A Paradox: Do LHV Theories Need the HUP?

[DrChinese]

The whole point of the EPR argument is to show that ***if*** you assume that QM is complete, the theory violates locality. Completeness entails non-locality.

Perhaps you would care to provide a quote from EPR that backs this up. FYI, here are the actual last 4 sentences of EPR. Note that the last 3 are now known to be WRONG and this is what got us debating in the first place.

"This makes the reality of P and Q depend on the process of measurement carried out on the first system, that does not affect the second system in any way."

(This is standard Copenhagen interpretation. It is also a way of saying that reality is observer dependent. Please note that this applies equally in any test of QED in which the HUP is used. The HUP tells us that reality IS observer dependent.)

"No reasonable definition of reality could be expected to permit this."

(This is an ad hoc assumption and is not warranted from the argument presented in EPR.)

"While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists."

(This deduction is invalid because the previous sentence is unwarranted. The correct conclusion is that EITHER QM is incomplete, OR there is not simultaneous reality to non-commuting observables. This correct conclusion was stated earlier in EPR.)

"We believe, however, that such a theory is possible."

(Because of Bell, we now know that NO such theory is possible, regardless of Einstein's faith in the matter. R.I.P. Local reality.)

 

[ttn]

Perhaps you would care to provide a quote from EPR that backs this up.

See quant-ph/0404016 for a detailed discussion, including lots of juicy quotes.

FYI, here are the actual last 4 sentences of EPR. Note that the last 3 are now known to be WRONG and this is what got us debating in the first place.
"This makes the reality of P and Q depend on the process of measurement carried out on the first system, that does not affect the second system in any way."
(This is standard Copenhagen interpretation. It is also a way of saying that reality is observer dependent. Please note that this applies equally in any test of QED in which the HUP is used. The HUP tells us that reality IS observer dependent.)

Huh? The point of this sentence you quote is to stress the locality assumption. EPR (i.e., *Podolsky*!) are here pointing out the non-locality implied by the standard "disturbance" view which says: the distant particle doesn't have a definite X or a definite P until the nearby measurement is made, the distant particle then "collapsing" into a state with a definite value for the appropriate operator. Their point is that this non-local collapsing violates locality.

"No reasonable definition of reality could be expected to permit this."
(This is an ad hoc assumption and is not warranted from the argument presented in EPR.)

Substitute "local" for "reasonable" and then it makes perfect sense.

"While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists."
(This deduction is invalid because the previous sentence is unwarranted. The correct conclusion is that EITHER QM is incomplete, OR there is not simultaneous reality to non-commuting observables. This correct conclusion was stated earlier in EPR.)

Blah.

"We believe, however, that such a theory is possible."
(Because of Bell, we now know that NO such theory is possible, regardless of Einstein's faith in the matter. R.I.P. Local reality.)

Agreed. But you still seem to be missing the main point here: EPR showed that orthodox QM violates locality. And that is simply a different point than their belief that a local theory might be possible. They hoped a local theory would be possible, yes. And now we know it isn't, yes. But none of that undermines their argument that orthodox QM (i.e., QM with the completeness doctrine) violates locality. That is, was and always will be true. So it's a mistake to say "RIP Local Reality" as if there was some "non-reality" *alternative* that *was* local. There isn't. Orthodox QM is nonlocal. It violates Bell Locality, which you can just test for yourself if you know how QM works and what Bell Locality means. EPR showed that the only way to save Locality was to reject the completeness doctrine, and supplement QM with some local hidden variables. But then Bell showed that such a LHV theory can't work. So the only way to save locality doesn't work. Locality can't be saved. Locality is false.
That is the real conclusion of this whole EPR + Bell issue, and you'll never see it so long as you bury your head in the sand w.r.t. EPR.

 

[DrChinese]

Maybe you should clarify your notation, but if it means what I think it means, then you are confused: the unit vector c isn't a hidden variable, it's the direction a certain person measures the spin of a certain particle along. The hidden variable is the "lambda" (Bell's notation) which determines what the *outcome* of that measurement will be.

Your claim was that the "unit vector c" was a *non-local* hidden variable.

I don't need to clarify my notation - it is straight from Bell. Please see just after equation (14) where this is introduced. It is axiomatic that vector c exists IF there is SIMULTANEOUS REALITY TO NON-COMMUTING OBSERVABLES. You can call it a hidden variable, hidden observable or anything you want to really. The point is that it maps to what EPR was assuming existed independently of the act of observation.

As presented by Bell, it is neither local nor non-local. This *despite* his statement that particle 1's result does not depend on particle 2's setting, and vice versa. Sure, this matters to the final conclusion (please don't misquote me on this point) but it is not part of the formal proof. Please note that a reasonable person could read Bell's words and conclude that he believes that Bohmian mechanics is the only possible solution to the conclusion he arrives at. Clearly, BM is not the same as QM! Yet, the fact is, today Bohmian mechanics is not really pursued too seriously. Why is that? Because there is absolutely no need to add anything to QM to fit with experiment.

 

[DrChinese]

That is the real conclusion of this whole EPR + Bell issue...

I'm waiting for the quotes. Meanwhile, please continue to give yourself pats on the back.

Meanwhile, on the original subject of this thread: can a local realistic theory (such as S.E.D. - see Vanesch's earlier references) operate without incorporating non-classical ideas such as the HUP or the projection postulate?

As a result of Bell, we now know that LHV theories cannot replicate all of the results of QM. With this knowledge in hand, my curiously was piqued. Presumably, there must be other areas in which the ideas of QM conflict with various fundamental elements of LHV theories. And sure enough, there is work being done to further distance QM from such theories. It turns out that attempts to present LHV theories consistent with Bell tests have not been going very well.

 

[ttn]

I don't need to clarify my notation - it is straight from Bell. Please see just after equation (14) where this is introduced. It is axiomatic that vector c exists IF there is SIMULTANEOUS REALITY TO NON-COMMUTING OBSERVABLES. You can call it a hidden variable, hidden observable or anything you want to really. The point is that it maps to what EPR was assuming existed independently of the act of observation.

I'm sorry, but none of this makes any sense. The lowercase a, b, and c refer simply to directions in space. They are the directions along which some hypothetical S-G apparatus is oriented to measure the spin component (along that direction) of an electron.

But if you think "c" is a hidden variable that has something to do with there being "SIMULTANEOUS REALITY TO NON-COMMUTING OBSERVABLES", there's really no point arguing further with you about this. You obviously just haven't seriously tried to understand Bell's paper(s).

Clearly, BM is not the same as QM! Yet, the fact is, today Bohmian mechanics is not really pursued too seriously. Why is that? Because there is absolutely no need to add anything to QM to fit with experiment.

Apparently the reason Bohmian Mechanics isn't pursued more seriously is that, like you, there are a lot of physicists out there who are seriously confused about these issues. Bohm's theory *shouldn't* be pursued because it conflicts with relativity, right? Oh, but we don't need to worry about the fact that orthodox QM also conflicts with relativity -- that's just a subjective interpretation. Yeah, right. Good physics.

 

[ttn]

I'm waiting for the quotes.

OK, fine, here's one:

"...the paradox [EPR] forces us to relinquish one of the following two assertions:

1. the description by means of the psi-function is complete

2. the real states of spatially separated objects are independent of each other

...it is possible to adhere to (2) if one regards the psi-function as the description of a (statistical) ensemble of systems (and therefore relinquishes (1) ). However, this blasts the framework of the 'orthodox quantum theory.'"

-Albert Einstein, "Reply to Criticisms", from Schilpp (Albert Einstein: Philosopher Scientist), pg 681.


As I said, see quant-ph/0404016 for a more detailed discussion.

Meanwhile, on the original subject of this thread: can a local realistic theory (such as S.E.D. - see Vanesch's earlier references) operate without incorporating non-classical ideas such as the HUP or the projection postulate?

I don't really have any interest in that question, since I don't think local realistic theories are viable. They're refuted by Bell's theorem, so who really cares what weird ideas they can or can't incorporate? Well, not me.

As a result of Bell, we now know that LHV theories cannot replicate all of the results of QM.

True. But an equally important point is: As a result of Einstein, we now know that orthodox quantum mechanics is not local.

 

[DrChinese]

... As a result of Einstein, we now know that orthodox quantum mechanics is not local.

No quote provided from EPR, as I said you won't be able to provide one which is relevant. EPR is about the reality of observables, and so is Bell. You know, is the moon there when no one is watching? If it was, then you could use information from an observation on one entangled particle to augment your knowledge of the other. But that doesn't happen, because there are limits to what we can know about any particle (entangled or not). So I guess I would ask you: does a single particle have a well defined position AND momentum simultaneously? If the answer is NO, then the results of Bell tests shouldn't seem surprising. Entangling them does not change this basic fact. Separating them also does not change this basic fact.

I cannot imagine too many scientists agreeing with your statement above. As a result of EPR, there was no significant change in the view of QM by the founders/followers of QM. You need to re-read the source papers and drop your bias. You can find them on my site if you don't have them: http://www.drchinese.com/David/EPR_Bell_Aspect.htm

And I'm not sure why you are hanging out in this thread if you are not interested in the subject matter.

 

[ttn]

You need to re-read the source papers and drop your bias.

Oh please. This discussion proves that you don't know the literature. I'm perfectly familiar with the "source papers" -- including the EPR paper itself and Bell's first proof of Bell's Theorem. But unlike you, I'm also quite familiar with the rest of the literature on this topic, both "source" and "secondary".

And I'm not sure why you are hanging out in this thread if you are not interested in the subject matter.

You made some false and misleading statements about EPR. Since you seem to comment on this topic a lot, I thought you might be interested to get straight on a few things. But that is apparently not the case... which leaves me with very little reason for continuing to hang out on this thread.

 

[DrChinese]

Moving on to a hopefully more productive discussion...

I have been reviewing Zz's reference on the state of the art in EPR and Bell written by Genovese. This monster has 504 references and is 78 pages long. It covers the history of EPR/Bell plus the state of the art in experiments; plus a discussion of the hypothetical loopholes.

Amazingly, virtually every LHV theory designed to be compatible with Bell test results has been eliminated. As detection efficiency has increased, there has been no degradation in the violations of Bell inequalities. It had previously been postulated that experiments ruling out of LHV theories might be flawed in some respects. While simultaneous elimination of all "loopholes" has not yet occurred, it is getting closer.

No amount of testing has yet indicated that locality vs. non-locality is an issue. I.e. changing the settings of polarizers mid-flight has no influence whatsoever on the results. In addition, no amount of testing has indicated that the sample size has any effect on the outcome. I.e. the detection efficiency is not a variable in the results in any experiment performed so far. However, the goal is to get a detection efficiency in excess of about 81% while simultaneously making random changes in the polarizer settings mid-flight. This is proving to be a difficult goal to achieve.

 

[DrChinese]

Genovese has also acknowledged the difficulty in getting all controversy removed from discussion of experimental results. In his opinion, the ultimate experiment might be performed within the next generation. Yet, even this would be unlikely to silence all voices on the subject.

Regardless, the door would still be open for non-local HV theories which would be possible alternatives to QM. So he expects there will be plenty to investigate for many years to come.

The shear amount of work that has been done in this area in recent years is absolutely astonishing to me. When Bell wrote his paper, he had trouble getting anyone to give it serious attention. Today, interest in the EPR Paradox and Bell's Theorem has never been greater. The advent of PDC technology has even made table-top tests in undergraduate settings possible.

 

[DrChinese]

One might wonder what I mean when I say that there are LHV theories compatible with Bell test results. Obviously, LHV theories are NOT compatible with the predictions of QM. And all tests to date soundly support QM. However...

There are those who hold out hope that QM is simply wrong. This is a difficult position to maintain given current experiments, but that does not stop diehard supporters of LHV theories.

Bell has already pointed out a substantial burden on LHV theories - the Bell Inequality. So if you assume that there is local reality, you are saying in essence that there is something that causes the experimental results to appear to support QM. Thus:

f(experiment) - f(LR) = f(experimental error/loopholes/etc.)

and yet:

f(experiment) - f(QM) = 0 as efficiency increases (frequently at the hundreds of Std Deviation level).

These equations are becoming increasing more difficult to explain for the local realist. Why - if QM is wrong - is it the exact result you get in every experiment? Why - if there are loopholes - is there no variation in results when any single loophole is closed?

It is almost as if someone is arguing that the Earth is 70,000,000 miles from the sun while experiments all say it is 93,000,000 miles away.

In addition, there are other burdens on LHV theories. After all, they need to explain all of the things that QM does too. Double slit, uncertainty, quantum model of the atom, etc. Is it possible that another competing theory could ever jump through all of these hoops?

 

[vanesch]

Yes, I don't think you understand Bell's derivation. Look at his paper, "On the EPR Paradox." Right after equation (1) he states openly: "The vital assumption is that the result B ... does not depend on the setting a ... nor A on b." (Check out the footnote, too.) This is the locality assumption. It's only because of the locality assumption that we *forbid* A to depend on b, and vice versa.

Well, a way of sneaking out is to say simply that there WAS no result at A, until it got transported at b. That A still contained both possible results, and that it was only decided upon when the signal arrived at b.

And without that assumption, the derivation (obviously) does not go through. Bell's inequality is a bound that applies to *local* theories only. So... how you can say "his primary argument...has nothing to do with locality", I have no idea. Again, all I can conclude is that you simply don't understand either EPR or Bell's Theorem. *Both* of these *crucially* involve locality.

This is correct, but they also assume that a measurement at A had a definite outcome.

You will have to flesh this out. What, exactly, is "observer dependent"? And please note: if your "observer dependence" includes a dependence of the A-side outcome on the B-side observation, your theory is *nonlocal*. Which means it isn't "both local and observer dependent."

What is observer-dependent is what the observer at b *learns* from what was supposed to be measured at a. He learns something about b and thinks that this was the "definite" result at A. But the observer at a might just "learn" something quite different about exactly that same outcome (in that case he'll be living in a different branch).

Or was your point that regular old Copenhagen-ish QM is "both local and observer dependent"? That is just patently false.

Orthodox Copenhagenish QM is both observer dependent and non-local in its mechanism.

In fact, I challenge you to provide any example of a theory that is local, predicts that experiments have definite outcomes, and consistent with the QM predictions.

*that* is impossible of course. So you shoot on the one you like least. As I said, it's a hard choice to have to let go either one of the 3 ; I take out the one in the middle, you take out the first one, and the LR crowd takes out the third one.

 

[DrChinese]

What is observer-dependent is what the observer at b *learns* from what was supposed to be measured at a. He learns something about b and thinks that this was the "definite" result at A. But the observer at a might just "learn" something quite different about exactly that same outcome (in that case he'll be living in a different branch).

Looking at it from the point of view of MW:

Bell's derivation is fully consistent with a MW interpretation in the sense that in MW, each branch contains only the actual outcomes. There is no c outcome in a branch in which a and b are measured. This exactly corresponds to Bell's proof.

It is true that Bell incorporates the idea that the setting at A does not affect the outcome at B. (For this to matter, there has to be a mechanism for this to take place.) BUT... In MW, this is not an issue because the main premise - that an observation could have been made at setting c - is explicitly false. A setting at c would be a different branch, and you cannot have settings at a, b and c simultaneously.

 

[Sherlock]

Yes, of course entanglement is locally produced at emission, that is entirely correct. I'm sorry, and no offense, but I think you never got the "click" of what Bell is all about.
Entanglement is a special kind of state description entirely proper to the formalism of quantum theory, and simply means that the way states of systems are described are, eh, well, entangled, meaning, you cannot disentangle the state description as "the state of A" and "the state of B". I don't know if you realize how revolutionary a concept that is. Never this occurred before in physics. In classical physics, if you have two systems which are in DIFFERENT LOCATIONS, it is always possible to describe the state of the TOTAL SYSTEM as "the state of A" and "the state of B". Of course there can be interactions between these states, and of course these states can have a "common origin" even if they are not interacting, because the systems interacted before.
But "the state of the sun-Betelgeuse system" can always be written as "the state of the sun" and "the state of Betelgeuse". All you can measure about the sun will depend ONLY on "the state of the sun" and all you can measure about Betelgeuse will depend only on "the state of Betelgeuse".
THAT DOESN'T MEAN that there cannot be correlations between both. Indeed, it could be that the sun and Betelgeuse had some interaction long ago, and the correlations of our measurements only measure that "common part" induced by that interaction long ago.
But, as Bell showed, when you have such a separate "this is the state of A" and "this is the state of B" state description EVEN IF THERE WAS A COMMON PART, the correlations you can obtain in such a way have to satisfy certain properties.
This is what is violated in QM. And it is (after the fact) not surprising because the states in QM are NOT of the form "the state of A" and "the state of B". There is only the state of AB.
Again, don't think that this is "simply because they have common origin". Classical systems can have "common origin", but that doesn't deny a reality both to the "state of A" and "the state of B". Measurements on A and B will show statistical correlations, but these correlations WILL SATISFY CERTAIN RULES (like Bell's inequalities). Quantum entanglement goes further and DENIES the existence of a state of A and a state of B.
But people feel uneasy about the fact that there is "no state of A" and "no state of B", and only a "state of AB", because we're used to thinking that what is right here, should have its own 'reality' (state). That's what local reality is all about.
Now it could be that you find it very normal for something NOT to have a state of its own (a reality of its own) just because it is confined to some space. You might have the intuition that "reality is holistic". But it is a very special way of thinking in physics, because VERY MANY USEFUL laws are based upon the locality principle. This is why people like Einstein thought that QM had an UNDERLYING theory which had identical predictions, but which had a (totally different) state description for A and for B. He called those state descriptions "hidden variables".
But Bell's theorem shows that this is not possible.
What is possible is that A and B DO have an individual state description ON THE CONDITION THAT they keep constantly in immediate interaction over long distances. Then, of course, the measurement of one can immediately change the STATE of the other, thus mimicking the quantum result. This is Bohmian mechanics.

Something did 'click' for me after I read this. It suddenly became clear to me why Bell *had* to use the form that he did. I don't really know if it's entirely due to the way you laid it out here, but this certainly had the effect of making me realize that at least one aspect of how I had been thinking about Bell-EPR consideration was wrong. So, I appreciate your efforts, as well as other mentors and advisors, here and in other threads. And, don't worry about offending -- some humiliation is part of learning.

 

[vanesch]

Looking at it from the point of view of MW:
Bell's derivation is fully consistent with a MW interpretation in the sense that in MW, each branch contains only the actual outcomes. There is no c outcome in a branch in which a and b are measured. This exactly corresponds to Bell's proof.

Yes, but that could be considered not sufficient, because you can consider the branch of that single observer that has done a lot of measurements, in different directions, and who would then have to conclude that in HIS branch, there seems to be something statistically fishy (as long as we suppose that there is some "free will" to set the polarizers - but let's for the moment not go into that mine field!) with his data.
I think the real point in MW is that when A has her results, but didn't learn yet from B what were the results at B, these results (with Bob and everything included) are still in a superposition. It is only when Bob gets to A, and tells Alice the result, that Alice "joins" one of the two possible branches of B (the two terms of the superposition). But this happened LOCALLY (at Alice's place). Now Alice will conclude from that that Bob DID have a result when he was far away, and that that result seemed fishy, but in fact, Bob DIDN'T have a result: he was in a superposition. So there is influence all right of Alice's settings on what she THINKS Bob measured (when she extrapolates back in time), but that influence was transmitted LOCALLY when Bob in superposition got to Alice and told her (in fact, when the TWO Bobs came to Alice, and Alice only saw one! The one that fitted her settings and result).
So YES, there is an action of Alice's settings on "Bob's" results, but we think that this happens when Bob does his measurement, and in fact it only happens when Bob tells Alice (when Alice chooses which Bob she will see!).
This is what circumvents Bell's theorem: there IS an action of the settings of Alice on "Bob's results" (but it is not at a distance! It happens when Bob tells Alice).

 

[Sherlock]

Yes, of course entanglement is locally produced at emission, that is entirely correct.
...
... as Bell showed, when you have such a separate "this is the state of A" and "this is the state of B" state description EVEN IF THERE WAS A COMMON PART, the correlations you can obtain in such a way have to satisfy certain properties.
This is what is violated in QM. And it is (after the fact) not surprising because the states in QM are NOT of the form "the state of A" and "the state of B". There is only the state of AB.
Again, don't think that this is "simply because they have common origin".

Please critique these statements and line of reasoning:
1. Bell tests are testing the viability of a certain general formulation wrt correlations of spatially separated quantum measurements involving entangled particles.
2. This general formulation involves the assumption (local realism) that the correlations can be adequately described in terms of the juxtaposition of the physical evolutions of the individual particles, A and B, of any and all entangled pairs.
3. In qm there is no description of the physical evolution of the individual particles, and due to HUP such a description is impossible in principle.
4. In qm, because there is no description of the physical evolution of the individual particles, but because the average joint results can be quantitatively reproduced, the state of the system is described holistically. That is, as the nonseparable, AB, state.
5. The entangled, qm nonseparable, state is locally produced at emission.
6. The correlations are produced via common settfings of spatially separated analyzers.
7. The observed predictable variations in the correlations occur because, i) the paired -- entangled -- particles have a common source, and ii) the paired particles are being analyzed by a common instrumental variable.
8. To date, the qm description of nonseparable states is quantitatively accurate, and the qm canon that a description of the physical evolution of individual particles is limited by HUP, and therefore that a complete description of such evolution is in principle impossible, is confirmed.
9. Since local realist theories are, to date, not quantitatively accurate, and since in order to match the quantitative accuracy of the qm formulation they would seem to require a more complete specification of the physical evolution of entangled particles than is physically possible according to qm, then *assuming* that the fundamental quantum of action is a universal limiting factor, then it can be concluded that the local realist form is, in principle, disallowed.

And, this tells us nothing about whether or not there are superluminally propagating disturbances in nature, or whether or not there is a reality independent of our observations.

 

[vanesch]

Please critique these statements and line of reasoning:
1. Bell tests are testing the viability of a certain general formulation wrt correlations of spatially separated quantum measurements involving entangled particles.

Bell tests verify whether the correlations found in spatially separated systems respect of violate Bell locality conditions, where Bell locality conditions are the conditions that come from NON-QUANTUM local realist theories. Local realist theories are a class of theories that assign a reality (a definite state) to each local system individually, and the outcome of ANY experiment on that local system is purely determined by that local state. So a Bell test has a priori NOTHING to do with quantum theory. It tests whether certain correlations could eventually be produced by a theory within the class of Local Realist theories.
We only use quantum theory (which is NOT a LR theory) to hint us where to look for VIOLATIONS of these conditions, and then do the experiments accordingly.

2. This general formulation involves the assumption (local realism) that the correlations can be adequately described in terms of the juxtaposition of the physical evolutions of the individual particles, A and B, of any and all entangled pairs.

Entangled or not. Because that's not the LR business. But the Bell tests are of course only INTERESTING with entangled quantum systems, as in this case, QM predicts violation of the Bell conditions. In non-entangled quantum systems, QM does NOT violate the Bell conditions, so we expect the Bell test to be satisfied (and hence allow for a LR theory). This is not interesting.

3. In qm there is no description of the physical evolution of the individual particles, and due to HUP such a description is impossible in principle.

I don't know if it is the HUP which does this. I would say that it is the core principle of quantum theory which does it: the superposition principle.

4. In qm, because there is no description of the physical evolution of the individual particles, but because the average joint results can be quantitatively reproduced, the state of the system is described holistically. That is, as the nonseparable, AB, state.

Yes. I could make a comment, but I'm affraid it would lead us away from the main topic.

5. The entangled, qm nonseparable, state is locally produced at emission.

Yes.

6. The correlations are produced via common settfings of spatially separated analyzers.

"produced" is maybe a bad choice of words. I'd say, that you can calculate the expected correlations of the measurements in QM, by considering a "common measurement" operator which describes the two settings of the two analysers, applied to the "holistic state" AB.

7. The observed predictable variations in the correlations occur because, i) the paired -- entangled -- particles have a common source, and ii) the paired particles are being analyzed by a common instrumental variable.

In the quantum formalism, the correlations are indeed, as I said, the result of applying a "holistic" observable (containing the two settings of the two analysers) to the "holistic state" (the entangled pair). I don't know if that is what you are saying.

8. To date, the qm description of nonseparable states is quantitatively accurate, and the qm canon that a description of the physical evolution of individual particles is limited by HUP, and therefore that a complete description of such evolution is in principle impossible, is confirmed.

Let's simply say that there are 2 results:
1) purely theoretically: Bell's theorem tells us that the ("holistically calculated") correlations we can CALCULATE in QM violate the Bell conditions for certain, entangled, states. As such, we already know that there can be no LR theory which makes, in all cases, identical predictions as QM. That's without any discussion (although some try to do so).
2) experimentally: it could of course simply be that QM is experimentally wrong in these cases. However, there are many experimental results which suggest very strongly that the quantum predictions are correct, even in those cases where QM predicts violation of the Bell locality conditions. The reason why I'm using a cautious tone is just for the sake of not being rebutted by "loophole finders", because indeed, for (to my knowledge) every experiment, there are "loopholes" in the setup, which allow LR proponents to 'save their ass'. These loopholes result from the fact that the setup is complicated and that you need to apply correction techniques (such as subtraction of background, and taking into account efficiencies - things that are usually accepted as standard experimental techniques).
So from the LR-proponent side, yes, we don't have ultimate experiments without any correction that show in the raw data clear Bell locality violations. We only obtain that with standard corrections of experimental techniques.
From the QM-proponent side, these measurements are awfully close to what standard QM predicts, including the prediction of the experimental corrections. So at least, QM is not falsified, even when it is used in the domain where its states predict ideally violations of Bell locality conditions.

9. Since local realist theories are, to date, not quantitatively accurate, and since in order to match the quantitative accuracy of the qm formulation they would seem to require a more complete specification of the physical evolution of entangled particles than is physically possible according to qm, then *assuming* that the fundamental quantum of action is a universal limiting factor, then it can be concluded that the local realist form is, in principle, disallowed.

I think this is badly formulated. Local realist theories are not "quantitatively inaccurate". We don't consider specific examples of LR theories. We know that ALL of them need to respect the Bell locality conditions, so we already know that they can never give identical results in all cases as QM.
But the reason is not that QM has a "less complete specification", or that this would "violate the HUP" or something. In fact, a priori, there would be nothing against a totally different theory, that allowed for "more complete state specifications" and would overthrow the HUP, as long as it made the same statistical predictions (statistical because of our ignorance of this "more complete part" - the hidden variables) as QM. This was in fact what Einstein was hoping for. What kills such a possibility is not QM's axioms of course (because we're talking about a DIFFERENT theory, with identical outcomes). What kills it is the fact that such a theory can never make identical predictions, as it has to respect Bell conditions, which are violated by QM.
However, if you drop the Locality condition, then you CAN construct a theory with a more complete specification of the state, which DOES assign individual reality to the systems A and B, and which makes identical predictions as QM. That theory exists, is known, and is called Bohmian mechanics.
Bohmian mechanics looks a lot like classical mechanics, except that there are forces at a distance (non-local dynamics). It makes identical predictions with QM. But it is of course NOT relativistically invariant in its mechanism.

And, this tells us nothing about whether or not there are superluminally propagating disturbances in nature, or whether or not there is a reality independent of our observations.

No, but at least it tells us that you cannot have both, in the way they were assumed in a LR theory. One thing has to give.

 

[Sherlock]

And, this tells us nothing about whether or not there are superluminally propagating disturbances in nature, or whether or not there is a reality independent of our observations.

No, but at least it tells us that you cannot have both, in the way they were assumed in a LR theory. One thing has to give.

I'm just saying that the Bell issue isn't telling us anything about nature, which you seem to agree with. Is that correct?

Thanks for the extended comments. I'm redoing my list of statements, and will resubmit (until I get it right :-) ). Is this thread ok for that or should I start a new one?

 

[vanesch]

I'm just saying that the Bell issue isn't telling us anything about nature, which you seem to agree with. Is that correct?

It tells us something about quantum mechanics. Whether quantum mechanics describes nature is another issue, but it tells us that, concerning a combined set of properties one would like to have, and which quantum mechanics doesn't possess, namely local reality, you will never find ANOTHER theory which does have these property (local reality) and which has identical predictions in all circumstances as quantum theory.
In as far as experiments seem to confirm the QM predictions for exactly these cases, I would say that it DOES tell us something about nature, namely that local reality, in the way it is imagined in the kind of theories considered by Bell, is not valid in nature.

However, I do not agree with the shortcut that people take, and that say that, for instance, Bell disproves *locality*. This is not correct, as there exists a version of QM that is local, namely MWI (but MWI does not assign any reality to the outcomes of remote measurements). Bell does not disprove either what one could call "reality" (or even determinism). Indeed, Bohmian mechanics is such a theory (but it contains non-local dynamics).

 

[ttn]

However, I do not agree with the shortcut that people take, and that say that, for instance, Bell disproves *locality*. This is not correct, as there exists a version of QM that is local, namely MWI (but MWI does not assign any reality to the outcomes of remote measurements). Bell does not disprove either what one could call "reality" (or even determinism). Indeed, Bohmian mechanics is such a theory (but it contains non-local dynamics).

Well, I'm one of the people who take the "shortcut" of saying that locality has been disproven (by some combination of EPR and Bell and experiment). So we might as well be clear on exactly what it is that is cut short -- i.e., exactly what other tacit premises are really needed to justify the claim that locality as such is refuted.
It's pretty simple and, Patrick, I'm pretty sure you and I agree about this: the other premise that you need is the idea that for each photon pair in the experiments, the measurements on both sides *have definite outcomes*. That is, for any incoming photon pair, both Alice and Bob see definitely either spin up or spin down (along whatever direction is being measured at that moment) for their photon. In particular, Alice has to say: I know Bob just made a measurement and I don't know yet what the outcome of that measurement was, but I know it had some one particular definite outcome.
If one accepts this, then there is no way around the conclusion that locality is false. Anyone disagree with that?
Now what does it mean to accept this extra premise? Is this some kind of weird thing to believe in? Is it tantamount to adding extra variables to QM or believing in epicycles or cold fusion or homeopathy? I'd be curious what others think.

 

[vanesch]

It's pretty simple and, Patrick, I'm pretty sure you and I agree about this: the other premise that you need is the idea that for each photon pair in the experiments, the measurements on both sides *have definite outcomes*.

I do agree with this, that this is the only extra hypothesis that you need and which can be used to "save" us potentially from the blunt rejection of locality as such.
Well, except of course the other hypothesis, that QM is NOT valid and that the loopholes in all these experiments ARE conspiring to make us believe so, as says the LR crowd. But without any indication of *failure* of QM, I find this highly highly improbable and not a fruitful working hypothesis.
And I can tell you that I do not find it comfortable to reject this very reasonable hypothesis of the existence of the other measurement, but nevertheless I do ! Because I'm a d**khead and still refuse to let locality go as of now.
Where comes my d**kheadedness from ? (ok, my mom will say: from your dad, but that's not what I mean ). It comes from 2 points:
1) we already accepted the "not having definite values until you measure it" idea for the microworld, in a way. It is only because now we could (potentially) apply the same reasoning to the quantity "outcome seen by my remote friend" and not only to "position of the electron in the atom" that we start having problems with this ; maybe because suddenly what we were willing to accept in the microworld didn't struck us as so weird as when you apply it to your remote friend ; but that's just a matter of scale.
2) I hate to give up relativity ; the space-time concept. And you have to, when you screw up the locality condition. It simply works too well: all that requirement of the Lagrangian having to be a lorentz scalar and so on, it's hard to let this go.
However, I recognize that this is somehow a personal choice, and ttn has convinced me now that the Bohmian view is not so outlandish, after all. Nevertheless, I stick with my view, but I respect his.

 

[ttn]

I do agree with this, that this is the only extra hypothesis that you need and which can be used to "save" us potentially from the blunt rejection of locality as such.

Good.

Well, except of course the other hypothesis, that QM is NOT valid and that the loopholes in all these experiments ARE conspiring to make us believe so, as says the LR crowd. But without any indication of *failure* of QM, I find this highly highly improbable and not a fruitful working hypothesis.

Yes, of course. It's possible the QM predictions are just wrong and the apparent experimental support for those predictions is due to some kind of systematic error in the experiments. But I don't think this is likely or fruitful.

1) we already accepted the "not having definite values until you measure it" idea for the microworld, in a way. It is only because now we could (potentially) apply the same reasoning to the quantity "outcome seen by my remote friend" and not only to "position of the electron in the atom" that we start having problems with this ; maybe because suddenly what we were willing to accept in the microworld didn't struck us as so weird as when you apply it to your remote friend ; but that's just a matter of scale.

There's a difference between "not having definite values for spin components" at the microlevel and "not having a clear ontology at all" at the microlevel. It's of course true that in the Copenhagen approach we do give up both of these things -- following Bohr/Heisenberg we basically don't think it's possible to talk about reality at the microlevel at all, and it just follows that, in particular, we shouldn't assign particular real values to spin components.
But for someone who rejects the Copenhagen approach (in favor, say, of de Broglie's old pilot wave approach that was later rediscovered by Bohm), this first argument doesn't work. In the de Broglie - Bohm theory, we always had a clear micro-ontology, but recognized that spin is a contextual property so that it doesn't make sense to assign definite pre-measurement values to spin components. But then there is no valid extrapolation to the macro-level. To reject the idea of experiments having definite outcomes is to reject that (for example) Bob either ran home to tell his mom that he got "spin up" as opposed to staying in the lab and crying that he got "spin down" -- that is, it is to reject statements about the positions of (huge collections of) particles. And that is the very kind of thing we Bohmians never rejected even at the micro-level.
But this is just a point about the ease of swallowing your point 1. I grant of course that no matter how easy or hard it is for someone to swallow, it is possible to avoid the conclusion of non-locality if you do swallow the idea that Bob's experiment didn't have a definite outcome (so he now doesn't have a definite position, etc...).

2) I hate to give up relativity ; the space-time concept. And you have to, when you screw up the locality condition. It simply works too well: all that requirement of the Lagrangian having to be a lorentz scalar and so on, it's hard to let this go.

The interesting question to me is whether or not you've really saved locality this way. You may still retain some kind of formal Lorentz invariance, yes. But is the resulting theory really local in the sense of respecting the principle of relativity? I'm inclined to think that it isn't. Part of relativity is the idea that physics looks the same for all observers. But in this version of MWI, physics isn't the same for all observers. There's one special observer who is dynamically special -- this is Alice in the standard example, since her experiment really *does* have a definite outcome (it having happened right where she is), while Bob's really doesn't have a definite outcome. The whole thing turns into a kind of solipsism for Alice, in which really all that exists is "information" in Alice's head. And, yes, the mathematical laws governing the influx of information are lorentz invariant... but have we really preserved the spirit of relativity here? Not only are Alice and Bob non-equivalent observers, but one of them doesn't even really *exist* as a conscious scientist. (That's why I say this turns into solipsism.)
Of course, at this point I stop caring whether or not there's some way of claiming to have respected relativity. It's just too crazy to even take that question seriously anymore.

However, I recognize that this is somehow a personal choice, and ttn has convinced me now that the Bohmian view is not so outlandish, after all. Nevertheless, I stick with my view, but I respect his.

Fair enough. But just to be clear, it's not like what I'm saying about locality is some part of "the Bohmian view." What I'm saying about locality is, I think, just plain true. The connection to Bohm's theory is that if you accept the truth of what I'm saying about locality, you have a hard time not becoming a Bohmian! If the only way to avoid rejecting locality is to accept something like solipsism (and if one is unwilling to go there), then you might as well opt for the non-local theory which makes the most intuitive sense, which helps you understand QM as much as possible, which doesn't suffer from any unprofessional vagueness and ambiguity like Copenhagen, which is known to be consistent with experiment, etc., etc. In short, as soon as you accept that non-locality is a fact which has to be incorporated into one's theory, it is practically impossible *not* to recognize that Bohm's theory is far and away the best option.

 

[vanesch]

The interesting question to me is whether or not you've really saved locality this way. You may still retain some kind of formal Lorentz invariance, yes. But is the resulting theory really local in the sense of respecting the principle of relativity? I'm inclined to think that it isn't. Part of relativity is the idea that physics looks the same for all observers. But in this version of MWI, physics isn't the same for all observers. There's one special observer who is dynamically special -- this is Alice in the standard example, since her experiment really *does* have a definite outcome (it having happened right where she is), while Bob's really doesn't have a definite outcome.

This, on the other hand, is not correct. There is still a symmetry between the observers, and what you just described is because we described everything from Alice's point of view. But you can repeat the story from Bob's point of view, and now, TO HIM AS AN OBSERVER, it is Alice who didn't have definite outcomes. The only difference is that the "Bob-observer" might have seen different results than the Bob-who-was-seen-by-Alice-observer, and this is the point where things get mind-boggling
The price to pay for that is that each of us lives then in his own little world with different outcomes, but also with copies of all the others which DID have outcomes which are consistent with ours.

The whole thing turns into a kind of solipsism for Alice, in which really all that exists is "information" in Alice's head. And, yes, the mathematical laws governing the influx of information are lorentz invariant... but have we really preserved the spirit of relativity here? Not only are Alice and Bob non-equivalent observers, but one of them doesn't even really *exist* as a conscious scientist. (That's why I say this turns into solipsism.)

Of course they exist BOTH as conscious scientists, but not necessarily in the same branch, in which case each of them is in contact with a "clone" of the conscious version of the other one - and I leave it up to your taste to declare that clone also a conscious one or not.

Of course, at this point I stop caring whether or not there's some way of claiming to have respected relativity. It's just too crazy to even take that question seriously anymore.

I will not disagree with you that it sounds crazy. The question is if it is crazy enough .
My point of view is that we shouldn't care about the "crazyness" of an explanation if it fits the formalism it is supposed to explain. Because one day, that formalism is going to change, and then the crazy explanation will go in the dustbin. And this is my main reason to prefer "crazy" MWI over "intuitive" Bohmian mechanics: "crazy" MWI is closer to the formalism of current QM and relativity than Bohmian mechanics (in which the spacetime manifold as a geometrical object doesn't make sense).

In short, as soon as you accept that non-locality is a fact which has to be incorporated into one's theory, it is practically impossible *not* to recognize that Bohm's theory is far and away the best option.

I fully agree with that. I'd say that if all we had was non-relativistic QM, then it would almost be obvious that Bohmian mechanics is a superior explanation. But as of today, I don't want to toss out GR. And that is what you do when you accept non-locality. So if I want to save GR, *I have no other option* as to consider that Bob, according to Alice, didn't have a definite outcome - and that Alice, according to Bob, didn't have one either, and that when they meet, each of them meets with ONE VERSION of the other, and as such, each of them is happy that way, each one in his/her own branch.
I think that the issue can only be settled if we have a full integration of GR and QM.

 

[ttn]

This, on the other hand, is not correct. There is still a symmetry between the observers, and what you just described is because we described everything from Alice's point of view. But you can repeat the story from Bob's point of view, and now, TO HIM AS AN OBSERVER, it is Alice who didn't have definite outcomes. The only difference is that the "Bob-observer" might have seen different results than the Bob-who-was-seen-by-Alice-observer, and this is the point where things get mind-boggling
The price to pay for that is that each of us lives then in his own little world with different outcomes, but also with copies of all the others which DID have outcomes which are consistent with ours.

I was under the assumption that there was only one world. I mean, for the sake of discussion, I am happy to allow that this world look quite crazy, that big macroscopic things are in crazy superpositions and entangled states, etc. But I don't know what you're talking about if you are literally saying that there is now a world associated with each person. "Real" ceases to have a meaning, and there is now only "real for me" and "real for you" and "real for Alice", etc.
Here's why this bothers me. You said in a previous post that you thought it was extremely unlikely that the apparent experimental confirmation of the QM predictions (that is, the experimental evidence that Bell's inequalities are violated) is due to some kind of systematic error, as the local realists say/want. I entirely agree with you. After all, a number of different experiments have been done at a number of locations around the world by independent people, etc... Well now you're saying that really there's no such thing as "the world" -- just personal fantasies that each of us create for ourselves that are radically inconsistent with each other's. So did those Bell test experiments even *happen*? That isn't even a meaningful question anymore, under this version of MWI that you're advocating.
My point is really that there's a kind of hierarchy to knowledge. Certain statements/conclusions rest on others such that if you give up one thing, you must also give up (as now meaningless) the other things that depend on it. So how can you claim that the experimental evidence supporting the QM predictions is strong, when in the next breath you say something that renders that statement totally meaningless? That's my fundamental problem with this approach. You talk as if you're making a choice from among several things to give up, but the fact is those several things are not all at the same level hierarchically. And you end up "opting" to give up one that means, really, you've given up all the others as well. As soon as you deny that there's one world, out there, independent of us, and it's science's job to figure out what that world is like, you render meaningless any debate about whether that world is as described by relativity, whether a certain theory's experimental predictions are correct, whether a given experiment even happened, etc., etc. So I just don't see the rationality of the option you're making here.

I fully agree with that. I'd say that if all we had was non-relativistic QM, then it would almost be obvious that Bohmian mechanics is a superior explanation. But as of today, I don't want to toss out GR. And that is what you do when you accept non-locality. So if I want to save GR, *I have no other option* as to consider that Bob, according to Alice, didn't have a definite outcome - and that Alice, according to Bob, didn't have one either, and that when they meet, each of them meets with ONE VERSION of the other, and as such, each of them is happy that way, each one in his/her own branch.
I think that the issue can only be settled if we have a full integration of GR and QM.

I disagree with this. I think it's you who's got a serious problem with relativity, not me. It's easy enough to keep the whole formalism of relativity (both S and G) but add some kind of preferred foliation to spacetime so that one can give meaning to the non-local interactions in Bohm's theory. There's a whole textbook that shows how to do this for GR. The book is by Janossy, and it's cited by Bell in, I think, "How to Teach SR". Basically what I'm talking about here is a kind of Lorentz Ether Theory -- something with a preferred rest frame, i.e., a notion of absolute simultaneity, but which otherwise shares the same formalism and empirical predictions as relativity. Such theories *exist* and they *work*. And one can easily embed a Bohmian theory on this kind of space-time background, and everything works fine. There are instantaneous action at a distance type interactions going on among all the particles, but this turns out to be masked by uncertainty about the particles' initial conditions -- in (rather amazingly, but it works out) just such a way so that all the empirical predictions come out to be Lorentz invariant, and you can never detect the ether.
Now, is this kind of theory consistent with relativity? Yes and no. It makes all the same predictions, and everything at the level of observations comes out Lorentz invariant. So far so good. But behind the scenes, the fundamental laws are not Lorentz invariant. (There's a preferred frame, or in GR a preferred foliation into spacelike hypersurfaces.) So that does conflict with the principle of relativity (which just basically asserts that there is no such preferred frame). But who cares? There's no empirical evidence for this principle anyway and, I say, some evidence against it (namely the empirical violations of Bell's inequalities).
So it's at least clear how to integrate Bohm's theory with relativity. What about MWI? Well, take GR. Energy density is related to spacetime curvature. Well what happens to Einstein's field equations in the situation I outlined a while ago -- Bob runs home to momma if he gets "spin up" but stays in the lab for a nap if he gets "spin down". What does the spacetime curvature look like? Well, if we go with the "one world" version of MWI (with everything "as seen by Alice") then Bob is just in a superposition of being in two different places. So what is the energy density associated with that? Not clear. So the whole thing is rather ambiguous. And it only gets worse if you go with the truly many worlds version of MWI. Then in Alice's fantasy world, there's this crazy ambiguity about gravitational fields over near Bob, while in Bob's fantasy world the gravitational field is perfectly sensible near him but has this crazy ambiguity over near Alice.
How do you resolve any of this?

 

[Sherlock]

... the other premise that you need is the idea that for each photon pair in the experiments, the measurements on both sides *have definite outcomes*. That is, for any incoming photon pair, both Alice and Bob see definitely either spin up or spin down (along whatever direction is being measured at that moment) for their photon. In particular, Alice has to say: I know Bob just made a measurement and I don't know yet what the outcome of that measurement was, but I know it had some one particular definite outcome.
If one accepts this, then there is no way around the conclusion that locality is false. Anyone disagree with that?

The "definite outcomes" of individual measurements are detection or nondetection. I don't see how one could conclude anything about the locality or nonlocality of nature from this.

 

[Sherlock]

My point is really that there's a kind of hierarchy to knowledge. Certain statements/conclusions rest on others such that if you give up one thing, you must also give up (as now meaningless) the other things that depend on it.
[

A good point. Your argument for nonlocality seems to rest on the relationship of the wave function to nature. The problem is that qm evolutions and interactions occur in an imaginary space. It would seem that you have the same problem as MWI'ers in that there's no compelling reason to accept the wave function as being a complete description of *physical reality* in the first place.

So, the question of locality-nonlocality in nature remains an open one.

 

[vanesch]

I was under the assumption that there was only one world. I mean, for the sake of discussion, I am happy to allow that this world look quite crazy, that big macroscopic things are in crazy superpositions and entangled states, etc. But I don't know what you're talking about if you are literally saying that there is now a world associated with each person. "Real" ceases to have a meaning, and there is now only "real for me" and "real for you" and "real for Alice", etc.

Well, what is real (in this view) is the superpositions of all these "real for X" states. A "real for X" state (a branch, or a world or whatever you call it) is nothing else but ONE TERM in the "wavefunction of the universe", and X happens to observe that. A "real for Y" is another term, which Y happens to observe. So there are 2 levels of "real". There is "really real" which is the total wavefunction, and there is "real for X" which is the term of that wavefunction which X happens to observe and which, to X, is his entire (observed) reality of which he cannot (or can only very difficultly) escape, and then there is the "deeper reality" which for all practical purposes can be done with, which is the wavefunction of the universe, and which is the only thing which obeys unitary dynamics which moreover, is local.

Here's why this bothers me. You said in a previous post that you thought it was extremely unlikely that the apparent experimental confirmation of the QM predictions (that is, the experimental evidence that Bell's inequalities are violated) is due to some kind of systematic error, as the local realists say/want. I entirely agree with you. After all, a number of different experiments have been done at a number of locations around the world by independent people, etc... Well now you're saying that really there's no such thing as "the world" -- just personal fantasies that each of us create for ourselves that are radically inconsistent with each other's. So did those Bell test experiments even *happen*? That isn't even a meaningful question anymore, under this version of MWI that you're advocating.

The answer would be: there's part of the wavefunction which corresponds to particle/field/whatever configurations which correspond to Bell-type experiments, and you and I happen to observe that branch where these experiments took place.

So how can you claim that the experimental evidence supporting the QM predictions is strong, when in the next breath you say something that renders that statement totally meaningless? That's my fundamental problem with this approach. You talk as if you're making a choice from among several things to give up, but the fact is those several things are not all at the same level hierarchically. And you end up "opting" to give up one that means, really, you've given up all the others as well. As soon as you deny that there's one world, out there, independent of us, and it's science's job to figure out what that world is like, you render meaningless any debate about whether that world is as described by relativity, whether a certain theory's experimental predictions are correct, whether a given experiment even happened, etc., etc.

In this MWI view, of course our "access" to the real reality (the wavefunction of the universe) is limited - we only see one branch of it, each for our own. Nevertheless, that's our "personal reality" and we happen (well, I at least) to be in a branch where there seems to be a witness of other scientists who did experiments ; from that information (all contained in the branch we are observing) we can derive laws of nature - which only pertain to our own branch of course, but of which we can extrapolate.
So up to the level of where you can say that the state I'm observing is "real for me", all those experiments done by others which I can observe are also "real for me".

It's easy enough to keep the whole formalism of relativity (both S and G) but add some kind of preferred foliation to spacetime so that one can give meaning to the non-local interactions in Bohm's theory.

Well, from the moment that you have such a preferred foliation, you have in fact destroyed the 4-d spacetime manifold, and replaced it with a 3-d fibre bundle over the 1-d time axis. Once you do that, there is no a priori requirement to obey Lorentz transformations. Lorentz transformations only make sense when there is NO such structure. Of course they CAN be present, but they don't have to.

Such theories *exist* and they *work*. And one can easily embed a Bohmian theory on this kind of space-time background, and everything works fine. There are instantaneous action at a distance type interactions going on among all the particles, but this turns out to be masked by uncertainty about the particles' initial conditions -- in (rather amazingly, but it works out) just such a way so that all the empirical predictions come out to be Lorentz invariant, and you can never detect the ether.

Yes, that's what I don't like about these theories. There's too much ad hoc things going on there. Too many symmetries which are not required by the inherent structure. For instance, there's no reason to have GR in the first place if you can have a preferred foliation of spacetime. Newtonian gravity is perfectly acceptable too in that case.

Now, is this kind of theory consistent with relativity? Yes and no. It makes all the same predictions, and everything at the level of observations comes out Lorentz invariant. So far so good. But behind the scenes, the fundamental laws are not Lorentz invariant. (There's a preferred frame, or in GR a preferred foliation into spacelike hypersurfaces.) So that does conflict with the principle of relativity (which just basically asserts that there is no such preferred frame). But who cares?

I do :-) For always the same reason: I give preference to the formalism, and adapt the story to it. I don't want to have the story sound nice, and adapt the formalism to it.

There's no empirical evidence for this principle anyway and, I say, some evidence against it (namely the empirical violations of Bell's inequalities).
So it's at least clear how to integrate Bohm's theory with relativity.

Well, I don't see how you get out gravitons from this construction for instance. Of course, that's not empirically confirmed, I know. But it does show some fundamental differences in predictions. I'm sure there are other issues, but I'm not knowledgeable enough to comment on that.

What about MWI? Well, take GR. Energy density is related to spacetime curvature. Well what happens to Einstein's field equations in the situation I outlined a while ago -- Bob runs home to momma if he gets "spin up" but stays in the lab for a nap if he gets "spin down". What does the spacetime curvature look like? Well, if we go with the "one world" version of MWI (with everything "as seen by Alice") then Bob is just in a superposition of being in two different places.

This is an extremely difficult problem ; I'd say that if I knew how to solve it, I would be famous . It is the holy grail of theoretical physics, to unify GR and quantum theory. You can, as you do, deny the problem. And indeed, maybe there isn't one. Maybe it is a chimera people are running after. I think that what is clear is that at this point, we're not talking anymore about different interpretations of theories with identical predictions, but about totally different theories with different predictions. But it might be empirically very hard to distinguish them.
However, (my hope) it could be that gravity is involved in some kind of true wavefunction collapse, which re-unifies the different branches into one and only branch - so that this MWI scheme is only temporary, for space-like events. Or maybe one can finally formulate a totally unitary version of quantum gravity, in which case there is no escaping from any MWI vision, given that even gravitational interaction is truly unitary. As far as I understand, most attempts at unification choose the latter direction. And maybe, who knows, nature is playing tricks on us, and just acts AS IF lorentz transformations are required but is in fact very non-local and Bohmians are right. Who will tell ?

 

[ttn]

A good point. Your argument for nonlocality seems to rest on the relationship of the wave function to nature. The problem is that qm evolutions and interactions occur in an imaginary space. It would seem that you have the same problem as MWI'ers in that there's no compelling reason to accept the wave function as being a complete description of *physical reality* in the first place.
So, the question of locality-nonlocality in nature remains an open one.

No, I don't think it's open. If you assume that the wave function alone is a complete description of reality (and if you believe that experiments always have definite outcomes, i.e., you believe in the collapse postulate) then your theory is non-local. Orthodox QM violates locality. Einstein pointed this out decades ago. See, e.g., quant-ph/0408105 for a recent discussion.
On the other hand, if you don't believe that the wave function alone provides a complete description of reality, i.e., you believe in some kind of "hidden variable theory", then your theory will have to be nonlocal if it is going to agree with experiment. So proves Bell's Theorem.
Now, for the record, what I just said in the above 2 paragraphs has some caveats: first off, I'm assuming that the *apparent* results of experiments (namely agreement with the QM predictions) are really right. Second, I'm assuming that those experiments have definite outcomes. Are these good assumptions? I sure think so. And with them, locality ceases to be an open question. With these assumptions we have to conclude that locality is simply false -- that nature is non-local.

 

[ttn]

... So up to the level of where you can say that the state I'm observing is "real for me", all those experiments done by others which I can observe are also "real for me".

Yes, well, no need to re-hash all this well-treaded ground. I'm just pointing out for the sake of the audience that this MWI "saving of locality" comes at a pretty steep price -- so steep that it's actually difficult to parse the meaning of the evidence which made us believe in such things as unitary QM evolution equations in the first place!

Well, from the moment that you have such a preferred foliation, you have in fact destroyed the 4-d spacetime manifold, and replaced it with a 3-d fibre bundle over the 1-d time axis. Once you do that, there is no a priori requirement to obey Lorentz transformations. Lorentz transformations only make sense when there is NO such structure. Of course they CAN be present, but they don't have to.
...
Yes, that's what I don't like about these theories. There's too much ad hoc things going on there. Too many symmetries which are not required by the inherent structure. For instance, there's no reason to have GR in the first place if you can have a preferred foliation of spacetime. Newtonian gravity is perfectly acceptable too in that case.

Yup. Of course, if you think theories should be based on experiment, then Newton doesn't look like such a good option compared to GR. But you're right that from a purely theoretical point of view, there's no *need* for Lorentz invariance in a Lorentz ether type theory. It's just some weird emergent behavior or some property of the laws that for all we know could have been different.

Well, I don't see how you get out gravitons from this construction for instance. Of course, that's not empirically confirmed, I know. But it does show some fundamental differences in predictions. I'm sure there are other issues, but I'm not knowledgeable enough to comment on that.

Me neither, except to echo something you said below: in this model there is no desperate need for a quantum theory of gravity. It's at least possible that a Bohmian version of the standard model of particle physics (assuming such a thing can be constructed...) can just live on a completely classical GR background. There's no desperate problem with unifying the quantum and the gravity. Of course, if we someday empirically discover gravitons, etc., we can always cook up a Bohmian type quantum theory for them. (Well, easier said than done, but you get the point.)

This is an extremely difficult problem ; I'd say that if I knew how to solve it, I would be famous . It is the holy grail of theoretical physics, to unify GR and quantum theory. You can, as you do, deny the problem.

That's an inflammatory way to put it. For me, there is no problem. That's a virtue. Don't try to make it sound like I'm burying my head in the sand to a problem that is somehow real. It's only a real problem from the MWI side.

And indeed, maybe there isn't one. Maybe it is a chimera people are running after. I think that what is clear is that at this point, we're not talking anymore about different interpretations of theories with identical predictions, but about totally different theories with different predictions. But it might be empirically very hard to distinguish them.

Yes, I agree. In fact, I'd say that long before we get to quantum gravity. The de Broglie - Bohm theory, orthodox QM, and MWI, are, I think, 3 very different theories. They make radically different claims about how the world really works. But, alas, it is difficult to distinguish them empirically.

However, (my hope) it could be that gravity is involved in some kind of true wavefunction collapse, which re-unifies the different branches into one and only branch - so that this MWI scheme is only temporary, for space-like events. Or maybe one can finally formulate a totally unitary version of quantum gravity, in which case there is no escaping from any MWI vision, given that even gravitational interaction is truly unitary. As far as I understand, most attempts at unification choose the latter direction. And maybe, who knows, nature is playing tricks on us, and just acts AS IF lorentz transformations are required but is in fact very non-local and Bohmians are right. Who will tell ?

I'll tell if you'll let me. =)

 

[Sherlock]

No, I don't think it's open. If you assume that the wave function alone is a complete description of reality (and if you believe that experiments always have definite outcomes, i.e., you believe in the collapse postulate) then your theory is non-local. Orthodox QM violates locality. Einstein pointed this out decades ago. See, e.g., quant-ph/0408105 for a recent discussion.

The wave function contains what's known about what it refers to. It would be an unfounded leap of faith to say that it's a complete description. And of course experiments always have definite outcomes. The probabiltiy interpretation of quantum theory is the most widely accepted because it makes the most sense. Wave function collapse happens in imaginary space. It doesn't necessarily follow that what is happening experimentally is a violation of locality in nature.

On the other hand, if you don't believe that the wave function alone provides a complete description of reality, i.e., you believe in some kind of "hidden variable theory", then your theory will have to be nonlocal if it is going to agree with experiment. So proves Bell's Theorem.

One can believe that the wave function alone is an incomplete description of physical reality, while also believing in the impossibility of hidden variable (ie., a separable formulation) theories that could match all of qm's quantitative predictions -- because to do this, the hidden variable theory would presumably have to provide a more complete description of the creation and evolution of the individual components of entangled pairs than quantum theory allows. That is, I can believe in the essential truth of the principles (and the limits they impose), and the continued efficacy of quantum theory while also believing that the theory isn't a complete description of physical reality.

Now, for the record, what I just said in the above 2 paragraphs has some caveats: first off, I'm assuming that the *apparent* results of experiments (namely agreement with the QM predictions) are really right. Second, I'm assuming that those experiments have definite outcomes. Are these good assumptions? I sure think so. And with them, locality ceases to be an open question. With these assumptions we have to conclude that locality is simply false -- that nature is non-local.

That qm has accurately predicted the average results of any set of quantum measurements, and that the individual measurement outcomes exist in definite, qualitative, verifiable macroscopic states, isn't in dispute.
These can be taken as matters of fact.

I think you'll need more than what you've offered so far to convincingly support your conclusion that nonlocality is a fact of nature.

 

[vanesch]

Yes, well, no need to re-hash all this well-treaded ground.

Yes, when typing this, I had a feeling of deja-vu
But I needed to point it out because you made it sound as if MWI makes ONE observer special ; which would of course be also a foliation of spacetime!

I'm just pointing out for the sake of the audience that this MWI "saving of locality" comes at a pretty steep price -- so steep that it's actually difficult to parse the meaning of the evidence which made us believe in such things as unitary QM evolution equations in the first place!

I will not deny that the price tag for locality has been rising since Bell . But I negociated with my bank and they are willing to let me have my loan

Yup. Of course, if you think theories should be based on experiment, then Newton doesn't look like such a good option compared to GR. But you're right that from a purely theoretical point of view, there's no *need* for Lorentz invariance in a Lorentz ether type theory. It's just some weird emergent behavior or some property of the laws that for all we know could have been different.

I understand that. But things are nicer when they are evident from the structure, than when you have to impose them (ok, I already know your reply: you prefer to pay this price than the price I negociated with my bank )

Yes, I agree. In fact, I'd say that long before we get to quantum gravity. The de Broglie - Bohm theory, orthodox QM, and MWI, are, I think, 3 very different theories. They make radically different claims about how the world really works. But, alas, it is difficult to distinguish them empirically.

Of course, they are totally different theories "as of the workings of the world" but NR QM and Bohm are empirically *indistinguishable*, so that's why I called it diffferent interpretations (pictures of the world) of identical theories (things that make numerical predictions of dials in the lab).
However, once we come to the gravity part, there will be of course genuine differences in the theoretical predictions of outcomes of experiments ; only we don't know how to do these experiments (we don't have the technology).

 

[ttn]

The wave function contains what's known about what it refers to. It would be an unfounded leap of faith to say that it's a complete description.

Fine, so you deny completeness. OK, good, I also think it's a ridiculous leap of faith to believe it.

And of course experiments always have definite outcomes. The probabiltiy interpretation of quantum theory is the most widely accepted because it makes the most sense. Wave function collapse happens in imaginary space. It doesn't necessarily follow that what is happening experimentally is a violation of locality in nature.

Yes, it does.

One can believe that the wave function alone is an incomplete description of physical reality, while also believing in the impossibility of hidden variable (ie., a separable formulation) theories that could match all of qm's quantitative predictions -- because to do this, the hidden variable theory would presumably have to provide a more complete description of the creation and evolution of the individual components of entangled pairs than quantum theory allows.

This makes me think you don't know what "hidden variables" means. If the wave function isn't a complete description, you'll need some additional variables to characterize the states of particles completely. Those are hidden variables.

That is, I can believe in the essential truth of the principles (and the limits they impose), and the continued efficacy of quantum theory while also believing that the theory isn't a complete description of physical reality.

Sure, the QM predictions can be right. That has nothing to do with completeness. See Bohm's theory.

That qm has accurately predicted the average results of any set of quantum measurements, and that the individual measurement outcomes exist in definite, qualitative, verifiable macroscopic states, isn't in dispute.
These can be taken as matters of fact.

Vanesch disputes them, for example.

I think you'll need more than what you've offered so far to convincingly support your conclusion that nonlocality is a fact of nature.

Well, I don't know what you're missing. No theory respecting Bell Locality can agree with the QM predictions. So if the QM predictions are right, nature violates Bell Locality. What part of that is inadequate?

 

[DrChinese]

See, e.g., quant-ph/0408105 for a recent discussion.

Yes, this is a good reference to the complexity of both the current state of things and some of the related history. This makes a lot of our posts clearer to me because there is definitely a lot of opinions on both sides of nearly every version of the logic expressed. It comes as no surprise then that nearly anyone who reads this will recognize their view somewhere in this paper.

Here is a link to a copy: http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai:arXiv.org:quant-ph/0408105

You don't need to agree with everything said to appreciate how much confusion is out there over what to conclude from EPR+Bell in terms of: a) are hidden variables still viable; and b) is QM non-local; and c) what is a definition of Bell Locality.

 

[Sherlock]

Vanesch disputes them, for example.

I'm thinking of the "definite outcomes" of individual measurements as referring to what is observed, and what is observed is either detection or nondetection wrt any given coincidence interval. Is this ok, or is there some other meaning of "definite outcomes" that's being used here?

No theory respecting Bell Locality can agree with the QM predictions. So if the QM predictions are right, nature violates Bell Locality. What part of that is inadequate?

The inadequate part is the notion that the locality assumption is what's being tested, that it's the key assumption in lhv formulations. But the key assumption is that the specification of some common hidden parameter or set of parameters (perhaps varying from pair to pair) is sufficient to mimic or perhaps even improve on qm predictions. Obviously, this isn't true for all cases, in particular the case of entangled particles. Now, one might think that it might still be conjectured that if the separate evolutions of, eg.,entangled particles could be described in sufficient detail, then an lhv theory would be possible. But the principles of quantum theory prohibit such a description. So, insofar as qm predictions are accurate, and therefore that quantum theory's principles are supported and held, then lhv theories (at least those pertaining to entangled particles) are, *in principle* excluded from consideration. But *not* because locality has been 'violated'. And since the principle of locality still holds, then nonlocal (deBroglie-Bohm) theories are excluded from consideration. MWI theories are excluded because there's no need to 'save' locality in the first place, and anyway because they're nonsensical.

Bell locality entails describing the separate (hidden variable) evolutions of the individual particles, A and B. The problem for the hidden variable formulation has to do with *limitations* on describing these separate evolutions. Presumably, if you had all of this information, then describing the joint results of entangled particles in a separable (Bell local) form would be possible. The qm prohibition on getting the information required to do a sufficiently complete hidden variable description of individual particles has nothing to do with whether or not nature is local or nonlocal. So, an experimental violation of a separable formulation of entangled particles (ie., an experimental violation of Bell locality) doesn't reveal nonlocality in nature. Rather it reveals that the hidden variables used are an insufficient description of the individual evolutions of the entangled particles.

In other words, the individual quanta in Bell type experiments can't, even in principle, be tracked sufficiently to make a separable formulation viable. This has to do with limitations intrinsic to any quantum measurement, rather than whether or not there is anything nonlocal happening.

Maybe there is something nonlocal happening, but it can't be deduced from Bell's theorem or Bell type experiments or quantum theory. So the assumption of locality remains -- jostled a bit, but so far undamaged.

 

[ttn]

I'm thinking of the "definite outcomes" of individual measurements as referring to what is observed, and what is observed is either detection or nondetection wrt any given coincidence interval. Is this ok, or is there some other meaning of "definite outcomes" that's being used here?

No, that's what is meant. None of us would waste our time talking about this, except that those crazy MWI people think maybe it's false. But I'm with you: it's very crazy to think this is false.

And since the principle of locality still holds, then nonlocal (deBroglie-Bohm) theories are excluded from consideration. MWI theories are excluded because there's no need to 'save' locality in the first place, and anyway because they're nonsensical.

If "the principle of locality still holds" maybe you could provide an example of a local theory which makes the same predictions as QM (which is *not* a local theory) for the standard EPR-Bohm/Bell situation.

So, an experimental violation of a separable formulation of entangled particles (ie., an experimental violation of Bell locality) doesn't reveal nonlocality in nature. Rather it reveals that the hidden variables used are an insufficient description of the individual evolutions of the entangled particles.

You haven't understood Bell's theorem. It is not based on some particular model of local hv's. It is very general. It assumes precisely the type of hv's that have to exist if locality is going to be true (given the EPR correlations). So if the inequality is violated, if the QM predictions are correct, locality is refuted. That's it.

 

[vanesch]

No, that's what is meant. None of us would waste our time talking about this, except that those crazy MWI people think maybe it's false. But I'm with you: it's very crazy to think this is false.

I agree with you that it is crazy, but it is the only way to save the relativity principle and a few other principles from which about all currently known laws are DERIVED. If you do away with it, then it is strange that these principles are fundamentally FALSE, but that a lot of their consequences turn out to be true - although now they have to be plugged in ad hoc.
From the general covariance principle (the basis of GR) follows all of relativity ; amongst it, the Lorentz transformations, and all gravity effects. Well, if you do not accept the "crazyness", then the general covariance principle is wrong, but nevertheless, the Lorentz transformations and all gravity effects have to be plugged in *as if the general covariance principle were true*.
This is of course not impossible, but hard to swallow. To me, this is similar to saying that planets move AS IF Newtonian gravity were true, with the 1/r^2 forces and so on, but IN FACT angels are pushing them in exactly that way. So in practice, we can calculate the motions with the 1/r^2 laws, but let us not forget that *in reality* angels are pushing them.
Or, that intelligent design is true. Only, creatures were created and destroyed in such a way, that it is AS IF natural selection were true, and for all practical purposes, we can pretend that natural selection works, only, let us not forget, DNA and mutations have nothing to do with it: bacteria grow resistance to antibiotics because the creator decides so, not because of any biological mechanism such as natural selection ; although it will behave in exactly the same way.
This is not impossible but hard to take. Why would an underlying principle from which we can derive many laws be false, but nature would pretend it to be true in all of its consequences ?
The only hope, I'd say, is that we discover another underlying principle which generates exactly the same consequences. In that case, we can maybe give up on the crazy MWI idea. As you pointed out already, MWI DOES HAVE a serious problem with GR ; but at least, this is recognized. That's what quantum gravity is all about. So we KNOW that there is a fundamental difficulty there, and we are looking on how to get out of it. So OR the MWI idea can be reconciled with a version of quantum gravity (in which the quantum aspect remains strictly unitary) OR we will find WHERE the MWI idea goes wrong, and we will find a totally new theory of which GR and (MWI) QM are limiting cases - in this case, the "crazy" idea might not be necessary anymore and it was just an extrapolation of a limiting case of the true theory, which we called unitary quantum mechanics.
Bohmians on the other hand, pretend that there IS no difficulty, but that locality is not true (hence shooting down the basic principle of relativity) WITHOUT REPLACING IT with another principle from which we can naturally derive things such as the Lorentz transformation. As such, ALL the consequences of relativity have to be PLUGGED IN BY HAND ONE BY ONE. I find this a step backward. We HAD a principle from which to derive them, and now we don't anymore. They have to do the same thing with quantum field theory. Many things which follow rather naturally from QFT now have to be plugged in BY HAND. Although all this is not impossible, I find this very "ugly".

 

[ttn]

I agree with you that it is crazy,

(Using George Costanza's memorable tone:) Ah -- HAAHHH!

but it is the only way to save the relativity principle and a few other principles from which about all currently known laws are DERIVED. If you do away with it, then it is strange that these principles are fundamentally FALSE, but that a lot of their consequences turn out to be true - although now they have to be plugged in ad hoc.

I know, we've been over this before. I just don't think it's such a big deal that some principle which has served well turns out not to be fundamental (but rather emergent from something deeper). The ideal gas law turned out to be only an approximation true in a certain range. No biggie. F=ma and the inverse square gravitational force are only approximations to some deeper more general principles, even though they basically drove physics and astronomy forward for 200 years. And so forth. I know, I know, you'll say: but this time we don't have anything to *replace* the principles with. When we gave up Newton's 1/r^2 force, we replaced it with GR, which reduces to 1/r^2 in a certain limit. Now we're giving up fundamental lorentz invariance and replacing it with nothing! Yup, that's true. But what can I say? I'm far more comfortable doing that and waiting to see what might happen tomorrow, than I am going into all this crazy solipsist many words craziness. Did I mention it was crazy?

This is not impossible but hard to take. Why would an underlying principle from which we can derive many laws be false, but nature would pretend it to be true in all of its consequences ?

You could ask that about Newton's 1/r^2 gravity law too. And it'd be a good question up until the point where there was real empirical evidence that the law just wasn't true universally. So it had to be given up -- whether or not there was anything to replace it (at that particular moment in history).

Bohmians on the other hand, pretend that there IS no difficulty, but that locality is not true (hence shooting down the basic principle of relativity)

It's not a matter of pretending there is not difficulty. There isn't one -- there really isn't. ...so long as you are willing to let go of locality.

WITHOUT REPLACING IT with another principle from which we can naturally derive things such as the Lorentz transformation. As such, ALL the consequences of relativity have to be PLUGGED IN BY HAND ONE BY ONE. I find this a step backward. We HAD a principle from which to derive them, and now we don't anymore. They have to do the same thing with quantum field theory. Many things which follow rather naturally from QFT now have to be plugged in BY HAND. Although all this is not impossible, I find this very "ugly".

Ah, but look at the kind of thing MWI has to plug in BY HAND -- experiments have definite outcomes, people experience a reasonable looking reality that is never in macroscopic superpositions, etc. On its face, MWI predicts that none of these things are true, and so you have to put in "by hand" all of this ridiculous stuff about consciousness to make it consistent with basic experience.

 

[vanesch]

I know, I know, you'll say: but this time we don't have anything to *replace* the principles with.

We seem to know pretty well of one another what the other will say

When we gave up Newton's 1/r^2 force, we replaced it with GR, which reduces to 1/r^2 in a certain limit. Now we're giving up fundamental lorentz invariance and replacing it with nothing! Yup, that's true. But what can I say? I'm far more comfortable doing that and waiting to see what might happen tomorrow, than I am going into all this crazy solipsist many words craziness. Did I mention it was crazy?

Oh, but that's exactly MY point of view: I don't mind taking on a crazy idea, which fits with the principles we have today, waiting to see what will happen tomorrow, and hope I'll be able to toss it. The problem is, you don't *wait* for something, because you don't have a problem to solve ! And this time, I don't think we can wait for the empirical evidence

Ah, but look at the kind of thing MWI has to plug in BY HAND -- experiments have definite outcomes, people experience a reasonable looking reality that is never in macroscopic superpositions, etc. On its face, MWI predicts that none of these things are true, and so you have to put in "by hand" all of this ridiculous stuff about consciousness to make it consistent with basic experience.

In fact, I got more seduced by MWI because you DIDN'T have to plug in a physical process by hand. Everything follows from some very general principles: the superposition principle, and invariance under Lorentz transformations. You have to add only very little to that to get where we are today. When you look at the formalism of quantum theory, then you almost *automatically* find that the bodies of Joe and Jack end up in superpositions. It is only because we don't observe that that we have to think of what could be the relationship between this prediction and observation, noticing that philosophers had such questions already since a long time. (ok, the other stance is that a theory that makes such a crazy prediction that Jack's body is at the same time in the grocery store and in a jet fighter, is blatantly wrong, I know, I know ... ).
It is actually in orthodox Copenhagen QM that one introduces a few extra things ad hoc. MWI is much, much closer to the spirit of the formalism of QM.
I think we both agree that the current state of physics is not the final one ; in that case it is probably just a matter of personal taste of to what one gives priority: a rather intuitively acceptable theory, but which butches up the basic principles on which the current formalism is based, or a totally crazy theory which tries to get as close to the formalism as it can.

 

[DrChinese]

It is actually in orthodox Copenhagen QM that one introduces a few extra things ad hoc.

I was content letting a Bohmian and an MWIer go after it with each other, but now you're lobbed one my way!

 

[Sherlock]

Note: My statements below should be taken as tentative, or better, as questions (even though they're not all formed as questions). I don't feel as though I necessarily 'understand' everything involved, so any corrections are appreciated. My current understanding is that Bell's analysis and Bell tests have pretty much disallowed local hidden variable theories, but that it is the consideration of hidden variables, and not the consideration of locality itself, that is essential to the disallowance of these sorts formal expressions wrt certain quantum states.

If "the principle of locality still holds" maybe you could provide an example of a local theory which makes the same predictions as QM (which is *not* a local theory) for the standard EPR-Bohm/Bell situation.

I've followed your reasoning (at least, I think I understand it) wrt your conclusion that qm is a nonlocal theory. I don't think it's quite correct to conclude that. The qm evolutions and wave function 'collapse' are happening in an imaginary space (for lack of knowledge of what is happening in reality), and no pretense is made (at least the way I'm learning quantum theory) about this being in 1-1 correspondence with the evolutions of quanta in the real three-dimensional world. So, what does any expansion or superposition or whatever tell you about exactly what's happening in reality? Well, I don't know. Do you? Does anyone? It seems like a pretty good bet that there's some sort of wave activity amenable to a wave mechanical description happening, but beyond that the particulars aren't exactly clear. So I don't think it can be justifiably concluded, from an examination of formal quantum theory alone, that qm is necessarily a nonlocal theory (in any sense that the term, 'nonlocal', has anything necessarily to do with nature).


Which brings us to the results of experiments and their interpretation. Can it be concluded from any of this that nature is nonlocal. My current answer is that it can't.

You haven't understood Bell's theorem. It is not based on some particular model of local hv's. It is very general. It assumes precisely the type of hv's that have to exist if locality is going to be true (given the EPR correlations). So if the inequality is violated, if the QM predictions are correct, locality is refuted. That's it.

Or maybe it's that if the inequality is violated, and if the qm predictions are correct, then the local hidden variable expression is refuted, but not locality itself. As you read through my comments, you'll hopefully get some idea why I think that locality isn't the essential consideration. And if this orientation is indeed wrong, then, also hopefully, you'll be able to tell me exactly where I'm erring.


The general lhv formulation is characterized by the factorizability of a joint (AB) state into its components A and B.


The factorizable form is incompatible with (gives different predictions for most joint settings of the analyzers) qm.


Bell tests provide a quantitative measure of the viability of this general lhv formulation and the qm formulation.


The tests support qm.


Assuming that nature is local, it can be concluded that the factorizable formulation lacks the specific information that would, conceivably, make it viable.


In the case of entangled particles, one might need a *complete* specification of the evolutionary histories of particles A and B in order to make accurate predictions using the factorizable form.


But, according to quantum theory, this is impossible. There are constraints on what we can know. So, it can be further concluded that the factorizable formulation is, in principle, not viable wrt certain quantum correlations.


In all of this, the assumptions that qm is an incomplete description of physical reality (after all, qm can't predict the results of individual measurements at A or B, or the results of individual joint, AB, measurements) and that nature is local still hold.


Nature seems to require a respect for the principle of locality, while at the same time making it impossible to develop a theory of quantum correlations that is explicitly Bell local.


This doesn't seem paradoxical to me.


Below are some excerpts from the paper, "EPR and Bell Locality", in quotations and italicized, wrt which I comment:


"In the case of the (reformulated) EPR argument, the relevant theory is the orthodox interpretation of quantum mechanics, according to which the wave function alone is regarded as providing a complete description of physical reality. We may thus state the upshot of the argument as follows: if you maintain that QM is complete (and that its empirical predictions are correct) you are forced to concede that the theory violates Bell Locality. Thus, the completeness assumption entails the failure of Bell Locality."


The interpretation of qm that I've learned says that the wave function contains what's known about the quantum system, not that it's a complete description of the physical reality of the quantum system. Thus, the incompleteness assumption allows us to conclude nothing about the locality or nonlocality of nature wrt the correlations that are examined.
------------------------


"Bell’s Theorem, on the other hand, tells us that a certain type of local hidden variable theory cannot agree with experiment – or, equivalently, the only way a hidden variable theory (i.e., a theory in which the wave function alone is regarded as an incomplete description of physical reality) can be made to agree with experiment is to violate the Bell Locality condition.
Combining these two arguments forces us to conclude (without qualification, for surely QM either is or is notcomplete) that Bell Locality fails."


Bell local formulations fail wrt certain (nonseparable) qm states. Is this because nature is nonlocal, or because the information required to adequately describe the states in factorizable form is unattainable (or at least so far unattained) ?
-------------------------


"Mermin is, strictly speaking, correct when he says: “to those for whom nonlocality is anathema, Bell’s Theorem finally spells the death of the hidden-variables program.” But he seems to have forgotten that, to those same people (for whom nonlocality is anathema), the EPR argument spells the death of the non-hidden-variables program – i.e., the orthodox interpretation of QM which upholds the completeness doctrine. For orthodox QM itself violates Bell Locality, the same locality condition that empirically-viable hidden-variable theories must, according to Bell’s Theorem, violate."


Nonlocality isn't anathema for me. It just can't be necessarily inferred from anything that's been observed or any analysis yet.


QM doesn't violate Bell locality in any sense that can be considered necessarily physically meaningful, and neither do empirically-viable hidden-variable theories. QM is an incomplete description of physical reality. And, assuming that nature is local, empirically-viable hidden-variable theories are just incorrect descriptions of physical reality, even though they can be constructed to give accurate empirical predictions.


Mermin is correct, and I don't think he forgot anything. In a universe where the speed of light is a limiting factor wrt any and all physical interactions, processes, transmissions, etc., and where the principles of quantum theory are essentially correct, then the hidden variables program is a lost cause.
--------------------------


"The choice between orthodox QM and hidden variables theories is thus not a choice between a local theory and a nonlocal theory; it is a choice between two non-local theories, two theories that violate Bell Locality. What Bell’s Theorem (combined with the reformulated EPR argument) spells the death of is thus the principle of Bell Locality – nothing more and nothing less. People “for whom [such] nonlocality is anathema” are therefore simply out of luck."


The choice between qm and lhv's is a choice between, as far as is known, two local theories. QM assumes a common emitter and a common measurement operator, and from that it's calculational principles of superposition and expansion can be applied. Nothing nonlocal is assumed or evident wrt the execution of qm procedures. That it isn't known exactly why qm works as well as it does is not evidence for, or a reason for positing the existence of, nonlocal transmissions.


LHV's assume that sufficient information regarding the evolutionary histories of A and B is attainable. The, thus far, falsification of this assumption is not evidence for, or a reason for positing the existence of, nonlocal transmissions. Rather, it can be understood in terms of the limits on what can be known wrt quantum phenomena.


That a nonlocal hidden variable theory can be constructed which mimics the predictions of qm is not evidence for, or a reason for positing the existence of, nonlocal transmissions.

-----------------------------


"This should clarify exactly why Bell understood his theorem not as ruling out the hidden-variables program, but rather as evidencing a deep conflict between the predictions of quantum theory as such, in any interpretation, and the locality principle suggested by relativity."


Could it be that Bell was wrong about that ? If Bell's theorem and Bell tests don't necessarily discern nonlocality in nature, then Bell interpreted the meaning of his theorem incompletely. Could it be that, in a universe governed by the principle of locality, the incompatibility between qm and lhv's is due to the unattainability, in (qm) principle, of the information required to make lhv's empirically viable wrt the sort quantum states Bell was considering ? If so, even if it's only just a possibility, then this obviates the considerations and inferences regarding nonlocality in nature due to Bell issues.

 

[vanesch]

I was content letting a Bohmian and an MWIer go after it with each other, but now you're lobbed one my way!

Well, we agreed that whichever of us is right, that's in any case better than Copenhagen

The problem with Copenhagen is of course that there is this projection postulate which is 1) considered as a physical mechanism and 2) is totally non-local (it affects the states of all subsystems at a constant-time plane which is strictly spacelike)
This is not less non-local (as a theoretical mechanism) than the non-local quantum potential in Bohmian mechanics, but moreover there is no clear prescription of what exactly is a "measurement" (what physical mechanism counts as measurement). So as much as this projection is considered a physical mechanism, the principle of relativity is out.

Bohm is just as non-local in its theoretical prescription, but has at least that advantage that there is no "special mechanism" that accounts for a "measurement", apart from all known interactions. But relativity goes down the drain.

MWI at least is totally local in its prescription, but still suffers from this ambiguity of what exactly is a "measurement" (which is considered something associated to a consciousness). This makes it crazy and unreal. However, it is the ONLY way to reconsile the principle of relativity as we know it (the principle!) with the predictions of QM.

 

[selfAdjoint]

The problem with Copenhagen is of course that there is this projection postulate which is 1) considered as a physical mechanism and 2) is totally non-local (it affects the states of all subsystems at a constant-time plane which is strictly spacelike)

It only does this IF you consider it to be physical. Your whole approach leading to your enthusiasm for MWI is based on reifying the wave function as a thing that can be tracked. But it doesn't have to be given that status. I am aware of the weakness of the Information Interpretation, but that's just a matter of contingent technology. I'm willing to bet the wave function at the end of the day is more like a "bit" than an "it".

 

[ttn]

It honly does this IF you consider it to be physical. Your whole approach leading to your enthusiasm for MWI is based on reifying the wave function as a thing that can be tracked. But it doesn't have to be given that status. I am aware of the weakness of the Information Interpretation, but that's just a matter of contigent technology. I'm willing to bet the wave function at the end of the day is more like a "bit" than an "it".

Let me just note that this excellent point is, in essence, the same one made by EPR so long ago. If you don't take the collapse postulate as describing a real physical change in the state of something, that means the real physical state can be the same for two different wave functions (pre- and post-collapse). And that means there isn't a one-to-one correspondence between wave functions and actual physical states. And that is just another way (Einstein's way, actually) of saying that the wave function doesn't provide a complete description of those actual physical states.

And the problem with trying to elude the apparent non-locality associated with wf collapse by denying the completeness doctrine, is that, well, it doesn't work. You can drop the completeness doctrine and hence no longer think of wf collapse as a real physical process. But then whatever theory you put in oQM's place will have to be nonlocal if it is going to agree with experiment.

This is all precisely why J.S. Bell believed his theorem (combined with the old EPR point that OQM, considered complete, entails nonlocality) proved that *nature* (and not just some class of theories) was nonlocal.

But now I'm repeating something I've said here a gazillion times... And nobody seems able or willing to believe me... Sigh... poor old me...

 

[DrChinese]

Well, we agreed that whichever of us is right, that's in any case better than Copenhagen

The problem with Copenhagen is of course that there is this projection postulate which is 1) considered as a physical mechanism and 2) is totally non-local (it affects the states of all subsystems at a constant-time plane which is strictly spacelike)

This is not less non-local (as a theoretical mechanism) than the non-local quantum potential in Bohmian mechanics...

I don't disagree that the PP (projection postulate) seems a bit strange and to some extent a bit arbitrary. Not sure why that should be a serious negative if it works, but in general I understand and accept the criticism.

But I don't know if I agree that it is non-local in the normal sense of the word. There has been plenty of philosophical discussion of that exact point. I do not think it beneficial to try and repeat that here.

I have always thought that the Bell Locality definition was intended to get around this in a way in which it was clear that the PP did NOT violate Bell Locality per se. In other words, Bell Locality is violated when a specific effect occurs outside of the cause's light cone. That doesn't happen with the PP because there is not any specific effect. For instance, we agree that there is no change in what is observed by Alice as a result of a change in setting by Bob. Only an observer who sees both Alice *and* Bob sees anything different.

The PP isn't really non-local, anyway. It is backwards in time, not exactly the same thing. It is "AS IF" (not being literal here, just pointing out how your perspective can change according to your description):

a) When we first consider a particle in a superposition, it has no specific eigenstate and it is waiting to have that filled in;
b) When you later measure that particle, you determine the eigenstate and project its current eigenvalue to the past;
c) Subsequent observations will be consistent with this knowledge.

This applies to systems of one or many particles.

Now of course there are perspectives in which the PP seems non-local too. EPR entanglement being one. So I am really saying that it comes back to your perspective, and there is plenty of debate on all sides.

If you asked a group of physicists: you might find that most believe oQM is non-local; but they might not agree that this position has been proven and is generally accepted. Hey, that might even be my view.

 

[vanesch]

It only does this IF you consider it to be physical. Your whole approach leading to your enthusiasm for MWI is based on reifying the wave function as a thing that can be tracked. But it doesn't have to be given that status. I am aware of the weakness of the Information Interpretation, but that's just a matter of contingent technology. I'm willing to bet the wave function at the end of the day is more like a "bit" than an "it".

I agree with this. I always insisted that MWI is the way to make a story around quantum theory as we know it today, and *within that theory* there's only the wavefunction that represents the physical state of the world - the purely epistemological viewpoint that the wavefunction is just a way of writing down our *knowledge* of the world is, in my opinion, "too easy a way out", because in that case you deny your theory to describe any reality at all, but just a way of organizing what you know (of what ?). But it could of course very well be that an underlying theory with a totally different description of nature will explain us one day why the wavefunction does describe our knowledge without being a state description. However, as long as we don't have that theory, we'll have to take this as part of the ontology of the world, and I'm just trying to make a consistent picture out of that view - temporary as it may be.

cheers,
Patrick.

 

[selfAdjoint]

in that case you deny your theory to describe any reality at all, but just a way of organizing what you know (of what ?).

And I agree with this. It's not that quantum mechanics is incomplete, it's that it just doesn't address ontological questions. And why should it? Maxwell's equations describe waves but not what they're "waving in". Newton made the point: "Hypothese non fingo". To try to shortcut this situation and make physics "be" ontology leads to taking science fiction ideas seriously; parallel worlds, time travel, there's not a piece of bafflegab that isn't in somebody's interpretation. Reification is a dangerous road for physicists; mathematicians aren't tempted.

 

[ttn]

And I agree with this. It's not that quantum mechanics is incomplete, it's that it just doesn't address ontological questions. And why should it? Maxwell's equations describe waves but not what they're "waving in". Newton made the point: "Hypothese non fingo". To try to shortcut this situation and make physics "be" ontology leads to taking science fiction ideas seriously; parallel worlds, time travel, there's not a piece of bafflegab that isn't in somebody's interpretation. Reification is a dangerous road for physicists; mathematicians aren't tempted.

But you make it sound like the argument for something like nature's non-locality is simply that this has been "read off" from a particular theory. It's certainly not just because the collapse postulate in OQM "looks nonlocal" that I think we can say that nature violates Bell Locality. That would be a very bad argument, because it would rest on exactly the error you're pointing out here: namely, one shouldn't take theories seriously willy-nilly. One shouldn't accept that what a certain theory says is true, is true, without having *extremely* strong reasons to believe it. And I agree that we definitely don't have such strong reasons for, say, accepting the completeness doctrine (which is what converts the apparent non-locality associated with the collapse postulate into a real physical non-locality). So the fact that OQM has this collapse postulate -- this fact alone -- is *not* sufficient reason to think that *nature* is nonlocal.
But that isn't the argument I'm making. It's mostly because of Bell's Theorem that we know that nature is nonlocal. And this theorem does *not* say: "Here's a theory I just made up; it's nonlocal; therefore, since my theory is probably right, nature is nonlocal." That just isn't the argument at all. Bell's theorem is cool because it's *general* -- it's not even about any particular theory, but about a whole broad class of theories (namely all of those which respect Bell Locality).
So... while I agree with you that one should be careful about reifying dubious theories, I don't agree that this is a valid reason for keeping an open mind about something like non-locality.

 

[selfAdjoint]

It's mostly because of Bell's Theorem that we know that nature is nonlocal.

I am just not "in" your arguments about nonlocality. It seems to me just a semantic difference. As you agreed before, you have a tendency to say "nature is nonlocal", when you mean our best theories and experiments violate "Bell nonlocality" which turns out to mean (correct me) that the Bell inequalities for separated events are violated. That is, after the fact data, collected by local means show a violation. If this is all you mean by "Nature is nonlocal", then it is well-known and not interesting. If it is not what you mean, you should clarify, using operational terms as much as possible.

 

[ttn]

I am just not "in" your arguments about nonlocality. It seems to me just a semantic difference. As you agreed before, you have a tendency to say "nature is nonlocal", when you mean our best theories and experiments violate "Bell nonlocality" which turns out to mean (correct me) that the Bell inequalities for separated events are violated. That is, after the fact data, collected by local means show a violation. If this is all you mean by "Nature is nonlocal", then it is well-known and not interesting. If it is not what you mean, you should clarify, using operational terms as much as possible.

No, violating Bell Locality does not just mean that Bell's inequalities are violated. Bell's inequalities are derived from several assumptions, notably Bell Locality and the assumption that there exist a certain kind of local deterministic hidden variables.

I've defined Bell Locality several times here in the last couple weeks. I'll just refer you to Bell's extended discussion of this in his beautiful article "La Nouvelle Cuisine" if what I said slipped through or you want more details. But suffice it to say that Bell Locality is Bell's attempt to get at the heart of what we mean when we say things like "relativity prohibits superluminal causation". Bell Locality is Bell's attempt to translate that prose phrase into a precise mathematical condition. So I think it is extremely profound to discover that it is violated in nature. This means basically that relativity is wrong! So not at all mere semantics.

Another point that I didn't make sufficiently clear before. There are a few people who think that Bell Locality is somehow the wrong condition, that it isn't at all equivalent to what relativity is supposed to require. But these people are a vast *minority*. I know this because it's well documented that the vast *majority* of people think that Bell's Theorem is important. They usually say that it's important because it proved that "local realism" (or "the EPR program" or...) is untenable. But to whatever extent a person thinks Bell's Theorem is interesting or important, that person tacitly accpets Bell Locality as an appropriate and important test of the genuine "local-ness" of a theory.

In short: the people who applaud Bell for snuffing out the hidden variables program, yet retreat to Orthodox QM as an acceptable theory, are engaged in a deadly contradiction. You can't have it both ways. If Bell Locality really is what relativity requires, then both OQM and hidden variable theories are going to have to be rejected as inconsistent with relativity (or, we'll have to junk relativity). On the other hand, if it's OK for orthodox QM to violate Bell Locality, then it's OK for hidden variable theories to violate it as well. In which case Bell's Theorem wouldn't rule out local hidden variable theories at all, and would cease to be interesting. All I'm suggesting is that we not tolerate double standards. Anyone who rejects (say) Bohm's theory because it violates Bell Locality, ought also to reject OQM on those same grounds. And vice versa, of course.

 

[vanesch]

And I agree with this. It's not that quantum mechanics is incomplete, it's that it just doesn't address ontological questions. And why should it?

At the end of the day, it should. After all, we identify, in the lab, certain things with certain mathematical entities. This very identification is somehow ontological up to a certain level. Of course, this identification is only partial, and usually very approximative, but nevertheless, we associate a mathematical entity in our theory with a certain physical object "out there". If we do not do that, we aren't doing physics and there is no way for us to "verify experimentally" our theory. At some level, some identification between the mathematical entities in our theory (or at least, some of them) and "things out there" must be made if we are to have a theory with claims to be a physical theory, making predictions of the world.
As such, a purely epistemological viewpoint is not really tenable IMHO, because it doesn't tell us what we should know things of. What does that voltmeter I'm staring at in the lab has to do with some abstract theory ? If my abstract theory says 15V and I see the digits 2 and 3 on the screen, why on Earth would that invalidate my epistemological theory ? Maybe I just didn't interpret it well, and the 15 I get out of my epistemological theory shouldn't be read on the display of the voltmeter, but, I don't know, on the clock under my TV set or something. Where does the association between "voltmeter reading" and "number coming out of my theory" come from ? That only makes sense if we assign some ontology to this situation. So something in my theory must CORRESPOND to the real world out there (this correspondence may be erroneous, of course, because my theory is not perfect). When you can associate *this* variable in my theory with *that reading on that instrument* you've made an ontological assignment of the variable to something "out there". I don't see how you can make ANY supposition of "physical principles" if it doesn't apply to a mathematical object that has been assigned to some "reality".
Now, I'm the first one to say that probably we make errors and our theories are not the "final" ones. As such, the descriptive value of our theories is only very relative. But you should make such an assignment. You cannot hide and say that, well, after all, all those mathematical objects simply don't correspond to anything out there, but they DO correspond to the right quantities I measure. Because that's using double language: in order for them to associate to experimental quantities, you HAVE to make the link, while denying it.
When looking at quantum theory, there's only one object that makes sense (all is relative) to "map" upon a "reality" and that's the wave function. Now, I can very well accept (I even am profoundly convinced!) THAT THIS IS PROBABLY TOTALLY WRONG on a fundamental level. But we don't have anything else, and *IF* we are going to use quantum mechanics, we cannot do but make such an assignment. And who knows, maybe it is even correct!

Reification is a dangerous road for physicists; mathematicians aren't tempted.

I thought I was doing the opposite: I'm just proposing a (probably totally wrong) ontological picture that fits to a theory. I would rather think that reifying happens when you say: this is fundamentally correct, but there is no real world out there, just my knowledge, which somehow is predicted by these magical rules.
To take your example of Maxwell equations. Of course it was silly to look after the material in which the EM fields are wobbling. But nevertheless, I think that everybody agrees that there is a real EM field out there (and that that is what you're thinking about when you do classical EM). Nobody is claiming - I presume - that those E and B fields "don't really exist but tell us something about what we know about moving charges" and somehow "magically" let us calculate how other charges move, far away. You usually picture an EM pulse as something physical, traveling from A to B, and you're not surprised about the "magic" of electrons in my eyes moving around about 8 minutes after some charges moved at the surface of the sun, where the EM field was "only a mathematical tool to organize our calculations of how charges interact".