measurement collapses the wave function of both photons.

Using q-information notation, if a photon is in state √½(|0⟩ + |1⟩) and it is measured using Z it collapses to either |0⟩ or |1⟩ (with probability ½ each).
If a pair of photons is in state √½(|00⟩ + |11⟩) and Alice (left photon) measures with Z what does the state collapse to?

 

[secur]

Gell-Mann seems to be saying that on this branch of history, Alice measures the circular polarization of her photon, and Bob's photon has a definite circular polarization state (either left-handed or right-handed). On some other branch (one that doesn't actually occur), Alice measured a different property of her photon, and Bob's photon was in some other definite state all along.

I sort of understand this point of view, but it seems a little mysterious, to me. After all, Alice chooses which branch is actual by choosing which measurement to make. (Actually, I guess her choosing a measurement means picking two possible branches; one in which she has a right-handed photon, and one in which she has a left-handed photon. She can't choose which of those she is in, but she can choose not to be in a possible branch in which her photon is linearly polarized.)

In "coherent histories", we have a Block Universe with a wave function that has only "legal" branches: ones in which A & B make measurements that are consistent with QM. As in MWI, all branches always exist. Alice doesn't "choose" anything. There's one branch where Alice incorrectly believes she "chooses" an angle, and others where she incorrectly thinks she "chooses" some other angle to measure. But in fact it's all pre-determined, there's no choice involved. In each branch Bob is also predestined to incorrectly think he makes a "choice". Of course, their measurements are predestined to agree with QM.

Gell-Mann doesn't need "elements of reality" because the measurements don't need any connection to reality (whatever that is). The only requirement, measurements must agree with QM. When Bob gets "spin up" you can incorrectly imagine there was some "cause" if you wish; like, the photon actually was already right-handed. But in fact there's no need for any so-called "cause". They get compatible measurements because these branches just happen to coincide with QM predictions, like all branches do throughout the universe. Why? Gell-Mann gives this comprehensive, detailed, satisfying explanation: "that's just the way QM works!"

The idea is worthless scientifically - even if it happens to be true! - being immune to the slightest shred of proof or disproof.

 

[rubi]

In "coherent histories", we have a Block Universe with a wave function that has only "legal" branches: ones in which A & B make measurements that are consistent with QM. As in MWI, all branches always exist.

That's not correct. In consistent histories, there is only one branch. The wave function is a probability distributions over the possible branches and one branch will be physically realized with a certain probability. It is completely analogous to the situation in classical Brownian motion. You also got a probability distribution over all possible paths of a particle, but the particle will only choose one path and this path will be chosen with a certain probability distribution. Consistent histories is a direct generalization of the theory of Brownian motion and classical stochastic processes.

 

[secur]

That's not correct. In consistent histories, there is only one branch. The wave function is a probability distributions over the possible branches and one branch will be physically realized with a certain probability. ...

You're right - but I'm righter :-) Wikipedia, and modern writers, seem to agree with you. But in fact consistent histories (or whatever we call it) is a "branch" of MWI, in the sense that ours is only one of many alternative realities, as is very clear from the original paper. I found a poor photocopy of it at http://tuvalu.santafe.edu/~mgm/Site/Publications_files/MGM 102.pdf, which is good enough to at least check my quotes.

Gell-Mann, M. & J.B. Hartle, 1990, “Quantum mechanics in the light of quantum cosmology”, in W. H. Zurek (ed.), Complexity, entropy and the physics of information. Redwood City, Calif.: Addison-Wesley, pp. 425–458

"It is an attempt at extension, clarification, and completion of the Everett interpretation."

"decohering sets of alternative histories give a definite meaning to Everett's "branches".

"Thus we can, at best, deal with quasiclassical maximal sets of alternative decohering histories, with trajectories that split and fan out at (sic) a result of the processes that make the decoherence possible. As we stressed earlier, there are no classical domains, only quasiclassical ones".

"mechanisms for decoherence will operate differently in different alternative histories of the universe".

"The histories in which an observer, as part of the universe, measures p and the histories in which that observer measures x are decohering alternatives."

'Everett and others have described this situation, not incorrectly, but in a way that has confused some, by saying that histories are all "equally real" (meaning only that QM prefers non over another except via probabilities) and by referring to "many worlds" instead of "many histories".'

Read that paper. There's no question about the MWI-ness of (original) decoherent histories.

However more recently proponents have de-emphasized this aspect, saying it "generalizes conventional Copenhagen interpretation" (Wikipedia). Yes, that was partly true in the original paper as well. They get their probabilities from Born, bypassing one of MWI's big problems. Wikipedia also notes that:

'In the opinion of others this still does not make a complete theory as no predictions are possible about which set of consistent histories will actually occur. ... However, Griffiths holds the opinion that asking the question of which set of histories will "actually occur" is a misinterpretation of the theory; histories are a tool for description of reality, not separate alternate realities.'

IOW, in the modern flavor, they want to ignore the fact that only one alternative actually seems to occur. This brings up the question, is the original Gell-Mann Hartle paper still authoritative? I'd say it's still applicable. But a physicist can't answer that question. It needs an English professor with a PhD in weasel wording.

I found this revealing thread on stackexchange http://physics.stackexchange.com/qu...rpretation-of-qm-a-many-worlds-interpretation

Question: Is the “consistent histories” interpretation of QM a “many worlds interpretation” in disguise?

Lubos Motl, a proponent, answered:

"People behind Consistent Histories usually admit that their interpretation - my favorite one - is just a refinement of the probabilistic Copenhagen interpretation. Nothing essential has changed; the predictions are still fundamentally probabilistic. Consistent Histories is the framework that incorporated the explanations of decoherence - the key process that calculates the boundary of the classical and quantum world - as the first one (and maybe still only one). Many-worlds interpretation is just a semi-popular psychological framework to think about quantum mechanics - and it hasn't been useful to do any actual, new calculations. One doesn't really know how to extract the numerical values of the probabilities from the many worlds, at least not in a way that would tell us more than any other interpretations."

He denigrates MWI as "just psychological" and emphasizes the Copenhagen connection. He ascribes opinion to "people behind consistent histories usually ...". But he doesn't actually deny MW - like alternate realities. You need to be an expert in weasel-wording (like myself) to understand this. But another poster named "understanding", amplifying Motl's comment, gives the game away:

"No, in the many worlds interpretation, every parallel universe is real, but in consistent histories, once you choose your projection operators, only one possibility is real, and all the others are imaginary. ... Why should one world be more real than the others? There is no reason. To copies of you living in a parallel world, they are more real than you are."

"understanding"'s weasel-wording skills are seriously deficient!

 

[rubi]

You're right - but I'm righter :-) Wikipedia, and modern writers, seem to agree with you. But in fact consistent histories (or whatever we call it) is a "branch" of MWI, in the sense that ours is only one of many alternative realities, as is very clear from the original paper.

Same is true for the different possible paths of a particle in Brownian motion. The situation is completely analogous. If you wouldn't say that all alternative branches in Brownian motion are equally real, you wouldn't say the same thing about the histories in CH either. If you restrict to a set of commuting observables, CH is even exactly a classical stochastic process and not just analogous to one. Of course you can always say that the alternative paths of a particle in a classical Brownian motion are realized in a parallel universe, but it would be pointless to do so and it would be a non-standard interpretation. The same is true for consistent histories.

(By the way: "It is not easy to ignore Lubos Motl, but it is always worth the effort" (John Baez))

 

[zonde]

Same is true for the different possible paths of a particle in Brownian motion. The situation is completely analogous. If you wouldn't say that all alternative branches in Brownian motion are equally real, you wouldn't say the same thing about the histories in CH either.

Alternative branches in Brownian motion do not show interference effects. So analogy does not hold.

 

[rubi]

Alternative branches in Brownian motion do not show interference effects. So analogy does not hold.

Alternative branches in CH don't show interference effects either. The analogy holds perfectly.

 

[zonde]

Alternative branches in CH don't show interference effects either.

Hmm, then how CH works out predictions for interference effects?

 

[rubi]

Hmm, then how CH works out predictions for interference effects?

Just like ordinary quantum mechanics. The formulas are identical. There is no interference between the individual branches, but there is interference in each individual branch. What's going on in one branch is completely independent of what happens in another branch. The branches are mutually exclusive, just like the Brownian paths.

 

[MrRobotoToo]

Just like ordinary quantum mechanics. The formulas are identical. There is no interference between the individual branches, but there is interference in each individual branch. What's going on in one branch is completely independent of what happens in another branch. The branches are mutually exclusive, just like the Brownian paths.

Wouldn't you have to invoke an explicit form of nonlocality, as per Bell's theorem, in order to claim that there's a single history that's actually taken? What you'd be left with is some form of Bohmian mechanics, with all its attendant problems.

 

[secur]

Same is true for the different possible paths of a particle in Brownian motion. The situation is completely analogous. If you wouldn't say that all alternative branches in Brownian motion are equally real, you wouldn't say the same thing about the histories in CH either. If you restrict to a set of commuting observables, CH is even exactly a classical stochastic process and not just analogous to one. Of course you can always say that the alternative paths of a particle in a classical Brownian motion are realized in a parallel universe, but it would be pointless to do so and it would be a non-standard interpretation. The same is true for consistent histories.

(By the way: "It is not easy to ignore Lubos Motl, but it is always worth the effort" (John Baez))

My point was really about history not "histories" :-) Historically, consistent histories began as "an attempt at extension, clarification, and completion" of MWI. Putting that aside, it does seem to have evolved to your position. Viz., denying or at least de-emphasizing the "reality" of the alternate branches. @zonde's point is well taken, though. Surely the original impetus for CH (and, I suppose, all interpretations) comes from the need to explain interference. But you can say that any "branches" that are still capable of interfering, because they're coherent enough, are not yet separated. And once they are, only one (ours) still has real existence. This denatured version seems to lack explanatory power, but that's a matter of taste I suppose.

BTW I was probably too hard on Gell-Mann. No one's perfect, why pick on him. Furthermore although I find the main idea of CH unconvincing he and Hartle did some good work with the details in that 1990 paper.

The John Baez quote is spot-on.

 

[stevendaryl]

Wouldn't you have to invoke an explicit form of nonlocality, as per Bell's theorem, in order to claim that there's a single history that's actually taken? What you'd be left with is some form of Bohmian mechanics, with all its attendant problems.

Not exactly.

There are (at least) two different approaches to describing the rules for how a system behaves:

1. A state-based approach
   • You specify the set of possible states of the system.
   • You specify the rules for one state leading to another state (usually via differential equations).
2. A history-based approach
   
   • You just directly specify the set of possible complete histories, and a probability distribution on that set.

The latter approach is how I understand consistent histories. There is a sense in which this approach throws out any notion of "interaction" or "forces". Those notions only come into play in a state-based approach.

I suppose you could re-interpret a history-based approach as a state-based approach by treating "which history you're in" as a "hidden variable". In general, that would be a superdeterministic model, rather than a nonlocal model.

 

[rubi]

Wouldn't you have to invoke an explicit form of nonlocality, as per Bell's theorem, in order to claim that there's a single history that's actually taken? What you'd be left with is some form of Bohmian mechanics, with all its attendant problems.

No, consistent histories is a fully local interpretation of QM. It has nothing to do with Bohmian mechanics, which is a hidden variables interpretation. CH doesn't have hidden variables and is as quantum as Copenhagen. However, CH nicely resolves issues like the measurement problem and apparent quantum non-locality. Unfortunately, one can only truly appreciate it with some background in the theory of stochastic processes. If you want to learn more about it, I suggest the book "Consistent Quantum Theory" by Griffiths as an introduction.

But you can say that any "branches" that are still capable of interfering, because they're coherent enough, are not yet separated. And once they are, only one (ours) still has real existence. This denatured version seems to lack explanatory power, but that's a matter of taste I suppose.

In order to apply the CH framework, you must first select a set of mutually exclusive histories that you want to take into consideration. (The physics will not depend on this choice. It's much like choosing a coordinate system.) The physically realized history will be compatible with some conjunction of the set of mutually exclusive histories that you chose. However, of course you can make a poor choice of histories that you consider and you would get a better resolution if you choose a set of histories that is adapted to the physical situation (just like you wouldn't choose spherical coordinates for a non-spherically symmetric situation). Nevertheless, any choice will be consistent with the physics. Now the great thing is that the set of histories is chosen in such a way that there is no interference between the histories, so this problem will automatically not occur and the formalism will tell you if made an incorrect choice. If you choose a set of histories that shows interference between the histories, you will get probabilities that don't add up to one and there is no reasonable way to interpret this.

There is a sense in which this approach throws out any notion of "interaction" or "forces". Those notions only come into play in a state-based approach.

I would say that the effect of forces is incorporated into the probability distribution. If you look at classical statistical mechanics, you have Gibbs distributions $e^{-\beta(\frac{p^2}{2m}+V)}$, where the distribution will be concentrated in the potential well of $V$. In the same way, the probability distribution on the set of histories will assign smaller probabilities to histories that would run against a potential hill. It's a probabilistic notion of force, like an entropic force.

 

[MrRobotoToo]

Not exactly.

There are (at least) two different approaches to describing the rules for how a system behaves:

1. A state-based approach
   • You specify the set of possible states of the system.
   • You specify the rules for one state leading to another state (usually via differential equations).
2. A history-based approach
   • You just directly specify the set of possible complete histories, and a probability distribution on that set.

The latter approach is how I understand consistent histories. There is a sense in which this approach throws out any notion of "interaction" or "forces". Those notions only come into play in a state-based approach.

I suppose you could re-interpret a history-based approach as a state-based approach by treating "which history you're in" as a "hidden variable". In general, that would be a superdeterministic model, rather than a nonlocal model.

No, consistent histories is a fully local interpretation of QM. It has nothing to do with Bohmian mechanics, which is a hidden variables interpretation. CH doesn't have hidden variables and is as quantum as Copenhagen. However, CH nicely resolves issues like the measurement problem and apparent quantum non-locality. Unfortunately, one can only truly appreciate it with some background in the theory of stochastic processes. If you want to learn more about it, I suggest the book "Consistent Quantum Theory" by Griffiths as an introduction.

What's nagging at me is the analogy being made between consistent histories and Brownian motion. Perhaps the analogy is an accurate one, and my hesitation in accepting it stems merely from my ignorance of CHs detailed formulation. But if I restrict myself instead to a comparison between standard quantum mechanics and Brownian motion, then I feel my skepticism is justified. No one who has studied physics at any depth will have failed to notice that the Schrödinger equation is formally almost identical to the diffusion equation (or to a reaction-diffusion equation to be more exact), the only differences being that the wave function is complex and there's a factor of i in front of the time derivative. This immediately leads one to wonder if perhaps the Schrödinger equation is describing some sort of diffusive process. This speculation is further bolstered by the realization that an analysis by Feynman diagrams of, say, a particle traveling through some potential is nearly identical to the analysis one would carry out of a classical particle taking a random walk through said potential. In the case of a classical random walk we know that the particle takes only one of the many possible paths that have to be taken into account in calculating the probability distribution. However, in quantum mechanics Bell's theorem prevents us from drawing the same conclusion, unless we're willing to invoke causal nonlocality. Resorting to superdeterminism to get rid of the nonlocal influences strikes me as highly ad hoc ('There is no nonlocal causation, there is merely the appearance of it.') (I'm not denying superdetermism, however; I'm simply rejecting its use as a Get Out of Jail Free card for those who don't want to be burdened by the implication of nonlocality.)

 

[stevendaryl]

No one who has studied physics at any depth will have failed to notice that the Schrödinger equation is formally almost identical to the diffusion equation (or to a reaction-diffusion equation to be more exact), the only differences being that the wave function is complex and there's a factor of i in front of the time derivative. This immediately leads one to wonder if perhaps the Schrödinger equation is describing some sort of diffusive process.

There is another big difference with diffusion, and that is that diffusion is a matter of some substance spreading out in physical space, while a wave function propagates in configuration space. The difference isn't apparent when you're talking about a single particle, but becomes important when you are talking about multiple particles. For two particles, the wave function is a function of 6 variables: \psi(x_1, y_1, z_1, x_2, y_2, z_2) where (x_1, y_1, z_1) refers to the location of the first particle, and (x_2, y_2, z_2) refers to the location of the second particle. Because it's a function of configuration space, there is no meaning to "the value of the wave function here". So, in spite of the similarity of form, the Schrodinger equation is nothing like a diffusion equation (at least not diffusion through ordinary 3-space).

 

[MrRobotoToo]

There is another big difference with diffusion, and that is that diffusion is a matter of some substance spreading out in physical space, while a wave function propagates in configuration space. The difference isn't apparent when you're talking about a single particle, but becomes important when you are talking about multiple particles. For two particles, the wave function is a function of 6 variables: \psi(x_1, y_1, z_1, x_2, y_2, z_2) where (x_1, y_1, z_1) refers to the location of the first particle, and (x_2, y_2, z_2) refers to the location of the second particle. Because it's a function of configuration space, there is no meaning to "the value of the wave function here". So, in spite of the similarity of form, the Schrodinger equation is nothing like a diffusion equation (at least not diffusion through ordinary 3-space).

Good points. I would just point out that even in the multiparticle case it would still make sense to draw an analogy with a random walk. In the latter case we would want to calculate $P\left(x_{1},y_{1},z_{1},x_{2},y_{2},z_{2}\right )$, i.e. the probability of finding the particles at $\vec{x}_{1}$ and $\vec{x}_{2}$ after the initial system preparation. The Feynman diagrams for two particles would have a natural translation into a random walk analysis for two classical particles.

 

[stevendaryl]

Good points. I would just point out that even in the multiparticle case it would still make sense to draw an analogy with a random walk. In the latter case we would want to calculate $P\left(x_{1},y_{1},z_{1},x_{2},y_{2},z_{2}\right )$, i.e. the probability of finding the particles at $\vec{x}_{1}$ and $\vec{x}_{2}$ after the initial system preparation. The Feynman diagrams for two particles would have a natural translation into a random walk analysis for two classical particles.

Right, but in classical probability theory (with no nonlocal interactions), the probabilities for random walks factor for particles that are too far apart to interact. That is, for two particles that are far apart,

P(x_1, y_1, z_1, x_2, y_2, z_2) \approx P(x_1, y_1, z_1) P(x_2, y_2, z_2)

The random walk taken by this particle is independent of the random walk taken by this other particle. If that fails to be the case, then one suspects that there is some unaccounted-for long range interaction or shared state.