Local realism ruled out? (was: Photon entanglement and )

[JesseM]

So yes, I do think that if you do not use such trick, you cannot prove violations in Bohmian mechanics. If you can offer a derivation that does not use something like this, I am all ears.

Well, take a look at section 7.5 of Bohm's book The Undivided Universe, which is titled "The EPR experiment according to the causal interpretation" (another name for Bohmian mechanics), which can be read in its entirety on google books here. Do you see any mention of a collapse assumption there?

And here's another:

A causal account of non-local Einstein-Podolsky-Rosen spin correlations

Section 5 on p.12-13 of the pdf says:

The preceding analysis enables us to see clearly the manner in which the assumptions made by Bell [7] in his derivation of an inequality that any local hidden variables theory must apparently satisfy are violated in the causal interpretation ...

In the causal interpretation the probability distribution of positions is derived from the quantum mechanical wavefunction which is a function of all the contributing parts of the process, including the orientation of the magnets ...

Bell's inequality is therefore violated because the hidden variables are non-locally interconnected by the quantum potential derived from the total quantum state. It is in this sense that the causal interpretation implies non-local correlations in the properties of distantly separated systems.

So it seems that the analysis is based only on the positions of the parts of the system (including which direction the particles are deflected by the magnets, which is what a determination of 'spin' is based on), and that "the system" explicitly includes the magnets and their orientations. And this Bohmian analysis does apparently show that Bell's inequality can be violated.

 

[akhmeteli]

My personal advice to an independent researcher:

Thank you for your advice, but I think it's completely misplaced. Let me explain.

Now, what’s my personal opinion on EPR-Bell experiments and loopholes? Well, I think you are presenting a terrible biased picture of the situation. You want us to believe that current experts in EPR-Bell experiments have the same bizarre valuation of their experiments as you have. Namely, that every performed EPR-Bell experiment so far is worth nothing?? Zero, zip, nada, zilch, 0!?

Before you start another episode of your soap opera here, why don't you just read the question you were asked?

I wrote the following:

"Those experts are telling us, mere mortals, that there have been no loophole-free Bell experiments. You are certainly free to disagree with them, but then why don’t you just pinpoint that loophole-free experiment? And it would be most helpful if you could explain how it so happened that Shimony, Zeilinger and Genovese have no knowledge whatsoever about this experiment.
Again, Ruta is no fan of local realism either, but he also admits that there are no such experiments.
So, to summarize, it seems obvious that there have been no such experiments so far (DrChinese will strongly disagree, but let me ask you, DevilsAvocado, what is your personal opinion?)"

So it should be clear that I asked you the following question: "Do you agree that there have been no loophole-free Bell experiments?" Did I say "that every performed EPR-Bell experiment so far is worth nothing", as you imply? No, I did not. In my opinion, those experiments are very valuable as they explored the new area of parameters, so we know now what Nature is like in this area. Why are you substituting my question with something very different? Why are you ascribing me an opinion that I don't share?

So let me ask you again:

"Do you agree that there have been no loophole-free Bell experiments?"

You are also trying to apply this faulty logic on RUTA:


Yes, RUTA is an honest scientist and he would never lie and say that a 100% loophole-free Bell experiment has been performed, when it hasn’t yet.

So you agree that a loophole-free Bell experiment has not been performed? Or not?

But where do you see RUTA saying that performed Bell experiments so far is worth absolutely nothing, nil?? Your twist is nothing but a scam:

But where do you see me saying that performed Bell experiments so far is worth absolutely nothing, nil?? Your twist is nothing but a scam

I can guarantee you that RUTA, Zeilinger or any other real scientist in the community all agree that all performed EPR-Bell experiments so far has proven with 99.99% certainty that all local realistic theories are doomed. But they are fair, and will never lie, and say 100%, until they are 100%.

You are exploiting this fact in a very deceive way, claiming that they are saying that there is 0% proof of local realistic theories being wrong.

And where am I "claiming that they are saying that there is 0% proof of local realistic theories being wrong"? I give their direct quotes confirming that there have been no loophole-free Bell experiments. Why twist my words again? They do believe there is little or no chance for local realism, but this is their opinion. The fact (that they admit) is, however, that there have been no loophole-free experiments ruling out local realism.

And then comes the "Grand Finale", where you use a falsification of Anton Zeilinger’s standpoint, as the "foundation" for this personal cranky statement:

Outrageous

Since when a literal quote is a falsification?

And I gave you the reasons, so there are indeed "some reasons to believe these inequalities cannot be violated either in experiments or in quantum theory, EVER". If you are outraged by this statement, that does not mean there are no such reasons.

 

[akhmeteli]

You can include the state of the measuring device in a quantum analysis (simplifying its possible states so you don't actually consider it as composed of a vast number of particles), see this google scholar search for "state of the measuring" and "quantum".

So was the violation in quantum theory derived in this way?

Or just include the measuring device in the quantum state, and apply the Born rule to the joint state of all the measuring devices/pointer states at some time T after the experiment is finished. Goldstein's point about the Bohmian probability being |ψ(q)|^2 means the probabilities for different joint pointer states at T should be exactly equal to the Bohmian prediction about the pointer states at T.

So was the violation in quantum theory derived without PP or something like that? Mind that "different joint pointer states" overlap in principle.

Huh? My understanding is that a purely Bohmian analysis of any physical situation will never make use of "collapse", it'll only find the probabilities for the particles to end up in different positions according to the quantum equilibrium hypothesis. The idea that "collapse is a good approximation" would only be used if you wanted to compare Bohmian predictions to the predictions of a QM recipe which uses the collapse assumption, but if you were just interested in what Bohmian mechanics predicted, you would have no need for anything but the Bohmian guiding equation which tells you how particle positions evolve.

So were violations proven in "a purely Bohmian analysis"? I am not aware of that.

OK, but have you actually studied the math of Bohmian mechanics and looked at how it makes predictions about any experiments, let alone Bell-type experiments? I haven't myself, but from what I've read I'm pretty sure that no purely Bohmian derivation of predictions would need to make use of any "trick" involving collapse.

Again, same question, is there a "purely Bohmian derivation of" violations? I am not aware of that.

Well, take a look at section 7.5 of Bohm's book The Undivided Universe, which is titled "The EPR experiment according to the causal interpretation" (another name for Bohmian mechanics), which can be read in its entirety on google books here. Do you see any mention of a collapse assumption there?

Yes: "Using the theory of measurement..." and "do not overlap for different j"

But Goldstein also says that the probabilities predicted by Bohmian mechanics are just the same as those predicted by QM. Again, I think the seeming inconsistency is probably resolved if by assuming that when he talks of agreement he's talking of a single application of the Born rule to a quantum system which has been evolving in a unitary way, whereas when he talks about "approximation" he's talking about a repeated sequence of unitary evolution, projection onto an eigenstate by measurement, unitary evolution starting again from that eigenstate, another projection, etc.

Very well, and this is what we have in Bell experiments, as there are two measurements.

 

[DevilsAvocado]

... And where am I "claiming that they are saying that there is 0% proof of local realistic theories being wrong"? I give their direct quotes confirming that there have been no loophole-free Bell experiments. Why twist my words again? They do believe there is little or no chance for local realism, but this is their opinion. The fact (that they admit) is, however, that there have been no loophole-free experiments ruling out local realism.

You are a funny guy, not a scientist.

Is this really so hard? You are continuously making the same cranky INSINUATIONS – as if all the hard work by one of the most famous experts in EPR-Bell experiments, Anton Zeilinger, has only resulted in a PERSONAL OPINION!?

You are way out my friend, and alone on your twisted road:

When I first entered the foundations community (1994), there were still a few conference presentations arguing that the statistical and/or experimental analyses of EPR-Bell experiments were flawed. SUCH TALKS HAVE GONE THE WAY OF THE DINOSAURS. VIRTUALLY EVERYONE AGREES THAT THE EPR-BELL EXPERIMENTS AND QM ARE LEGIT, SO WE NEED A SIGNIFICANT CHANGE IN OUR WORLDVIEW. There is a proper subset who believe this change will be related to the unification of QM and GR :-)

Stanford Encyclopedia of Philosophy – Bell's Theorem
...
In the face of the spectacular experimental achievement of Weihs et al. and the anticipated result of the experiment of Fry and Walther THERE IS LITTLE THAT A DETERMINED ADVOCATE OF LOCAL REALISTIC THEORIES CAN SAY except that, despite the spacelike separation of the analysis-detection events involving particles 1 and 2, the backward light-cones of these two events overlap, and it is conceivable that some controlling factor in the overlap region is RESPONSIBLE FOR A CONSPIRACY AFFECTING THEIR OUTCOMES. THERE IS SO LITTLE PHYSICAL DETAIL IN THIS SUPPOSITION that a discussion of it is best delayed until a methodological discussion in Section 7.

I made the important parts in upper-case + bold, since you seem to having trouble understanding simple English.

 

[akhmeteli]

Yes, they aren't quite happy yet. The departure from the old concepts is just too great.

This isn't much different than Darwin's TOE in the mid-nineteen century. Not everyone would immediately recognize the evidence(no matter what), for the idea of a fish turning into a human being was just too radical, as you are saying about local realism. The TOE turned the world upside down, but we made do with it. Controversial or not, the theory of evolution is here to stay and so is the death of classical realism.

So TOE has been confirmed by now. So what? Should we consider that a confirmation of elimination of local realism? No way. This elimination must be confirmed independently. Has it been confirmed experimentally so far? As there are no experimental demonstrations of violations of genuine Bell inequalities, local realism has not been ruled out so far. What should we expect? In 10 years? In fifty years? It's a matter of opinion. You believe local realism will be eliminated by future experiments, I don't expect that. But both of us will have to accept the results of the future experiments, whether we'll like them or dislike them.
We have yet to see decisive experiments, so we both still have the right to have our opinions.

 

[JesseM]

You can include the state of the measuring device in a quantum analysis (simplifying its possible states so you don't actually consider it as composed of a vast number of particles), see this google scholar search for "state of the measuring" and "quantum".

So was the violation in quantum theory derived in this way?

I'm pretty sure you can derive any quantum statistics in this way. Doing a little research, it turns out this was essentially Von Neumann's approach to the measurement problem--he conceived of two stages of the measurement process, a first where the system being measured simply becomes entangled with the measuring-device, and a second where the measuring-device is "observed" and found to be in some definite pointer state, with the probability of different pointer states determined by the Born rule. See this paper where on page 3 they write:

The crucial step to describe the measurement process as an interaction of two quantum systems [as is implicit in (2.2)] was made by von Neumann [6], who recognized that an interaction between a classical and a quantum system cannot be part of a consistent quantum theory. In his Grundlagen, he therefore proceeded to decompose the quantum measurement into two fundamental stages. The first stage (termed "von Neumann measurement") gives rise to the wavefunction (2.2). The second stage (which von Neumann termed "observation" of the measurement) involves the collapse described above, i.e., the transition from (2.2) to (2.3).

The same authors have another paper here where they apply this sort of analysis to "Bell-type measurements" on p. 16, with two quantum particles Q1 and Q2 along with two measuring-devices or "ancillae" A1 and A2, such that after the ancillae interact with the particles they are all in one entangled state $$\mid Q_1 Q_2 A_1 A_2 \rangle = \frac{1}{\sqrt{2}} (\mid \uparrow \uparrow 1 1 \rangle + \mid \downarrow \downarrow 0 0 \rangle )$$. They then say that "after observing A1, for instance, the state of A2 can be inferred without any uncertainty". Unfortunately they don't give explicit calculations for the probabilities of different results on A1 and A2 when the ancillae aren't measuring spin on the same axis, so they don't clearly show how von Neumann's approach predicts Bell inequality violations. And although I came across a lot of other papers that model measurement in terms of measuring-devices becoming entangled with measuring-systems, like http://www.hep.princeton.edu/~mcdonald/examples/QM/zurek_prd_24_1516_81.pdf , most did not use von Neumann's approach of assuming a collapse at the very end when the measuring devices were all "observed", instead they were generally trying to show how one could make meaningful statements about measurement results without making use of even a single "collapse" or application of the Born rule (perhaps part of the problem is that von Neumann's approach is rather old hat so most physicists would just consider it pedantic to explicitly demonstrate what predictions it would give for a Bell-type experiment). But anyway, given that this approach has been around for so many years, I seriously doubt that it would fail to predict Bell inequality violations without anyone having noticed this fact! (or without it being widely commented-on in these sorts of papers if it was known that it failed to predict BI violations)

Also, I found one other interesting paper http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf which discusses what happens if we assume measurement just creates entanglement between pointer states and particle states with no collapse ever (what the author calls the 'bare theory' of QM0, and then we consider the limit as an observer makes an infinite series of measurements in an EPR type experiment. On p. 13-14 the author discusses the result:

For another example suppose that two systems S_A and S_B are initially in the EPR state (2) and that A and B make space-like measurements of their respective systems ... What does the bare theory predict in the limit as this experiment is performed an infinite number of times? ... given the general limiting property, A and B will approach an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts .. if they perform an appropriate sequence of different experiments, then they will approach an eigenstate of reporting that their results fail to satisfy the Bell-type inequalities.

Again, same question, is there a "purely Bohmian derivation of" violations? I am not aware of that.

I believe so, the section of Bohm's book I linked to and the paper I linked to in post #701 both appeared to analyze EPR-type experiments from a purely Bohmian perspective.

Well, take a look at section 7.5 of Bohm's book The Undivided Universe, which is titled "The EPR experiment according to the causal interpretation" (another name for Bohmian mechanics), which can be read in its entirety on google books here. Do you see any mention of a collapse assumption there?

Yes: "Using the theory of measurement..." and "do not overlap for different j"

I think you're probably misunderstanding the import of those phrases. When Bohm wrote on p. 122 "Using the theory of measurement described in chapters 2 and 6, we may assume an interaction Hamiltonian..." and gives an equation, that's the Hamiltonian equation which guides the continuous time evolution of the system, I don't see how it has anything to do with discontinuous collapse. And the "theory of measurement" described in chapter 6 appears to be one that does not involve collapse--scroll down to p. 104 here to look at that chapter, he says on p. 109:

At this stage we can say that everything has happened as if the overall wave function had 'collapsed' to one corresponding to the actual result obtained in the measurement. We emphasise, however, that in our treatment there is no actual collapse; there is merely a process in which the information represented by the unoccupied packets effectively loses all potential for activity ... It follows that in this regard measurement is indeed just a special case of a transition process in which the two systems interact and then come out in correlated states. It is this correlation that enables us, from the observed result, to attribute a corresponding property to the final state of the observed system.

In the transition process that takes place in a measurement, it is clear that (as happens indeed in all transition processes) there is no need to place any 'cuts' or arbitrary breaks in the description of reality, such as that, for example, introduced by von Neumann between the quantum and classical levels.

I also don't see why "$$\alpha \Delta t$$ must be large enough so that the $$\Phi_A (y - j \alpha \Delta t )$$ do not overlap for different j" lower on the same page has anything to do with collapse, $$\Phi_A (y)$$ is supposed to represent the "initial wave packet of the apparatus" so this condition also may express some constraint on the design of the apparatus (maybe something like the idea that it should be designed so there isn't significant interference between different possible pointer states), I'm not sure. Do you actually understand the detailed meaning of the math in this section or are you just looking at the verbal descriptions of Bohmian calculations like me? You didn't answer the question I asked earlier:

OK, but have you actually studied the math of Bohmian mechanics and looked at how it makes predictions about any experiments, let alone Bell-type experiments? I haven't myself, but from what I've read I'm pretty sure that no purely Bohmian derivation of predictions would need to make use of any "trick" involving collapse.

But Goldstein also says that the probabilities predicted by Bohmian mechanics are just the same as those predicted by QM. Again, I think the seeming inconsistency is probably resolved if by assuming that when he talks of agreement he's talking of a single application of the Born rule to a quantum system which has been evolving in a unitary way, whereas when he talks about "approximation" he's talking about a repeated sequence of unitary evolution, projection onto an eigenstate by measurement, unitary evolution starting again from that eigenstate, another projection, etc.

Very well, and this is what we have in Bell experiments, as there are two measurements.

Have you not been paying attention to the distinction I've been making in previous posts between two procedures for calculating probabilities in QM? I have been saying over and over that if you have a series of measurements, you don't have to treat each measurement as leading to a collapse, you can instead treat each measurement as just creating entanglement between measuring apparatus and system being measured, and then apply the Born rule once to the final pointer states after a long series of measurements. That seems to be exactly the approach von Neumann used to deal with measurement too, as noted at the top. So my point is that as long as you only apply the Born rule once in this way, I think there is perfect agreement in the probabilities for different pointer states between this approach and Bohmian mechanics; it's only when you use the projection postulate repeatedly at the moment of each measurement that the agreement with Bohmian mechanics may only be "approximate".

 

[akhmeteli]

I'm pretty sure you can derive any quantum statistics in this way.

Being pretty sure is one thing. Giving a proof or a reference is something else. I comment on your references below.

Doing a little research, it turns out this was essentially Von Neumann's approach to the measurement problem--he conceived of two stages of the measurement process, a first where the system being measured simply becomes entangled with the measuring-device, and a second where the measuring-device is "observed" and found to be in some definite pointer state, with the probability of different pointer states determined by the Born rule.

Again, we may have some opinion about adequacy of this procedure, but it is not quite relevant. This procedure is about just one measurement, the Bell theorem is about two measurements.

See this paper where on page 3 they write:

The same authors have another paper here where they apply this sort of analysis to "Bell-type measurements" on p. 16, with two quantum particles Q1 and Q2 along with two measuring-devices or "ancillae" A1 and A2, such that after the ancillae interact with the particles they are all in one entangled state $$\mid Q_1 Q_2 A_1 A_2 \rangle = \frac{1}{\sqrt{2}} (\mid \uparrow \uparrow 1 1 \rangle + \mid \downarrow \downarrow 0 0 \rangle )$$. They then say that "after observing A1, for instance, the state of A2 can be inferred without any uncertainty". Unfortunately they don't give explicit calculations for the probabilities of different results on A1 and A2 when the ancillae aren't measuring spin on the same axis, so they don't clearly show how von Neumann's approach predicts Bell inequality violations.

So no proof.

And although I came across a lot of other papers that model measurement in terms of measuring-devices becoming entangled with measuring-systems, like http://www.hep.princeton.edu/~mcdonald/examples/QM/zurek_prd_24_1516_81.pdf , most did not use von Neumann's approach of assuming a collapse at the very end when the measuring devices were all "observed", instead they were generally trying to show how one could make meaningful statements about measurement results without making use of even a single "collapse" or application of the Born rule (perhaps part of the problem is that von Neumann's approach is rather old hat so most physicists would just consider it pedantic to explicitly demonstrate what predictions it would give for a Bell-type experiment).

So no proof.

But anyway, given that this approach has been around for so many years, I seriously doubt that it would fail to predict Bell inequality violations without anyone having noticed this fact! (or without it being widely commented-on in these sorts of papers if it was known that it failed to predict BI violations)

In this case you are right to seriously doubt it:-), as "someone" has indeed noticed this fact, and it was not me! You see, I clearly said in this thread and in my article that I have little, if anything new to say about the Bell theorem, I just repeat other people's analysis. These people are nightlight and Santos (nightlight told me that they corresponded for years via emails). I give the references in my article. If you feel the references are not specific enough, let me know, I'll try to do something about that.

I'll try to address the other points of your post later.

 

[JesseM]

Yes, I haven't linked to a proof, and I don't feel like spending hours combing through papers looking for one (as I said, most modern papers would probably just consider the result too trivial to explicitly demonstrate). Are you just being pedantic in noting I haven't proved it, or do you actually believe it is plausible that von Neumann's approach to QM measurement, which has been around for decades, would fail to predict Bell inequality violations without anyone noticing this fact? (or if physicists had noticed, without it being a widely discussed result?) Or does your claim here:

as "someone" has indeed noticed this fact, and it was not me! You see, I clearly said in this thread and in my article that I have little, if anything new to say about the Bell theorem, I just repeat other people's analysis. These people are nightlight and Santos (nightlight told me that they corresponded for years via emails). I give the references in my article.

...mean that you believe "nightlight and Santos" have actually proved that von Neumann's approach, where we model measurements as just creating entanglement and we then "observe" the measurement records later (using the Born rule on the records), fails to predict violations of Bell inequalities in those records?

Also, note the paper http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf I linked to above, which shows that in the limit as the number of measurements (without collapse) in an EPR type experiment goes to infinity the state vector will approach "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". This does at least imply that in the limit as the number of measurements goes to infinity, if we "collapse" the records at the very end, the probability that the records will show measurement results that were "randomly distributed and statistically correlated in just the way the standard theory predicts" should approach 1 in this limit. Do you disagree?

 

[akhmeteli]

Also, I found one other interesting paper http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf which discusses what happens if we assume measurement just creates entanglement between pointer states and particle states with no collapse ever (what the author calls the 'bare theory' of QM0, and then we consider the limit as an observer makes an infinite series of measurements in an EPR type experiment. On p. 13-14 the author discusses the result:

JesseM, with all due respect, a couple of lines later the author writes: "Note, however, that since the linear dynamics can be written in a perfectly local form, there are in fact no nonlocal causal connections in the bare theory. ...Just as reports of determinate results, relative frequencies, and randomness would generally be explained by the bare theory as illusions the apparent nonlocality here would be just that, apparent." :-) And on page 4: "According to the bare theory,
an observer who begins in an eigenstate of being ready to make a
measurement would end up in an eigenstate of reporting that he has
an ordinary, determinate result to his measurement. This might mean
that the observer believes that he has a determinate measurement
result, but in the context of the bare theory this would not generally
mean that there is any determinate result that the observer believes he
has. Contrary to what Everett and others have claimed, the bare theory
does not make the same empirical predictions as the standard theory;
rather, the bare theory at best provides an explanation for why it might
appear to an observer that the standard theory's empirical predictions
are true when they are in fact false. That is, the bare theory provides
the basis for claiming in some circumstances that some of one's beliefs
are the result of an illusion." So no, this link, while indeed interesting, does not prove what you want.

I believe so, the section of Bohm's book I linked to and the paper I linked to in post #701 both appeared to analyze EPR-type experiments from a purely Bohmian perspective.

I commented on the Bohm's book, and in the paper by Dewdney e.a., they take their formulae for correlations 3.2 and 3.2a from nowhere, just as "well known expectation value for the correlations". After that, the inequalities are violated. But you cannot get these formulae without the projection postulate, at least that's what I think so far.

I think you're probably misunderstanding the import of those phrases. When Bohm wrote on p. 122 "Using the theory of measurement described in chapters 2 and 6, we may assume an interaction Hamiltonian..." and gives an equation, that's the Hamiltonian equation which guides the continuous time evolution of the system, I don't see how it has anything to do with discontinuous collapse. And the "theory of measurement" described in chapter 6 appears to be one that does not involve collapse--scroll down to p. 104 here to look at that chapter, he says on p. 109:

I also don't see why "$$\alpha \Delta t$$ must be large enough so that the $$\Phi_A (y - j \alpha \Delta t )$$ do not overlap for different j" lower on the same page has anything to do with collapse, $$\Phi_A (y)$$ is supposed to represent the "initial wave packet of the apparatus" so this condition also may express some constraint on the design of the apparatus (maybe something like the idea that it should be designed so there isn't significant interference between different possible pointer states), I'm not sure. Do you actually understand the detailed meaning of the math in this section or are you just looking at the verbal descriptions of Bohmian calculations like me?

While you may regard the mention of measurement theory as purely formal (I did not check it), the "overlap" phrase is critical. No overlap - no interference. This is where they get rid of superposition. And no condition can prevent overlap. The word "significant" is not good enough.

I did not check the "proof" in detail, but I know Bohm's theory of measurement and know where they get rid of superposition to get "appearance of collapse".

You didn't answer the question I asked earlier:

Sorry, as I said, I am struggling trying to keep up with you:-)

Yes, I studied their math, and it is my understanding that the neglect of the overlap takes care of superpositions, so I disagree with your "pretty sure".

Have you not been paying attention to the distinction I've been making in previous posts between two procedures for calculating probabilities in QM? I have been saying over and over that if you have a series of measurements, you don't have to treat each measurement as leading to a collapse, you can instead treat each measurement as just creating entanglement between measuring apparatus and system being measured, and then apply the Born rule once to the final pointer states after a long series of measurements. That seems to be exactly the approach von Neumann used to deal with measurement too, as noted at the top. So my point is that as long as you only apply the Born rule once in this way, I think there is perfect agreement in the probabilities for different pointer states between this approach and Bohmian mechanics; it's only when you use the projection postulate repeatedly at the moment of each measurement that the agreement with Bohmian mechanics may only be "approximate".

I got your idea, but, as I said, the procedure you describe has nothing to do with real Bell experiments, where measurements are done separately on each particle, they actually use the results of two measurements. So your procedure applying the Born rule once does not seem relevant to experiments. How do you get the correlation in your procedure?

 

[akhmeteli]

Yes, I haven't linked to a proof, and I don't feel like spending hours combing through papers looking for one (as I said, most modern papers would probably just consider the result too trivial to explicitly demonstrate).

I fully understand.

Are you just being pedantic in noting I haven't proved it, or do you actually believe it is plausible that von Neumann's approach to QM measurement, which has been around for decades, would fail to predict Bell inequality violations without anyone noticing this fact? (or if physicists had noticed, without it being a widely discussed result?)

I would like to be accurate here, as it is my understanding that the projection postulate was also introduced by Neumann. But I believe you have in mind an approach where actual measurement is performed only once. I just don't understand how this approach is relevant to Bell experiments where measurements are performed twice. And I really don't think you can get theoretical violations in standard QM or in Bohmian mechanics without the projection postulate or something like that.

Or does your claim here:

...mean that you believe "nightlight and Santos" have actually proved that von Neumann's approach, where we model measurements as just creating entanglement and we then "observe" the measurement records later (using the Born rule on the records), fails to predict violations of Bell inequalities in those records?

See my comment above on "Neumann's approach". I cannot say in good faith that nightlight or Santos "proved" that violations in QM cannot be proven without using the projection postulate or something like that (maybe they did, but I am not sure). What they did do (at least this is my understanding), they noted that the projection postulate is used in standard proofs of the Bell theorem where it is proven that the inequalities can be violated in QM, and they also noted that the projection postulate contradicts unitary evolution. Can you prove the violations without this postulate? I cannot eliminate such a possibility, but I don't think it is possible. I perfectly understand that you don't want to spend hours to find a proof of what you think is true, but I hope you'll understand that neither I want to spend hours to find a proof of what you think is true and I think is false:-) My logic is as follows. Violations spell nonlocality, the projection postulate spells nonlocality (as soon as the spin projection of one particle is measured, the spin projection of the other particle, however remote, becomes determinate - this stinks to heaven!), so a suspicion that this is the only source of nonlocality seems quite natural.

Also, note the paper http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf I linked to above, which shows that in the limit as the number of measurements (without collapse) in an EPR type experiment goes to infinity the state vector will approach "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". This does at least imply that in the limit as the number of measurements goes to infinity, if we "collapse" the records at the very end, the probability that the records will show measurement results that were "randomly distributed and statistically correlated in just the way the standard theory predicts" should approach 1 in this limit. Do you disagree?

I commented on that in my post 709.

 

[DevilsAvocado]

My logic is as follows. Violations spell nonlocality, the projection postulate spells nonlocality (as soon as the spin projection of one particle is measured, the spin projection of the other particle, however remote, becomes determinate - this stinks to heaven!), so a suspicion that this is the only source of nonlocality seems quite natural.

What also stinks to heaven, is when wannabes pretend to have "serious proof" that dismiss all work of John Bell, and all serious scientist who worked on EPR-Bell experiments for decades – without even a basic understanding of Bell's Theorem!?

EPR-Bell experiments is not about "the other particle, however remote, becomes determinate"! This is only the case when the polarizers are aligned parallel! EPR-Bell experiments are all about statistics, and there is no way one could violate Bell's Inequality when the polarizers are aligned parallel only, JesseM can verify this.

What is also hilarious is that when the polarizers are aligned parallel, and the correlation is 100%, anyone can easily construct LHV that explains this in a LR model, except you.

But I’m not surprised you have missed this. You seem to spend all your time looking for irrelevant "stuff" to discredit the work of John Bell.

 

[JesseM]

I would like to be accurate here, as it is my understanding that the projection postulate was also introduced by Neumann. But I believe you have in mind an approach where actual measurement is performed only once. I just don't understand how this approach is relevant to Bell experiments where measurements are performed twice.

You seem to be misunderstanding something really basic about my argument--you are conflating "measurement" with "projection", but my whole point is that they don't need to be treated as equivalent! You can instead assume that each interaction between the quantum system and the measuring-device can be treated in a purely unitary way--i.e. these measurements do not involve projection--and that after all the measurements in your experiment are done, you have a pure state where all the records of the previous measurements are in a massive superposition, and only then do you use the projection postulate once on the whole collection of records (records of many different prior measurements). I've already explained this several times in the past but you continue to misunderstand...for example, from post #706:

Have you not been paying attention to the distinction I've been making in previous posts between two procedures for calculating probabilities in QM? I have been saying over and over that if you have a series of measurements, you don't have to treat each measurement as leading to a collapse, you can instead treat each measurement as just creating entanglement between measuring apparatus and system being measured, and then apply the Born rule once to the final pointer states after a long series of measurements. That seems to be exactly the approach von Neumann used to deal with measurement too, as noted at the top. So my point is that as long as you only apply the Born rule once in this way, I think there is perfect agreement in the probabilities for different pointer states between this approach and Bohmian mechanics; it's only when you use the projection postulate repeatedly at the moment of each measurement that the agreement with Bohmian mechanics may only be "approximate".

And post #694:

Suppose "as a matter of formalism" we adopt the procedure of applying unitary evolution to the whole experiment and then applying the Born rule to joint states (which includes measurement records/pointer states) at the very end. And suppose this procedure gives predictions which agree with the actual statistics we see when we examine records of experiments done in real life. Then don't we have a formalism which has a well-defined procedure for making predictions and whose predictions agree with experiment? It doesn't matter that the formalism doesn't make predictions about each individual measurement at the time it's made, as long as it makes predictions about the final results at the end of the experiment which we can compare with the actual final results (or compared with the predictions about the final results that any local realist theory would make).

post #690:

But in terms of the formalism, do you agree that you can apply the Born rule once for the amplitude of a joint state? One could consider this as an abstract representation of a pair of simultaneous measurements made at the same t-coordinate, for example. Even if the measurements were made at different times, one could assume unitary evolution for each measurement so that each measurement just creates entanglement between the particles and the measuring devices, but then apply the Born rule once to find the probability for the records of the previous measurements ('pointer states' in Bohmian lingo)

So, after reviewing these comments, do you understand what I mean now? That if we want to make predictions about what our records will show at the end of a series of N measurements, we can assume unitary evolution until after all N measurements are complete, and then just apply the Born rule to the records at that time to get a prediction about the statistics?

If you do understand this, note that this is exactly what von Neumann's approach was. In his approach we do not assume that each measurement collapses the wavefunction, instead it just causes entanglement, and then only later are the measurement records "observed". In post #706 I quoted this paper which described his approach on p. 3:

The crucial step to describe the measurement process as an interaction of two quantum systems [as is implicit in (2.2)] was made by von Neumann [6], who recognized that an interaction between a classical and a quantum system cannot be part of a consistent quantum theory. In his Grundlagen, he therefore proceeded to decompose the quantum measurement into two fundamental stages. The first stage (termed "von Neumann measurement") gives rise to the wavefunction (2.2). The second stage (which von Neumann termed "observation" of the measurement) involves the collapse described above, i.e., the transition from (2.2) to (2.3).

Similarly, consider the paper Quantum Mechanics and Reality which discusses different approaches to "measurement", and on p. 16 describes von Neumann's approach:

In contrast to Bohr, the measuring apparatus A as well as systems S are both to be described by quantum mechanics.

...

The state $$\sum c_n \phi_n f(a_n)$$ is a linear superposition of states with different pointer states. It is a grotesque state. We still have not obtained a definite value of the pointer reading. Von-Neumann now postulates that when the measurement is completed, and not before that, the wave function collapses to one of the terms in the linear superposition e.g. to $$\phi_N f(a_N)$$. It is this collapse postulate which adds an extra ingredient to Quantum mechanics and making quantum mechanical description nonclosed.

In an elaboration of von-Neumann view by London and Bauer, and also subscribed to by Wigner and Stapp, this final collapse of wave function takes place when the result of measurement is recorded in a human mind.

Anyway, if you now understand the approach I'm suggesting but aren't convinced that von Neumann's was the same, I can try to find more sources explaining his approach. But I want to make sure that you actually do understand my approach now, given that you still seem to be conflating "measurement" with "collapse"...

 

[akhmeteli]

You seem to be misunderstanding something really basic about my argument--you are conflating "measurement" with "projection", but my whole point is that they don't need to be treated as equivalent! You can instead assume that each interaction between the quantum system and the measuring-device can be treated in a purely unitary way--i.e. these measurements do not involve projection--and that after all the measurements in your experiment are done, you have a pure state where all the records of the previous measurements are in a massive superposition, and only then do you use the projection postulate once on the whole collection of records (records of many different prior measurements). I've already explained this several times in the past but you continue to misunderstand...for example, from post #706:

OK, so you just use the projection postulate, not the Born rule? Then I agree that you can prove violations in quantum mechanics. But this is exactly where you introduce nonlocality. Remember that actual records are not even permanent. Where exactly do you perform this second stage of your procedure, the "observation"? Near the point where the first particle is? Or where the second particle is? If where the first particle is, as soon as you "observe" its spin projection, the spin projection of the second one becomes immediately determinate, according to the projection postulate, and remember that you can choose on the spot which spin projection you want to determine. So you do introduce nonlocality. Or are you trying to say that the Born rule and the projection postulate are one and the same thing? But as far as I understand, the Born rule does not state that after the measurement the system is in a certain eigenstate, it just gives the probability of a certain measurement result.

So, after reviewing these comments, do you understand what I mean now? That if we want to make predictions about what our records will show at the end of a series of N measurements, we can assume unitary evolution until after all N measurements are complete, and then just apply the Born rule to the records at that time to get a prediction about the statistics?

No, I don't understand what you mean. Now you're telling me that you use the Born rule. A few lines before you said you were using the projection postulate. Please explain.

 

[akhmeteli]

EPR-Bell experiments is not about "the other particle, however remote, becomes determinate"! This is only the case when the polarizers are aligned parallel! EPR-Bell experiments are all about statistics, and there is no way one could violate Bell's Inequality when the polarizers are aligned parallel only, JesseM can verify this.

With all due respect, you did not understand anything I said. I did not speak about two polarizers at all. Let me try to explain. Suppose you have two particles of a singlet, and you are measuring the spin projection of the first particle, so you need just one polarizer. The projection postulate says that after you measure the spin projection on some axis, say, it is +1, the wavefunction immediately collapses into an eigenstate of this spin projection of the first particle. That means that the spin projection of the second particle on the same axis immediately becomes determinate, it equals -1. That's where nonlocality is introduced through the projection postulate. Then you may measure the spin projection of the second particle on a different axis using another polarizer to prove violations or for whatever purpose you want, but that is a different story.

 

[DevilsAvocado]

With all due respect, you did not understand anything I said.

With all due respect, I think you are talking bull. If it’s one thing Bell showed, it’s that the Einsteinian argument fails:

no action on a distance (polarisers parallel) ⇒ determinism
determinism (polarisers nonparallel) ⇒ action on a distance

Determinism is stone dead.

That's where nonlocality is introduced through the projection postulate.

Are you talking about John von Neumann and the "wavefunction collapse" from 1932?? The collapse of the wavefunction is just an interpretation?? And AFAICT, it not very "hot" either?? Are you saying that John von Neumann, who died in 1957, proved John Bell wrong in 1964?? Or are you saying that you have discovered "something" that John Bell and the whole scientific community totally missed??

http://en.wikipedia.org/wiki/Wave_function_collapse#History_and_context"
...
Although von Neumann's projection postulate is often presented as a normative description of quantum measurement, it was conceived by taking into account experimental evidence available during the 1930s (in particular the Compton-Simon experiment has been paradigmatic), and that many important http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Wavefunction_collapse" do not satisfy it (so-called measurements of the second kind).[4]

The existence of the wave function collapse is required in

• the Copenhagen interpretation
• the objective collapse interpretations
• the so-called transactional interpretation
• in a "spiritual interpretation" in which consciousness causes collapse.

On the other hand, the collapse is considered as a redundant or optional approximation in

• interpretations based on Consistent Histories
• the Many-Worlds Interpretation
• the Bohm interpretation
• the Ensemble Interpretation

http://en.wikipedia.org/wiki/Dunning–Kruger_effect"

 

[JesseM]

OK, so you just use the projection postulate, not the Born rule?

If you only use it once, at the very end, and then don't attempt to predict anything about what happens to the records afterwards, I don't see the difference. For example, if there were three measurements which could each yield result 1 or 0, then at the end right before "observation" the records will be a single quantum state which can be expressed as a sum of eigenstates:

$$\alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +$$$$\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle$$

where the $$\alpha_i$$ are complex amplitudes. Then if you apply the "projection postulate", you're saying the quantum state will randomly become one of those eigenstates, with the probability of it going to a given eigenstate like $$\mid 010 \rangle$$ being $$\alpha_3 \alpha_3*$$ (i.e. the amplitude times its complex conjugate). And the "Born rule" just tells you that the probability of getting a given result like 010 is $$\alpha_3 \alpha_3*$$. So if you're not interested in what happens to the quantum state later, but just in the probabilities of seeing different combinations of measurement records at some time T after all the measurements are complete, I don't see the distinction between applying the "projection postulate" at T to get these probabilities vs. applying the "Born rule" at T. What difference are you seeing?

But this is exactly where you introduce nonlocality. Remember that actual records are not even permanent. Where exactly do you perform this second stage of your procedure, the "observation"? Near the point where the first particle is?

If you see a paper listing a bunch of results taken at different places, how do you think they got into that one paper? Presumably the information from each measuring device was transferred to a common location at some point, so you're free to assume that each measuring-device was transferred to a common location before the "observation" of their records happened, or that each sent an email to a common location before "observation", whatever.

 

[akhmeteli]

With all due respect, I think you are talking bull. If it’s one thing Bell showed, it’s that the Einsteinian argument fails:

no action on a distance (polarisers parallel) ⇒ determinism
determinism (polarisers nonparallel) ⇒ action on a distance

Determinism is stone dead.



Are you talking about John von Neumann and the "wavefunction collapse" from 1932?? The collapse of the wavefunction is just an interpretation?? And AFAICT, it not very "hot" either?? Are you saying that John von Neumann, who died in 1957, proved John Bell wrong in 1964?? Or are you saying that you have discovered "something" that John Bell and the whole scientific community totally missed??



http://en.wikipedia.org/wiki/Dunning–Kruger_effect"

I give up. You have no use for any explanations, and I have no use for your soap opera.

 

[DevilsAvocado]

I give up.

This is often the case when frauds are proven wrong:

http://en.wikipedia.org/wiki/Wave_function_collapse#History_and_context"
...
Although von Neumann's projection postulate is often presented as a normative description of quantum measurement, it was conceived by taking into account experimental evidence available during the 1930s (in particular the Compton-Simon experiment has been paradigmatic), and that many important http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Wavefunction_collapse" do not satisfy it (so-called measurements of the second kind).[4]

The existence of the wave function collapse is required in

• the Copenhagen interpretation
• the objective collapse interpretations
• the so-called transactional interpretation
• in a "spiritual interpretation" in which consciousness causes collapse.

On the other hand, the collapse is considered as a redundant or optional approximation in

• interpretations based on Consistent Histories
• the Many-Worlds Interpretation
• the Bohm interpretation
• the Ensemble Interpretation

 

[akhmeteli]

If you only use it once, at the very end, and then don't attempt to predict anything about what happens to the records afterwards, I don't see the difference. For example, if there were three measurements which could each yield result 1 or 0, then at the end right before "observation" the records will be a single quantum state which can be expressed as a sum of eigenstates:

$$\alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +$$$$\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle$$

where the $$\alpha_i$$ are complex amplitudes. Then if you apply the "projection postulate", you're saying the quantum state will randomly become one of those eigenstates, with the probability of it going to a given eigenstate like $$\mid 010 \rangle$$ being $$\alpha_3 \alpha_3*$$ (i.e. the amplitude times its complex conjugate). And the "Born rule" just tells you that the probability of getting a given result like 010 is $$\alpha_3 \alpha_3*$$. So if you're not interested in what happens to the quantum state later, but just in the probabilities of seeing different combinations of measurement records at some time T after all the measurements are complete, I don't see the distinction between applying the "projection postulate" at T to get these probabilities vs. applying the "Born rule" at T. What difference are you seeing?

I don't know. Generally speaking, the projection postulate immediately introduces nonlocality. Right now I don't quite know how the procedure you describe is supposed to be used to prove the violations in quantum mechanics. Before I see the proof, I cannot tell you if there is any difference or not. Anyway, strictly speaking, the projection postulate is not compatible with unitary evolution, whether you use the postulate at the end, at the beginning, or in the middle.

If you see a paper listing a bunch of results taken at different places, how do you think they got into that one paper? Presumably the information from each measuring device was transferred to a common location at some point, so you're free to assume that each measuring-device was transferred to a common location before the "observation" of their records happened, or that each sent an email to a common location before "observation", whatever.

Then problems with spatial separation may arise. Again, until I see how your procedure is used in a proof of violations, it is difficult to say what is important and what isn't. And remember, in principle, records are not permanent.

 

[DevilsAvocado]

I give up.

Ohh! Sorry, I missed the most important part:

http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Measurements_of_the_second_kind"
...
Note that many present-day measurement procedures are measurements of the second kind, some even functioning correctly only as a consequence of being of the second kind (for instance, a photon counter, detecting a photon by absorbing and hence annihilating it, thus ideally leaving the electromagnetic field in the vacuum state rather than in the state corresponding to the number of detected photons; also the http://en.wikipedia.org/wiki/Stern-Gerlach_experiment" would not function at all if it really were a measurement of the first kind).

 

[JesseM]

I don't know. Generally speaking, the projection postulate immediately introduces nonlocality.

Is there something wrong with "introducing nonlocality" in this context? All I'm claiming is that the rule of assuming unitary evolution, and then applying the Born rule/projection postulate at the very end to determine probabilities of different recorded outcomes, is a well-defined pragmatic procedure for generating theoretical predictions about experiments which can be compared with the actual results you find when the experiment is done in real life and the measurement results all written down somewhere. As always, it's just a pragmatic rule for generating predictions about the kinds of results we can write down, it's not meant to be a coherent description of what actually goes on physically at all moments.

Do you disagree that this is a well-defined procedure for generating predictions about the actual results seen in quantum experiments?

Right now I don't quite know how the procedure you describe is supposed to be used to prove the violations in quantum mechanics. Before I see the proof, I cannot tell you if there is any difference or not.

Again, I don't feel like spending a lot of time looking for a paper that specifically uses the von Neumann approach to derive theoretical predictions about EPR type experiments. But do you disagree that the procedure I'm using is the same one von Neumann was proposing? If you don't disagree, don't you think it's fairly implausible that this procedure would fail to predict Bell inequality violations, but no one would have noticed this before despite the procedure being known for decades?

Also, now that you hopefully understand that I'm not talking about applying to projection postulate to each measurement but only once at the very end to all the records, you might reconsider the comment I made about one of the papers I linked to:

Also, note the paper http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf I linked to above, which shows that in the limit as the number of measurements (without collapse) in an EPR type experiment goes to infinity the state vector will approach "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". This does at least imply that in the limit as the number of measurements goes to infinity, if we "collapse" the records at the very end, the probability that the records will show measurement results that were "randomly distributed and statistically correlated in just the way the standard theory predicts" should approach 1 in this limit. Do you disagree?

To put it another way, applying only unitary evolution to a series of N measurements and looking at the state S at the end means that, in the limit as N approaches infinity, S approaches "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". So, this implies that if we apply unitary evolution to a series of N measurements and then apply the projection postulate/Born rule at the very end, then in the limit as N approaches infinity, the probability that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" must approach 1. This isn't quite what I wanted to prove (that even for a small number of measurements, the von Neumann rule gives probabilities which violate Bell inequalities) but it's close.

Anyway, strictly speaking, the projection postulate is not compatible with unitary evolution, whether you use the postulate at the end, at the beginning, or in the middle.

Who cares if it's incompatible when it's just a pragmatic rule for making predictions, not intended to be a coherent theoretical description of what's really going on at all times? The pragmatic rule says that you model the system as evolving in a unitary way until all the measurements are done, then at the end you apply the projection postulate/Born rule to get predictions about the statistics of measurement records. If you see this final application of the projection postulate/Born rule as a violation of unitary evolution, fine, the pragmatic rule says you apply unitary evolution up to the final time T, then at time T you discard unitary evolution and apply the projection postulate. That's a coherent pragmatic rule (nothing wrong with requiring different rules at different times, as long as you know which to use when) even if it makes little sense as a theoretical picture.

 

[akhmeteli]

Is there something wrong with "introducing nonlocality" in this context?

JesseM, everything is wrong with it. Let us remember what we are talking about, in the first place. The question in the title of this thread is "Local realism ruled out?" I offered two arguments (sorry that I have to repeat them one more time):

1. There has been no experimental evidence of violations of the genuine Bell inequalities.
2. The violation of the inequalities in quantum theory is theoretically proven using mutually contradictory assumptions.

And then the conclusion: both experimental and theoretical arguments in favor of nonlocality are controversial, to say the least.

Now, what are trying to prove?

That it is possible to theoretically prove the violations in quantum theory, if you preliminarily introduce nonlocality in the measurement procedure? I could not agree more! But how does this proves nonlocality? This is circular reasoning, for crying out loud!

I fully agree that you can theoretically prove violations if you use the projection postulate! But I reject the projection postulate as anything but an approximation, because it contradicts unitary evolution! Take a standard proof of the Bell theorem, and it proves violations in quantum theory using the projection postulate! No need to spend hours looking for the proof!

All I'm claiming is that the rule of assuming unitary evolution, and then applying the Born rule/projection postulate at the very end to determine probabilities of different recorded outcomes, is a well-defined pragmatic procedure for generating theoretical predictions about experiments which can be compared with the actual results you find when the experiment is done in real life and the measurement results all written down somewhere. As always, it's just a pragmatic rule for generating predictions about the kinds of results we can write down, it's not meant to be a coherent description of what actually goes on physically at all moments.

Do you disagree that this is a well-defined procedure for generating predictions about the actual results seen in quantum experiments?

I do agree that this is is a well-defined procedure for generating... But what does this prove? Let me give you an example of a well-defined procedure: at the end of any experiment aimed at measuring some value you don't bother to read any records and just declare that this value is equal to 5 (in your favorite system of units). Do you agree that this is a well-defined procedure? I bet you do! It cannot even be disproven by experiments! What's wrong then with this procedure? Everything! I don't even know where to start to criticize it! Your procedure is not so absurd, as the projection postulate is at least an approximation, but strictly speaking it's still absurd, as the projection postulate contradicts unitary evolution.

Another thing. I suspect that you can prove nonlocality of classical electromagnetism if you introduce nonlocality in the measurement procedure. But is this what you really want?

Again, I don't feel like spending a lot of time looking for a paper that specifically uses the von Neumann approach to derive theoretical predictions about EPR type experiments. But do you disagree that the procedure I'm using is the same one von Neumann was proposing? If you don't disagree, don't you think it's fairly implausible that this procedure would fail to predict Bell inequality violations, but no one would have noticed this before despite the procedure being known for decades?

I agree that you can prove violations if you use the projection postulate. And no need to look for such a proof - a standard proof of the Bell inequality will do. But how does this undermine my arguments?

Also, now that you hopefully understand that I'm not talking about applying to projection postulate to each measurement but only once at the very end to all the records, you might reconsider the comment I made about one of the papers I linked to:

To put it another way, applying only unitary evolution to a series of N measurements and looking at the state S at the end means that, in the limit as N approaches infinity, S approaches "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". So, this implies that if we apply unitary evolution to a series of N measurements and then apply the projection postulate/Born rule at the very end, then in the limit as N approaches infinity, the probability that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" must approach 1. This isn't quite what I wanted to prove (that even for a small number of measurements, the von Neumann rule gives probabilities which violate Bell inequalities) but it's close.

I commented on this article in post 709.

Who cares if it's incompatible when it's just a pragmatic rule for making predictions, not intended to be a coherent theoretical description of what's really going on at all times? The pragmatic rule says that you model the system as evolving in a unitary way until all the measurements are done, then at the end you apply the projection postulate/Born rule to get predictions about the statistics of measurement records. If you see this final application of the projection postulate/Born rule as a violation of unitary evolution, fine, the pragmatic rule says you apply unitary evolution up to the final time T, then at time T you discard unitary evolution and apply the projection postulate. That's a coherent pragmatic rule (nothing wrong with requiring different rules at different times, as long as you know which to use when) even if it makes little sense as a theoretical picture.

You can say the same about my "5-procedure". And that's not very good for your procedure.

I'd say your procedure's viability hinges on how good an approximation the projection postulate is. But when you start to use this procedure in the area where the projection postulate is not a good approximation, your procedure will probably no better than my "5-procedure". And, as I said, I doubt that you can use approximations, such as the projection postulate, to prove nonlocality, as "approximate nonlocality" does not make much sense.

 

[JesseM]

JesseM, everything is wrong with it. Let us remember what we are talking about, in the first place. The question in the title of this thread is "Local realism ruled out?" I offered two arguments (sorry that I have to repeat them one more time):

1. There has been no experimental evidence of violations of the genuine Bell inequalities.
2. The violation of the inequalities in quantum theory is theoretically proven using mutually contradictory assumptions.

And then the conclusion: both experimental and theoretical arguments in favor of nonlocality are controversial, to say the least.

Now, what are trying to prove?

That it is possible to theoretically prove the violations in quantum theory, if you preliminarily introduce nonlocality in the measurement procedure? I could not agree more! But how does this proves nonlocality? This is circular reasoning, for crying out loud!

How could a proof possibly prove an empirical result? The proof is just intended to show that the statistical predictions of a local realist theory would differ from the statistical predictions of QM. If everyone agrees the pragmatic procedure I described is one way to define the "predictions of QM", then if that procedure predicts Bell inequality violations, that's all you need for the proof. No one would claim that the proof alone shows that QM's predictions will turn out to be empirically true, that of course is a matter for experiment.

I fully agree that you can theoretically prove violations if you use the projection postulate! But I reject the projection postulate as anything but an approximation, because it contradicts unitary evolution! Take a standard proof of the Bell theorem, and it proves violations in quantum theory using the projection postulate! No need to spend hours looking for the proof!

Sure, if you apply the projection postulate multiple times. I was just making the point that I think you can just apply it (or the Born rule, whichever) once at the very end, once all the measurements have been completed. The advantage of this is twofold:

1. You don't have to worry about the definition of which interactions constitute "measurements" and which don't, so there isn't the same ambiguity about how to apply the pragmatic rule

2. If you take a quantum system and model it as evolving in a unitary rule throughout some time interval, then apply the Born rule once at the very end to find the probability it'll be in different states, my understanding is that the probabilities you derive should be identical to those predicted by Bohmian mechanics (where there is no need for the Born rule since the measuring-device pointers have well-defined positions at all times, and the wavefunction is just understood as a classical ensemble of possible arrangements of positions with different probabilities). I believe it's only if you model each measurement as causing a separate "collapse" according to the projection postulate that your predictions would only be "approximately" equal to those given by the Bohmian analysis of the same situation.

I do agree that this is is a well-defined procedure for generating... But what does this prove? Let me give you an example of a well-defined procedure: at the end of any experiment aimed at measuring some value you don't bother to read any records and just declare that this value is equal to 5 (in your favorite system of units). Do you agree that this is a well-defined procedure? I bet you do!

No, it's not solely a procedure "for generating predictions about the actual results seen in quantum experiments", because you've also added a rule about what we must do when conducting the actual experiments (not look at the results). My procedure didn't tell you anything about how the experiments should be conducted, it was just a procedure to generate theoretical predictions about any quantum experiment (or at least any where you have measured the initial state of the system so you can evolve it forward) which could be compared with the empirical results of that experiment.

Another thing. I suspect that you can prove nonlocality of classical electromagnetism if you introduce nonlocality in the measurement procedure. But is this what you really want?

In classical electromagnetism all the local variables have well-defined values at all times (just like Bohmian mechanics), and their values evolve in a local way, so even if we assume we can magically become aware of all the values throughout space at a single instant, there will be no Bell inequality violations in the statistics. Of course if you imagined a "measurement procedure" that instantly changed all the local values at the moment of measurement, just like the projection postulate instantly changes the system's quantum state, then you might get Bell inequality violations depending on the nature of this change, but this theory would no longer resemble what we mean by "classical electromagnetism". In contrast, the procedure I describe above where you use the Born rule to get predictions about measurement-records is one that everyone would agree matches what physicists mean when they talk about the predictions of "QM". And again, Bell was just trying to prove that local realism is inconsistent with what everyone understands to be the predictions of "QM." You seem to be making some theoretical point that you don't find this surprising since the predictions of "QM" involve a nonlocal rule, but who cares? The proof is not intended to show that this result is surprising.

Also, now that you hopefully understand that I'm not talking about applying to projection postulate to each measurement but only once at the very end to all the records, you might reconsider the comment I made about one of the papers I linked to:

To put it another way, applying only unitary evolution to a series of N measurements and looking at the state S at the end means that, in the limit as N approaches infinity, S approaches "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". So, this implies that if we apply unitary evolution to a series of N measurements and then apply the projection postulate/Born rule at the very end, then in the limit as N approaches infinity, the probability that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" must approach 1. This isn't quite what I wanted to prove (that even for a small number of measurements, the von Neumann rule gives probabilities which violate Bell inequalities) but it's close.

I commented on this article in post 709.

Yes, but your comment was made when you still seemed confused about the procedure I was suggesting, that's why I re-introduced it with the comment in bold. Your comments in post #709 were:

JesseM, with all due respect, a couple of lines later the author writes: "Note, however, that since the linear dynamics can be written in a perfectly local form, there are in fact no nonlocal causal connections in the bare theory. ...Just as reports of determinate results, relative frequencies, and randomness would generally be explained by the bare theory as illusions the apparent nonlocality here would be just that, apparent." :-)

Of course, the "bare theory" is local, but it also doesn't make any well-defined statistical predictions about empirical results. My point was that if you combined their conclusion about the "bare theory" with the procedure I (and von Neumann) suggest where you do introduce a single application of the Born rule/projection postulate at the very end of a series of measurements, then you can show that in the limit as the number of measurements approaches infinity, the von Neumann procedure will predict with probability 1 that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts".

Now, it may be that you have no objection to the idea that this procedure will predict Bell inequality violations, as suggested by your comment "I fully agree that you can theoretically prove violations if you use the projection postulate!" I thought, though, that previously when you were asking me to "prove it", you were asking for a proof that the procedure I described (unitary evolution with a single application of the Born rule at the very end) would predict Bell inequality violations. That's why I brought up this paper, since it helps justify the conclusion that this is almost certainly true, even if I can't provide a detailed proof.

Who cares if it's incompatible when it's just a pragmatic rule for making predictions, not intended to be a coherent theoretical description of what's really going on at all times? The pragmatic rule says that you model the system as evolving in a unitary way until all the measurements are done, then at the end you apply the projection postulate/Born rule to get predictions about the statistics of measurement records. If you see this final application of the projection postulate/Born rule as a violation of unitary evolution, fine, the pragmatic rule says you apply unitary evolution up to the final time T, then at time T you discard unitary evolution and apply the projection postulate. That's a coherent pragmatic rule (nothing wrong with requiring different rules at different times, as long as you know which to use when) even if it makes little sense as a theoretical picture.

You can say the same about my "5-procedure". And that's not very good for your procedure.

Except that your procedure is useless for making predictions about the sort of experiments physicists actually do in quantum physics (since your procedure requires that physicists discard measurement results without looking at them), while mine works just fine for this pragmatic purpose.

I'd say your procedure's viability hinges on how good an approximation the projection postulate is.

As I said, I think my (and von Neumann's) procedure would exactly agree with the predictions of Bohmian mechanics for a given system at the end of a given time period, and Bohmian mechanics does not require the projection postulate. I think you'll probably disagree with that statement about Bohmian mechanics, though, so I need to go back and address your most recent posts on that subject.

 

[akhmeteli]

How could a proof possibly prove an empirical result? The proof is just intended to show that the statistical predictions of a local realist theory would differ from the statistical predictions of QM.

I fully agree. But QM is a well established (experimentally as well) theory, so such a proof of difference, generally speaking, could be an argument against all local realistic theories.

If everyone agrees the pragmatic procedure I described is one way to define the "predictions of QM", then if that procedure predicts Bell inequality violations, that's all you need for the proof. No one would claim that the proof alone shows that QM's predictions will turn out to be empirically true, that of course is a matter for experiment.

I agree (subject to your “ifs”).

Sure, if you apply the projection postulate multiple times. I was just making the point that I think you can just apply it (or the Born rule, whichever) once at the very end, once all the measurements have been completed. The advantage of this is twofold:

1. You don't have to worry about the definition of which interactions constitute "measurements" and which don't, so there isn't the same ambiguity about how to apply the pragmatic rule

2. If you take a quantum system and model it as evolving in a unitary rule throughout some time interval, then apply the Born rule once at the very end to find the probability it'll be in different states, my understanding is that the probabilities you derive should be identical to those predicted by Bohmian mechanics (where there is no need for the Born rule since the measuring-device pointers have well-defined positions at all times, and the wavefunction is just understood as a classical ensemble of possible arrangements of positions with different probabilities). I believe it's only if you model each measurement as causing a separate "collapse" according to the projection postulate that your predictions would only be "approximately" equal to those given by the Bohmian analysis of the same situation.

JesseM, my response still crucially depends on what exactly you use –the projection postulate or the Born rule.
If you use the projection postulate, no matter one time or a billion times, you manually introduce nonlocality. In this case I immediately concede that you can prove violations in QM (it does not matter if I am right or wrong about it), but I refuse to accept this proof as an argument against local realism, as this proof a) contains mutually contradictory assumptions, and 2) uses nonlocality as one of its assumptions.
If you use the Born rule… Well, the objections I offered above would not look equally strong (although it is not quite clear to me how compatible with dynamics the Born rule is). But then another issue arises: can you get a proof of violations in QM? I am not ready to concede this point. Again, I fully understand that you have better things to do than to look for such a proof, but that does not mean I must concede this point. I think the burden of proof of nonlocality is on those who want nonlocality. The Bell theorem, on the face of it, looks like such a proof, but, as I said repeatedly, it contains mutually contradictory assumptions. If you want to convince me that it is possible to cure this defect, or to prove violations in Bohmian mechanics without using the projection postulate or something similar, I need more than your word, sorry.

No, it's not solely a procedure "for generating predictions about the actual results seen in quantum experiments", because you've also added a rule about what we must do when conducting the actual experiments (not look at the results). My procedure didn't tell you anything about how the experiments should be conducted, it was just a procedure to generate theoretical predictions about any quantum experiment (or at least any where you have measured the initial state of the system so you can evolve it forward) which could be compared with the empirical results of that experiment.

I disagree. This “rule” is not essential and can be removed (so, if you wish, you can look at the results and still say that the value equals 5 :-) ). My idiotic procedure still has something in common with your much more decently looking procedure: it is not compatible with dynamics.

In classical electromagnetism all the local variables have well-defined values at all times (just like Bohmian mechanics), and their values evolve in a local way, so even if we assume we can magically become aware of all the values throughout space at a single instant, there will be no Bell inequality violations in the statistics. Of course if you imagined a "measurement procedure" that instantly changed all the local values at the moment of measurement, just like the projection postulate instantly changes the system's quantum state, then you might get Bell inequality violations depending on the nature of this change, but this theory would no longer resemble what we mean by "classical electromagnetism".

I am certainly not trying to prove that classical electrodynamics is nonlocal, I am just trying to say that you can prove nonlocality where there is no trace of it, if you use a nonlocal measurement procedure.

In contrast, the procedure I describe above where you use the Born rule to get predictions about measurement-records is one that everyone would agree matches what physicists mean when they talk about the predictions of "QM".

Again, if it’s the Born rule, I could tentatively agree (but then you don’t have a proof of violations in QM), but if it’s the projection postulate, I stand by my objections.

And again, Bell was just trying to prove that local realism is inconsistent with what everyone understands to be the predictions of "QM." You seem to be making some theoretical point that you don't find this surprising since the predictions of "QM" involve a nonlocal rule, but who cares? The proof is not intended to show that this result is surprising.

It does not matter much if this inconsistency is surprising or not. It does matter though if Nature is local realistic or not (at least it matters for me; that does not mean that I won’t be able to accept nonlocality if and when it is thoroughly confirmed experimentally). So I am trying to make point that the proof of inconsistency is dubious, as it uses mutually contradictory assumptions. I am also trying to make a point that it is not possible to reasonably embrace those contradictory assumptions anyway, and I put my bet on unitary evolution and against the projection postulate. You see, irrespective of the results of future experiments, we’ll have to modify either unitary evolution or the projection postulate anyway, local realism or no local realism. A logical contradiction is just not acceptable.

Yes, but your comment was made when you still seemed confused about the procedure I was suggesting, that's why I re-introduced it with the comment in bold. Your comments in post #709 were:

Of course, the "bare theory" is local, but it also doesn't make any well-defined statistical predictions about empirical results. My point was that if you combined their conclusion about the "bare theory" with the procedure I (and von Neumann) suggest where you do introduce a single application of the Born rule/projection postulate at the very end of a series of measurements, then you can show that in the limit as the number of measurements approaches infinity, the von Neumann procedure will predict with probability 1 that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts".

Now, it may be that you have no objection to the idea that this procedure will predict Bell inequality violations, as suggested by your comment "I fully agree that you can theoretically prove violations if you use the projection postulate!" I thought, though, that previously when you were asking me to "prove it", you were asking for a proof that the procedure I described (unitary evolution with a single application of the Born rule at the very end) would predict Bell inequality violations. That's why I brought up this paper, since it helps justify the conclusion that this is almost certainly true, even if I can't provide a detailed proof.

Again, I don’t care about any proof if you use the projection postulate (as in this case the proof of nonlocality contains circular reasoning anyway), but I need a proof if you use the Born rule. As confirmed by my quotes from the article, the latter does not contain anything like such proof.

Except that your procedure is useless for making predictions about the sort of experiments physicists actually do in quantum physics (since your procedure requires that physicists discard measurement results without looking at them), while mine works just fine for this pragmatic purpose.

Yes, but just because it uses a better approximation than my procedure. Where this approximation fails (and it cannot but fail somewhere, as, strictly speaking, it is incompatible with unitary evolution), your procedure will fail.

As I said, I think my (and von Neumann's) procedure would exactly agree with the predictions of Bohmian mechanics for a given system at the end of a given time period, and Bohmian mechanics does not require the projection postulate. I think you'll probably disagree with that statement about Bohmian mechanics, though, so I need to go back and address your most recent posts on that subject.

Again, if you use the Born rule in your procedure, I could tentatively agree, if it’s the projection postulate, then I disagree, as there is no collapse in Bohmian mechanics

 

[JesseM]

I fully agree. But QM is a well established (experimentally as well) theory, so such a proof of difference, generally speaking, could be an argument against all local realistic theories.

Well, yes--exactly! If you take "QM" to just mean the pragmatic procedure for making predictions that I describe, then this procedure has a great track record of agreement with experiment. So, even if this pragmatic procedure makes little sense as an ontological picture of what's "really going on", it should be inherently interesting to physicists to know whether the predictions of the pragmatic procedure are compatible with local realism. Of course showing that they're incompatible doesn't prove local realism is false in the real world, since it's possible you could have some local realist model whose predictions matched those of the pragmatic procedure in all the experiments that have been done to date, but which would differ from the pragmatic procedure in an ideal Bell test. Still most physicists would consider this unlikely, owing to the fact that most would agree such a model would almost certainly be very contrived and inelegant.

JesseM, my response still crucially depends on what exactly you use –the projection postulate or the Born rule.

But I already explained in post #716 that I didn't see a difference between the two if it was only done once at the end, they are both just ways of getting the same probabilities for the end results. I concluded by asking "So if you're not interested in what happens to the quantum state later, but just in the probabilities of seeing different combinations of measurement records at some time T after all the measurements are complete, I don't see the distinction between applying the "What difference are you seeing?" and your response in post #719 was "I don't know." So I would still say that there's no meaningful difference between them--if you want to say that the Born rule itself introduces nonlocality since it gives probabilities for a combination of simultaneous physical facts at different spatial locations, that's fine with me!

But then another issue arises: can you get a proof of violations in QM? I am not ready to concede this point.

I think so, if by "QM" you mean the pragmatic rule for generating predictions that I described (and which is the same as von Neumann's rule), which requires a single application of the Born rule to the quantum state of the system at some time after all measurements are completed and recorded. Are you actually suggesting that von Neumann's procedure might not actually predict Bell inequality violations, and that this has just gone unnoticed by physicists for decades? Or are you using "QM" to mean unitary evolution only, with no invoking the projection postulate or the Born rule? (unless the Born rule can somehow be derived from unitary evolution, which is what many-worlds advocates often try to do)

Again, I fully understand that you have better things to do than to look for such a proof

See above, I'm not even clear on what you're asking me to prove here.

The Bell theorem, on the face of it, looks like such a proof, but, as I said repeatedly, it contains mutually contradictory assumptions.

Bell's theorem has two parts: 1) in the type of experiment he specifies, local realism predicts that some Bell inequality will be obeyed, and 2) in the type of experiment he specifies, the predictions of "QM" as understood by physicists are that the Bell inequality will be violated. Your objection about "mutually contradictory assumptions" only seems to be an objection to 2), correct? But isn't it basically just a semantic disagreement, since you seem to define "QM" to mean "unitary evolution only" (which cannot be used to make predictions about any real-world experiment, since unitary evolution only gives complex amplitudes and empirically we never measure complex amplitudes), whereas most physicists would understand "QM" to mean the sort of pragmatic rule for making predictions that I describe.

If you want to convince me that it is possible to cure this defect, or to prove violations in Bohmian mechanics without using the projection postulate or something similar, I need more than your word, sorry.

Even if I could show that Bohmian mechanics can produce predictions of Bell inequality violations without invoking the projection postulate (and I think the links I gave already do this, despite your objections), what difference would it make to your argument? After all the guiding equation of Bohmian mechanics is explicitly nonlocal, so if you objected to the use of the projection postulate because it's nonlocal wouldn't you have the same objection to Bohmian mechanics?

I disagree. This “rule” is not essential and can be removed (so, if you wish, you can look at the results and still say that the value equals 5 :-) ).

But then you aren't comparing theoretical predictions with measurement results, you're comparing them with what you "say" about measurement results, where what you say is in most cases a lie.

I am certainly not trying to prove that classical electrodynamics is nonlocal, I am just trying to say that you can prove nonlocality where there is no trace of it, if you use a nonlocal measurement procedure.

Again, if by "nonlocal measurement procedure" you just mean instantly learn the values of the electromagnetic field at different locations without actually changing them in the process, then no, this won't lead to any Bell inequality violations in the results you learn.

Again, if it’s the Born rule, I could tentatively agree (but then you don’t have a proof of violations in QM), but if it’s the projection postulate, I stand by my objections.

But you never gave a coherent reason for disagreeing that there is no reason for distinguishing the two if we just make one "observation" of the records at the end of all measurements. Do you agree that if at the time we make an observation the quantum state of the records (obtained by unitary evolution) is $$\alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +$$$$\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle$$ then if we "observe" these records, regardless of whether we apply the Born rule or the projection postulate we will predict that the probability of a given result like 010 will just be the amplitude for that eigenstate times its complex conjugate, i.e. $$\alpha_3 \alpha_3*$$? Please tell me clearly whether you agree or disagree that the probability of 010 is going to be $$\alpha_3 \alpha_3*$$ either way. If you don't disagree, then obviously the Born rule and the projection postulate are both making the exact same predictions about the statistics seen in the records at this time, so the probability of statistics that violate the Bell inequalities is the same either way.

So I am trying to make point that the proof of inconsistency is dubious, as it uses mutually contradictory assumptions. I am also trying to make a point that it is not possible to reasonably embrace those contradictory assumptions anyway, and I put my bet on unitary evolution and against the projection postulate. You see, irrespective of the results of future experiments, we’ll have to modify either unitary evolution or the projection postulate anyway, local realism or no local realism. A logical contradiction is just not acceptable.

But you never really addressed my point in post #721 that the "contradiction" only arises if you take the procedure as an ontological description of reality, that purely as a pragmatic procedure it's not contradictory since it's just telling you to use different rules at different times. Your response was just to compare this with your silly "pretend the answer is always 5" procedure, but of course that procedure doesn't have a long track record of accurately predicting experimental results like the QM procedure.

Again, I don’t care about any proof if you use the projection postulate (as in this case the proof of nonlocality contains circular reasoning anyway), but I need a proof if you use the Born rule.

Do you disagree that if a system's state is in an eigenstate of some operator, the Born rule says that on "observation" you are guaranteed to find the value associated with that eigenstate with probability 1? So, that means their conclusion (if we do N measurements, pure unitary evolution predicts that in the limit as N approaches infinity, the measurement records approach an eigenstate where "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts") implies the conclusion (if we do N measurements modeled by unitary evolution and then at the end apply the Born rule to the measurement records, in the limit as N approaches infinity the probability of finding that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" approaches 1)

As I said, I think my (and von Neumann's) procedure would exactly agree with the predictions of Bohmian mechanics for a given system at the end of a given time period, and Bohmian mechanics does not require the projection postulate. I think you'll probably disagree with that statement about Bohmian mechanics, though, so I need to go back and address your most recent posts on that subject.

Again, if you use the Born rule in your procedure, I could tentatively agree, if it’s the projection postulate, then I disagree, as there is no collapse in Bohmian mechanics

And again, if you assume unitary evolution until some time T, then regardless of whether you invoke "the Born rule" or "the projection postulate" at time T, the probabilities of finding different possible combinations of measurement results at time T will be exactly the same. And my argument is that Bohmian mechanics will also yield exactly the same predictions for probabilities of different possible combinations of measurement results at time T.

 

[akhmeteli]

Well, yes--exactly! If you take "QM" to just mean the pragmatic procedure for making predictions that I describe, then this procedure has a great track record of agreement with experiment. So, even if this pragmatic procedure makes little sense as an ontological picture of what's "really going on", it should be inherently interesting to physicists to know whether the predictions of the pragmatic procedure are compatible with local realism. Of course showing that they're incompatible doesn't prove local realism is false in the real world, since it's possible you could have some local realist model whose predictions matched those of the pragmatic procedure in all the experiments that have been done to date, but which would differ from the pragmatic procedure in an ideal Bell test. Still most physicists would consider this unlikely, owing to the fact that most would agree such a model would almost certainly be very contrived and inelegant.

So it’s a matter of opinion. Note that this pragmatic procedure is doomed to fail somewhere anyway, as it contradicts the unitary evolution.

But I already explained in post #716 that I didn't see a difference between the two if it was only done once at the end, they are both just ways of getting the same probabilities for the end results. I concluded by asking "So if you're not interested in what happens to the quantum state later, but just in the probabilities of seeing different combinations of measurement records at some time T after all the measurements are complete, I don't see the distinction between applying the "What difference are you seeing?" and your response in post #719 was "I don't know." So I would still say that there's no meaningful difference between them

If you believe there is no difference, why don’t you choose just one of those two that you like more, even if just to give some focus to the discussion? But I explained to you how my reasoning will depend on your choice: if you choose the projection postulate, I’ll say that your proof of nonlocality in QM contains circular reasoning; if you choose the Born rule, then I’ll say that you don’t have a proof of nonlocality. So the difference is in how the discussion will develop depending on your choice. You may call this difference meaningful or not meaningful, but it is at least important for the course of further discussion.

--if you want to say that the Born rule itself introduces nonlocality since it gives probabilities for a combination of simultaneous physical facts at different spatial locations, that's fine with me!

On the face of it, this may be a possibility, but I think I won’t try to formulate my opinion on this issue at this point, because right now it does not look critical for the discussion.

I think so, if by "QM" you mean the pragmatic rule for generating predictions that I described (and which is the same as von Neumann's rule), which requires a single application of the Born rule to the quantum state of the system at some time after all measurements are completed and recorded.

Again, if you use the Born rule, rather than the projection postulate in your procedure, it’s not at all obvious that you’ll be able to prove violations in QM.

Are you actually suggesting that von Neumann's procedure might not actually predict Bell inequality violations, and that this has just gone unnoticed by physicists for decades?

Yes, I am actually suggesting that (again, provided you use the Born rule, not the projection postulate). As for “gone unnoticed”… I don’t know. For many people, the difference between the Born rule and the projection postulate may be just a meaningless subtlety :-)

Or are you using "QM" to mean unitary evolution only, with no invoking the projection postulate or the Born rule? (unless the Born rule can somehow be derived from unitary evolution, which is what many-worlds advocates often try to do)

This is an interesting question. I cannot exclude a possibility that my criticism of the projection postulate is actually valid for the Born rule as well (or maybe just for some forms of the Born rule), but I am not sure. There is no doubt that the projection postulate is incompatible with unitary evolution as it destroys superpositions and creates irreversibility. Is the Born rule compatible with unitary evolution? I don’t know. Let me just mention that an acquaintance of mine, who coauthored a series of articles describing the quantum measurement procedure by a rigorous model (http://arxiv.org/abs/quant-ph/0702135), told me that, according to the results for their model, the Born rule is also just an approximation. But it does not look like the Born rule in its simplest form (i.e. as it is used in Bohmian mechanics, for example) introduces nonlocality.

See above, I'm not even clear on what you're asking me to prove here.

I am just saying that I do not accept without proof that it is possible to prove violations in QM using just unitary evolution and the Born rule.

Bell's theorem has two parts: 1) in the type of experiment he specifies, local realism predicts that some Bell inequality will be obeyed, and 2) in the type of experiment he specifies, the predictions of "QM" as understood by physicists are that the Bell inequality will be violated. Your objection about "mutually contradictory assumptions" only seems to be an objection to 2), correct?

Correct.

But isn't it basically just a semantic disagreement, since you seem to define "QM" to mean "unitary evolution only" (which cannot be used to make predictions about any real-world experiment, since unitary evolution only gives complex amplitudes and empirically we never measure complex amplitudes), whereas most physicists would understand "QM" to mean the sort of pragmatic rule for making predictions that I describe.

As I said, to make predictions, you may use some form of the Born rule as a purely operational principle.

Even if I could show that Bohmian mechanics can produce predictions of Bell inequality violations without invoking the projection postulate (and I think the links I gave already do this, despite your objections), what difference would it make to your argument?

I do not agree that your links do that, and I offered specific arguments.
As for what difference it would make to my argument… I’d say significant difference. Right now my argument is quite simple: violations in quantum mechanics are proven using 1) unitary evolution and 2) the projection postulate, and 1) and 2) are mutually contradictory. If you prove violations in Bohmian mechanics without using the projection postulate or something similar, this proof could be translated into a proof for standard QM, so my argument in its current form will not hold, and I’ll have to analyze the Born rule trying to find out if it is compatible with unitary evolution.

After all the guiding equation of Bohmian mechanics is explicitly nonlocal, so if you objected to the use of the projection postulate because it's nonlocal wouldn't you have the same objection to Bohmian mechanics?

It is explicitely nonlocal, but it is not obvious that it cannot have a local form. For example, there is no faster-than-light signaling in Bohmian mechanics, if we assume the standard equivariant distribution. Furthermore, the evolution there is the same unitary evolution as in standard quantum mechanics, which has a solid experimental basis. I reject the projection postulate not just because it is nonlocal, but because it contradicts unitary evolution. Let me also mention that “my” model, while local, can have a seemingly nonlocal form (that of a quantum field theory).

But then you aren't comparing theoretical predictions with measurement results, you're comparing them with what you "say" about measurement results, where what you say is in most cases a lie.

But still, using your wording, it “is a well-defined pragmatic procedure for generating theoretical predictions about experiments which can be compared with the actual results you find when the experiment is done in real life and the measurement results all written down somewhere.” I just wanted to show you that this is not enough. The procedure must make sense.

Again, if by "nonlocal measurement procedure" you just mean instantly learn the values of the electromagnetic field at different locations without actually changing them in the process, then no, this won't lead to any Bell inequality violations in the results you learn.

But the projection postulate changes the values in the process.

But you never gave a coherent reason for disagreeing that there is no reason for distinguishing the two if we just make one "observation" of the records at the end of all measurements. Do you agree that if at the time we make an observation the quantum state of the records (obtained by unitary evolution) is $$\alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +$$$$\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle$$ then if we "observe" these records, regardless of whether we apply the Born rule or the projection postulate we will predict that the probability of a given result like 010 will just be the amplitude for that eigenstate times its complex conjugate, i.e. $$\alpha_3 \alpha_3*$$? If you don't disagree, then obviously the Born rule and the projection postulate are both making the exact same predictions about the statistics seen in the records at this time, so the probability of statistics that violate the Bell inequalities is the same either way.

Please see the answer above in this post starting with words “If you believe there is no difference,”

But you never really addressed my point in post #721 that the "contradiction" only arises if you take the procedure as an ontological description of reality, that purely as a pragmatic procedure it's not contradictory since it's just telling you to use different rules at different times. Your response was just to compare this with your silly "pretend the answer is always 5" procedure, but of course that procedure doesn't have a long track record of accurately predicting experimental results like the QM procedure.

No, it does not, and it is extremely silly indeed, but its mere existence suggests that if you use some nonsense as a measurement procedure, there is always a risk of getting some nonsense as a result. I just cannot embrace logical contradictions, sorry. There is a theorem in logic that if you assume that some false statement is true, that implies that any false statement is true.

Do you disagree that if a system's state is in an eigenstate of some operator, the Born rule says that on "observation" you are guaranteed to find the value associated with that eigenstate with probability 1? So, that means their conclusion (if we do N measurements, pure unitary evolution predicts that in the limit as N approaches infinity, the measurement records approach an eigenstate where "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts") implies the conclusion (if we do N measurements modeled by unitary evolution and then at the end apply the Born rule to the measurement records, in the limit as N approaches infinity the probability of finding that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" approaches 1)

I gave the quote from his article suggesting that those records may be an illusion. Rather damning:-) If you think such an illusion may be OK, then what exactly is wrong with my 5-procedure?:-)

And again, if you assume unitary evolution until some time T, then regardless of whether you invoke "the Born rule" or "the projection postulate" at time T, the probabilities of finding different possible combinations of measurement results at time T will be exactly the same. And my argument is that Bohmian mechanics will also yield exactly the same predictions for probabilities of different possible combinations of measurement results at time T.

Please see the answer above in this post starting with words “If you believe there is no difference,”

 

[JesseM]

So it’s a matter of opinion. Note that this pragmatic procedure is doomed to fail somewhere anyway, as it contradicts the unitary evolution.

Why is it doomed to fail? You think nature must obey unitary evolution? Isn't it possible nature follows some other nonlocal rule like the guiding equation of Bohmian mechanics, and that the predictions of this nonlocal rule about measurement records would happen to agree mathematically with the pragmatic procedure of calculating a "wavefunction" for the system, evolving it in a unitary way according to the Schroedinger equation, and then applying the Born rule/projection postulate to the records once all measurements in the experiment are finished?

If you believe there is no difference, why don’t you choose just one of those two that you like more, even if just to give some focus to the discussion? But I explained to you how my reasoning will depend on your choice: if you choose the projection postulate, I’ll say that your proof of nonlocality in QM contains circular reasoning; if you choose the Born rule, then I’ll say that you don’t have a proof of nonlocality.

That still doesn't make sense to me. If we find that unitary evolution predicts a system's wavefunction is in state S at time T, then if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T. Thus, if applying the "projection postulate" predicts statistics which violate Bell inequalities, applying the "Born rule" is guaranteed to do so as well. Do you have the slightest doubt that this is true? If so that would suggest to me that you just aren't very well-versed in the mathematical formalism of QM, that your understanding is more conceptual. There's no shame in that, I said before that this was true of my understanding of Bohmian mechanics (and my knowledge of QM math doesn't go beyond the undergrad level), but if that's the case it would help me understand your doubts about my argument if you would say so. On the other hand, if you do claim to understand the mathematical meaning of things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule, then please tell me if you have any mathematical doubts about this argument from post #716, and if so what they are:

For example, if there were three measurements which could each yield result 1 or 0, then at the end right before "observation" the records will be a single quantum state which can be expressed as a sum of eigenstates:

$$\alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +$$$$\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle$$

where the $$\alpha_i$$ are complex amplitudes. Then if you apply the "projection postulate", you're saying the quantum state will randomly become one of those eigenstates, with the probability of it going to a given eigenstate like $$\mid 010 \rangle$$ being $$\alpha_3 \alpha_3*$$ (i.e. the amplitude times its complex conjugate). And the "Born rule" just tells you that the probability of getting a given result like 010 is $$\alpha_3 \alpha_3*$$.

Would you disagree with the idea that if the measurement records constitute an "observable" we can express the quantum state as a sum of eigenstates of that observable? Would you disagree that both the Born rule and the projection postulate would say the probability of getting a given value for an observable is found by taking the amplitude associated with the corresponding eigenstate (when you express the quantum state as a sum of eigenstates for that observable) and multiplying it by its complex conjugate?

 

[akhmeteli]

Sorry, I have not replied for some time – was a bit busy.

Why is it doomed to fail? You think nature must obey unitary evolution? Isn't it possible nature follows some other nonlocal rule like the guiding equation of Bohmian mechanics, and that the predictions of this nonlocal rule about measurement records would happen to agree mathematically with the pragmatic procedure of calculating a "wavefunction" for the system, evolving it in a unitary way according to the Schroedinger equation, and then applying the Born rule/projection postulate to the records once all measurements in the experiment are finished?

Well, generally speaking, a lot of things are possible, but I am pretty conservative and try to preserve as much of what we have as possible. Unitary evolution has been thoroughly tested, and I don’t see any reason to discard it. It may happen that the projection postulate is correct, and unitary evolution is wrong, but my bet is on unitary evolution.

That still doesn't make sense to me. If we find that unitary evolution predicts a system's wavefunction is in state S at time T, then if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T. Thus, if applying the "projection postulate" predicts statistics which violate Bell inequalities, applying the "Born rule" is guaranteed to do so as well. Do you have the slightest doubt that this is true? If so that would suggest to me that you just aren't very well-versed in the mathematical formalism of QM, that your understanding is more conceptual. There's no shame in that, I said before that this was true of my understanding of Bohmian mechanics (and my knowledge of QM math doesn't go beyond the undergrad level), but if that's the case it would help me understand your doubts about my argument if you would say so. On the other hand, if you do claim to understand the mathematical meaning of things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule, then please tell me if you have any mathematical doubts about this argument from post #716, and if so what they are:

OK, so you refuse to choose just one of those: either the Born rule or the projection postulate. Then I have to retract (or caveat, if you wish:-) ) my concession that it is possible to prove nonlocality using the projection postulate. Indeed, I am inclined to agree that “if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T.” However, I don’t think you can prove the violations using just probabilities from the projection postulate, but not the collapse, so we have not moved any further.

Would you disagree with the idea that if the measurement records constitute an "observable"

I am not sure about this “if”, as records are not permanent.

we can express the quantum state as a sum of eigenstates of that observable? Would you disagree that both the Born rule and the projection postulate would say the probability of getting a given value for an observable is found by taking the amplitude associated with the corresponding eigenstate (when you express the quantum state as a sum of eigenstates for that observable) and multiplying it by its complex conjugate?

I would agree with that, but, as I explained above, this does not seem to lead to any progress in our discussion. If you remove collapse from the projection postulate, I don’t think you’ll be able to prove the violations.

 

[JesseM]

OK, so you refuse to choose just one of those: either the Born rule or the projection postulate. Then I have to retract (or caveat, if you wish:-) ) my concession that it is possible to prove nonlocality using the projection postulate. Indeed, I am inclined to agree that “if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T.” However, I don’t think you can prove the violations using just probabilities from the projection postulate, but not the collapse, so we have not moved any further.

That doesn't make sense to me either. The "probabilities from the projection postulate" are precisely the probabilities that the state will "collapse" onto each possible eigenstate, which is supposed to be the eigenstate corresponding to what's actually observed. So if at time T the amplitude for $$\mid 010 \rangle$$ is $$\alpha_3$$ (obtained via unitary evolution), that means that if you observe the records at time T there is a probability of $$\alpha_3 \alpha_3*$$ that the state will collapse to the eigenstate $$\mid 010 \rangle$$ and that you will observe results 010.

And remember, the Bell inequalities deal with probabilities too! For example, one inequality says that if two experimenters are measuring spins of entangled particles, and each experimenter has a choice of three possible angles to measure spin along, then if there is a probability 1 that they see opposite results when they measure spin along the same axis, that means there must be a probability of at least 1/3 that they see opposite results when they measure along different axes, according to local realism. Meanwhile for a certain choice of detector angles the QM prediction is that the probability of seeing opposite results for different angles is only 1/4, so QM is understood to be incompatible with local realism. If we pick a time T shortly after both particles' spins have been measured and recorded, and "observe" the measurement records at T, then if the "projection postulate" predicts a probability 1 of opposite results for detectors set to the same angle but a probability 0.25 of opposite results for detectors set to different angles, that prediction is incompatible with local realism.

Meanwhile, it would help me if you would tell me whether you do have a good working understanding of the QM math or if your understanding is more conceptual...like I asked before, do you understand the mathematical meaning of "things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule"?

 

[Eye_in_the_Sky]

I rather see QM as non-separable, causally local ...

Exactly what we believe ...

It sounds to me like the two of you are agree upon (... among other things) the following:

The entanglement phenomenon exhibited in the Alice-and-Bob scenario can be construed as:

(i) "nonseparable" ,

and

(ii) obeying the principle of "local causality" .

... Am I correct in this assessment?

 

[RUTA]

It sounds to me like the two of you are agree upon (... among other things) the following:

The entanglement phenomenon exhibited in the Alice-and-Bob scenario can be construed as:

(i) "nonseparable" ,

and

(ii) obeying the principle of "local causality" .

... Am I correct in this assessment?

I can't speak for jambaugh, but this is correct for Relational Blockworld.

 

[akhmeteli]

Sorry, it has taken me a long time to reply – was a bit busy.

That doesn't make sense to me either. The "probabilities from the projection postulate" are precisely the probabilities that the state will "collapse" onto each possible eigenstate, which is supposed to be the eigenstate corresponding to what's actually observed. So if at time T the amplitude for $$\mid 010 \rangle$$ is $$\alpha_3$$ (obtained via unitary evolution), that means that if you observe the records at time T there is a probability of $$\alpha_3 \alpha_3*$$ that the state will collapse to the eigenstate $$\mid 010 \rangle$$ and that you will observe results 010.

I agree, if you use the projection postulate, you can prove the violation of the Bell inequalities in QM. The question is can you prove that using the Born rule? It is my understanding that the Born rule gives the probability that the system is in a certain state, And I conceded that these probabilities may be the same that you get from the projection postulate. However, to prove the violation of the Bell inequalities you need the correlations. To get the correlations, you need the values of the observables. If, according to measurement results, the system is in the eigenstate $$\mid 010 \rangle$$, that does not mean automatically that you will observe results 010. This may sound outrageous, but what can I do? This is a direct consequence of unitary evolution: measurement cannot turn a superposition into a mixture. You need the projection postulate to get the values of the observables, and what projection postulate states directly contradicts unitary evolution.

Meanwhile, it would help me if you would tell me whether you do have a good working understanding of the QM math or if your understanding is more conceptual...like I asked before, do you understand the mathematical meaning of "things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule"?

I am not enthusiastic about broadcasting details of my background, so I’ll try to PM you.

 

[JesseM]

I agree, if you use the projection postulate, you can prove the violation of the Bell inequalities in QM. The question is can you prove that using the Born rule? It is my understanding that the Born rule gives the probability that the system is in a certain state,

Depends what you mean by that--the Born rule gives probabilities of measurement results, not of quantum states.

And I conceded that these probabilities may be the same that you get from the projection postulate. However, to prove the violation of the Bell inequalities you need the correlations. To get the correlations, you need the values of the observables. If, according to measurement results, the system is in the eigenstate $$\mid 010 \rangle$$, that does not mean automatically that you will observe results 010.

But the measurement results are the "results 010". We never measure the quantum state directly, we measure observables like position (including the position of pointers), it's only if we use the projection postulate that we can infer a measurement of result 010 implies the system is in an eigenstate $$\mid 010 \rangle$$ (in an everett interpretation where there is no 'collapse', this inference would be unjustified since there might be some other versions of ourselves who got different measurement results, so the system can still be in a superposition of different eigenstates).

This may sound outrageous, but what can I do? This is a direct consequence of unitary evolution: measurement cannot turn a superposition into a mixture. You need the projection postulate to get the values of the observables

...or the Born rule.

and what projection postulate states directly contradicts unitary evolution.

While the Born rule does not as explicitly contradict unitary evolution, it also seems that no one has a very convincing way of deriving it from unitary evolution alone (and those that attempt to do so usually assume a many-worlds type framework where parallel versions of the experimenter experience different outcomes). So you're free to say that the Born rule doesn't really make sense given the hypothesis of unitary evolution alone, but I don't think there's any good basis for denying that modeling Aspect-type experiments using unitary evolution until time T, then applying the Born rule to find the probabilities of different combinations of observable measurement records, yields probabilistic predictions that violate Bell inequalities.

I am not enthusiastic about broadcasting details of my background, so I’ll try to PM you.

Thanks. But to be clear, I wasn't asking for personal information about universities attended and so forth, just a general statement about your level of technical knowledge in this subject (and your PM suggests that you do have an in-depth knowledge of the math).

 

[akhmeteli]

Depends what you mean by that--the Born rule gives probabilities of measurement results, not of quantum states.

Sometimes the Born rule is defined in terms of probabilities of states – see, e.g. http://plato.stanford.edu/entries/qm/.

But the measurement results are the "results 010". We never measure the quantum state directly, we measure observables like position (including the position of pointers), it's only if we use the projection postulate that we can infer a measurement of result 010 implies the system is in an eigenstate $$\mid 010 \rangle$$ (in an everett interpretation where there is no 'collapse', this inference would be unjustified since there might be some other versions of ourselves who got different measurement results, so the system can still be in a superposition of different eigenstates).

OK, so you define the Born rule in terms of probabilities of outcomes of measurements and, in particular, use it for measurement of more than one observable.

...or the Born rule.

Perhaps I could agree that if you formally apply this definition of the Born rule, you can get violations in quantum mechanics, but this has little to do with the actual measurements in Bell experiments (see below), so the Born rule for several measurements is little if at all better than the projection postulate.

While the Born rule does not as explicitly contradict unitary evolution, it also seems that no one has a very convincing way of deriving it from unitary evolution alone (and those that attempt to do so usually assume a many-worlds type framework where parallel versions of the experimenter experience different outcomes). So you're free to say that the Born rule doesn't really make sense given the hypothesis of unitary evolution alone, but I don't think there's any good basis for denying that modeling Aspect-type experiments using unitary evolution until time T, then applying the Born rule to find the probabilities of different combinations of observable measurement records, yields probabilistic predictions that violate Bell inequalities.

I think there is such a basis. Indeed, there is nothing either in unitary evolution or in the Born rule about “observable measurement records”. As I said, those “records” are not even permanent. The Born rule only tells us about some abstract results of some abstract measurements. So you should modify your statement. In Bell experiments, the spin projections of the two particles of the singlet are measured independently. I cannot imagine how the spin projections of two spatially separated particles can be measured in one measurement. If, however, you apply the Born rule to the actual measurements, you get something that contradicts unitary evolution. Indeed, after the measurement on the first particle, whatever “record” you get, the system is still in a superposition, so you can get both results for the other particle.
So I’d say the replacement of the projection postulate by the Born rule for several variables does not change the reasoning: the Born rule still contradicts unitary evolution, at least for the actual Bell experiments. And it is difficult to agree with your approach. As far as I understand, you are saying that yes, there is a contradiction, but it’s OK for some reason. I see this differently. While for some purposes this may be "OK", it's not "OK" when we are trying to decide, for example, the issue in the title of this thread: Has local realism been ruled out? What happens is people first adopt assumptions that contradict both unitary evolution and local realism, such as the projection postulate or the Born rule for several variables, and then “rule out” local realism.

 

[JesseM]

Sometimes the Born rule is defined in terms of probabilities of states – see, e.g. http://plato.stanford.edu/entries/qm/.

No, I don't think so. If you look at the actual equation they give for the Born rule in section 3.4, the equation is giving a probability of getting a given eigenvalue, not a given eigenstate/eigenvector. The verbal discussion in the paragraph preceding that equation is a bit confusing because they assume the Born rule is always coupled with the collapse postulate, so that the probability of getting a given eigenvalue would be the same as the probability of collapsing to the corresponding eigenstate, but the two assumptions are logically separable, and the article follows every other source I've seen in defining the Born rule in terms of the probability of getting a particular eigenvalue (which is understood as a possible measurement result).

OK, so you define the Born rule in terms of probabilities of outcomes of measurements and, in particular, use it for measurement of more than one observable.

Applying the Born rule to pointer states at the end of the experiment is just the von Neumann procedure, as I pointed out before.

I think there is such a basis. Indeed, there is nothing either in unitary evolution or in the Born rule about “observable measurement records”.

I don't understand what you mean by "nothing in" them "about" measurement records. Unitary evolution and the Born rule apply the same way to all quantum systems, they don't give specific rules for pointer states so I guess in that sense you could say there is "nothing in" them about pointer states, but nor do they give specific rules for electrons going through a double-slit or for any other particular quantum system, would you say "there is nothing in unitary evolution or in the Born rule about electrons"? The point is that unitary evolution and the Born rule can be applied in exactly the same way to any quantum system you like, so why not apply them to the macroscopic measuring devices and their records/pointer states in just the way you'd apply them to microscopic systems?

As I said, those “records” are not even permanent.

Who said they had to be permanent? The point is just to pick some time T shortly after all the experiments have been done, and apply the Born rule at T to find the probabilities of observing different measurement records at T. Maybe in the distant future all records of this experiment will be lost and no one will remember what the actual results were, but so what? This is just a procedure for making predictions about empirical results in the here-and-now.

The Born rule only tells us about some abstract results of some abstract measurements.

Don't know what you mean by that. Any time you use a theoretical model to make predictions about a real-world experiment, the model is always simplified, you couldn't possibly model the precise behavior of every single particle involved in the experiment, so in that sense all models are "abstract", but they are nevertheless highly useful in making predictions about real-world experiments, otherwise we'd just be doing pure math and not physics!

So you should modify your statement. In Bell experiments, the spin projections of the two particles of the singlet are measured independently. I cannot imagine how the spin projections of two spatially separated particles can be measured in one measurement.

I think you need to review the links I gave you earlier about von Neumann's procedure for calculating probabilities (see post #706 in particular). Again, there is no problem with measurements being made prior to the moment we apply the Born rule, it's just that each measurement is modeled as causing the measuring-device to become entangled with the system being measured exactly as you'd expect from unitary evolution, with no attempt to talk about probabilities at that point. Then at some time T after all measurements have already been performed, the Born ruler is applied to the pointer states of all the measuring devices. Obviously in the a real Bell experiment, at some point all the data will be collected in one place so scientists can review it, what's wrong with waiting until then to apply the Born rule to find the probability that a scientist will see different combinations of results on their computer screen?

If, however, you apply the Born rule to the actual measurements,

Any time someone looks at data you could call it a type of "measurement", including looking at a computer screen where the results of some prior measurements at different locations have been collected. The point of von Neumann's procedure is not to apply the Born rule to those prior measurements, to just model them according to standard unitary evolution, and just apply the Born rule at the very end to the collected measurement records.

you get something that contradicts unitary evolution.

How so?

Indeed, after the measurement on the first particle, whatever “record” you get, the system is still in a superposition, so you can get both results for the other particle.

But von Neumann's approach doesn't involve multiple successive applications of the Born rule, just a single one after all the experiments have been completed.

So I’d say the replacement of the projection postulate by the Born rule for several variables does not change the reasoning: the Born rule still contradicts unitary evolution, at least for the actual Bell experiments.

You haven't really explained why you think it contradicts unitary evolution. Many advocates of the many-worlds interpretation have tried to argue that the Born rule would still work for a "typical" observer in that interpretation, despite the fact that in the MWI unitary evolution goes on forever and thus each experiment just results in a superposition of different versions of the same experimenter seeing different results. Also, have a look at the paper at http://www.math.ru.nl/~landsman/Born.pdf which I found linked in wikipedia's article on the Born rule, the concluding paragraph says "The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle."

Besides, you talk as though "unitary evolution" were a sacred inviolate principle, but in fact all the empirical evidence in favor of QM depends on the fact that we can connect the abstract formalism of wavefunction evolution to actual empirical observations via either the Born rule or the collapse postulate--without them you can't point to a single scrap of empirical evidence in favor of unitary evolution! Of course if unitary evolution + collapse/Born rule produces a lot of successful predictions, then on the grounds of elegance there seems to be a good basis for hoping that the same unitary evolution that governs interactions between particles between measurements also governs interactions between particles and measuring devices (since measuring devices are just very large and complex collections of particles)...that's why my hope is that a totally convincing derivation of the Born rule from the MWI will eventually be found. But to just say "the Born rule and the collapse postulate violate the sacred principle of unitary evolution, therefore they must be abandoned", and to not even attempt to show how "unitary evolution" alone can yield a single solitary prediction about any empirical experiment ever performed, seems to be turning unitary evolution into a religious creed rather than a scientific theory.

I see this differently. While for some purposes this may be "OK", it's not "OK" when we are trying to decide, for example, the issue in the title of this thread: Has local realism been ruled out?

If the predictions of "quantum mechanics" are understood in von Neumann's way, then we can say that local realism is incompatible with the predictions of "quantum mechanics", and that "quantum mechanics" has a perfect track record so far in all experimental tests that have been done (including Aspect-type experiments, although none so far have done a perfect job of closing all loopholes). If on the other hand you choose to define "quantum mechanics" as unitary evolution alone, then unless you have some argument for why the Born rule should still work as MWI advocates do, your version of "quantum mechanics" is a purely abstract mathematical notion that makes no predictions about any real-world empirical experiments whatsoever.