A Paradox: Do LHV Theories Need the HUP?

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ttn said:
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.
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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

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ttn said:
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" :smile: 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 :smile:. 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 truely 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

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Sherlock said:
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

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vanesch said:
..... 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 :smile:. 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 truely 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. =)
 
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ttn said:
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.
ttn said:
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.
ttn said:
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.
 
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vanesch

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ttn said:
Yes, well, no need to re-hash all this well-treaded ground.
Yes, when typing this, I had a feeling of deja-vu :smile:
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 :smile:. But I negociated with my bank and they are willing to let me have my loan :rofl:

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 :smile:)

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

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Sherlock said:
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

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ttn said:
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 [Broken]

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.
 
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ttn said:
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?
ttn said:
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.
 
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ttn

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Sherlock said:
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

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ttn said:
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

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vanesch said:
I agree with you that it is crazy,
(Using George Costanza's memorable tone:) Ah -- HAAHHH!!!! :smile:



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

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ttn said:
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 :approve: :smile:
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 :frown:
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 ... :rofl: :smile: :smile: ).
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

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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! :rofl:
 
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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.

ttn said:
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.


ttn said:
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.
 
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vanesch

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DrChinese said:
I was content letting a Bohmian and an MWIer go after it with each other, but now you're lobbed one my way! :rofl:
Well, we agreed that whichever of us is right, that's in any case better than Copenhagen :rofl:

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

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vanesch said:
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".
 
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ttn

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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

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

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. :wink:
 

vanesch

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selfAdjoint said:
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

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vanesch said:
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

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selfAdjoint said:
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

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ttn said:
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

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selfAdjoint said:
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

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selfAdjoint said:
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, travelling 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".
 

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