What is the wave function about?


by bohm2
Tags: function, wave
Demystifier
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Oct4-11, 09:42 AM
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Quote Quote by ThomasT View Post
But then there's BM's nonlocality.
And then there is the Bell theorem saying that any hidden variable theory (compatible with QM) MUST be nonlocal.
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Oct4-11, 09:52 AM
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Quote Quote by wuliheron View Post
For that matter viewing physics as the "science of long shots" doesn't look particularly rewarding either. After 85 years of producing nothing useful Bohmian mechanics are about as big a long shot as they get.
Quote Quote by wuliheron View Post
Being more efficient in some cases without making any new predictions just isn't terribly useful. I'm sure we could say the same thing about any number of other theories including phlogiston theory. It needs to prove itself uniquely useful in some significant way.
First you indicate that you would be satisfied with something useful. Then, when I show that there is something useful you want terribly useful, and later you want even more - uniquely useful. What will be next? Absolutely useful? Ultimatively useful?
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Oct4-11, 10:02 AM
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Quote Quote by bohm2 View Post
I have to admit, I couldn't help but enjoy the humour (and truth?) about this statement by Fuchs:

Whatever it is, it cannot be for want of a self-ordained solution: Go to any meeting, and it is like being in a holy city in great tumult. You will find all the religions with all their priests pitted in holy war—the Bohmians, the Consistent Historians, the Transactionalists, the Spontaneous Collapseans, the Einselectionists, the Contextual Objectivists, the outright Everettics, and many more beyond that. They all declare to see the light, the ultimate light. Each tells us that if we will accept their solution as our savior, then we too will see the light.But there has to be something wrong with this! If any of these priests had truly shown the light, there simply would not be the year-after-year conference. The verdict seems clear enough: If we—i.e., the set of people who might be reading this paper—really care about quantum foundations, then it behooves us as a community to ask why these meetings are happening and find a way to put a stop to them.

http://perimeterinstitute.ca/persona...VaccineQPH.pdf
To me, many interpretations give some light, but at the moment neither of them gives the light. So I think we should not stop these meetings, but we should also not think of them as a place where we will learn the final truth.
bohm2
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Oct4-11, 01:23 PM
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Quote Quote by Demystifier View Post
To me, many interpretations give some light, but at the moment neither of them gives the light. So I think we should not stop these meetings, but we should also not think of them as a place where we will learn the final truth.
I agree. But I found it funny. Interestingly this paper on that same topic is arguing the opposite of Fuchs:

Does Quantum Mechanics Need Interpretation:

Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, namely that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. If interpreting quantum mechanics means answering the question, “How can the world be for quantum mechanics to be true?”, there seems to be no way around it.

http://arxiv.org/PS_cache/arxiv/pdf/...902.3005v1.pdf
apeiron
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Oct4-11, 04:48 PM
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Quote Quote by bohm2 View Post
[I]Whatever it is, it cannot be for want of a self-ordained solution: Go to any meeting, and it is like being in a holy city in great tumult. You will find all the religions with all their priests pitted in holy war—the Bohmians, the Consistent Historians, the Transactionalists, the Spontaneous Collapseans, the Einselectionists, the Contextual Objectivists, the outright Everettics, and many more beyond that.
The Fuchs paper goes further than poking fun as it tries to diagnose the essential flaw in these interpretations. He points out that the one idea people can't seem to let go is that reality must be made of crisply existent "something" at the fundamental level. So even if these atomistic things are just probability states projected to some complex Hilbert space, they are still definite and actual in some ontological sense.

Fuchs then tries to let go of this (reductionist) axiom and describe reality from the view of its global constraints. Each observer forms a context for observation. That is what is "definite". And the world is an unbounded potential that conforms to fit.

That is a view I share in essence. But much more work has to be done on now defining the notion of an observer - generalising it away from any notion of "conscious human" and towards "the ambient constraints represented by the structuration of the universe".

Fuchs explores doing this by generalising to "general positive operator-valued measurements" (POVMs) - the more constraints applied from a locale, the more definite the world becomes.

He also employs Bayesian statistics - again a revolution in working from the constraints side of the story, the imposition of "reasonable" expectations on unbounded possibility rather than starting with atomistic, already limited, probabilities.

So the standard stance on QM interpretational issues is that the measured must be "real" at some fundamental level (even if it inhabits some weird unobservable realm like pilot waves, alternative universe branches, etc) and the measurement issue becomes a problem of simple access to this ontic truth. If we could only imagine how to make the right measurement, we would surely finally glimpse the definite things which are there just waiting to be measured.

But the switch around is taking an observer-created reality seriously (by dropping the notion of particular observers, such as conscious humans). Measurement (in some new sense, not the familiar one) is responsible for shaping up the measured, making it also now "real" - part of the realm of the classically decohered.

Need I say that this is back into Peircean semiotics, Pattee's epistemic cut, systems science, etc?

However, here Fuchs is putting forward a specific proposal as well as diagnosing the general fault in the standard reductionist paradigm that informs most QM interpretations. So that would be interesting to consider further?

For instance, I would argue that once you set off down Fuchs route, you start to have to ask the question about what makes our universe the right kind of measurement device? It is not just measurement in general that constrains QM potential but the actual structured realm which is our universe. So attention has to turn to understanding how the universe does what it does by virtue of its general organisation.

You will note how truly radical that is. Instead of the universe being a "result" (of unknown QM states acting as its definite causes), it is instead creating that which it appears to be composed of (the macro is making the micro rather than the other way round).

Again, this has nothing to do with consciousness or any other connotations commonly ascribed to "measurement" or "observer". But it is a way of modelling reality that is familiar from the philosophy of semiosis, and more recently, the field of dissipative structure theory in thermodynamics.
wuliheron
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Oct4-11, 08:09 PM
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Quote Quote by Demystifier View Post
First you indicate that you would be satisfied with something useful. Then, when I show that there is something useful you want terribly useful, and later you want even more - uniquely useful. What will be next? Absolutely useful? Ultimatively useful?
Physics isn't mysticism which I'm sure is also quite useful in limited situations. Personally, I always use a screw driver to open cans of paint, but that is not what the screw driver was designed to do and if it did not fulfill its intended purpose people might easily find something else to open their cans of paint. Again, Bohmian mechanics needs to produce unique predictions that can be verified or at least prove itself significantly more efficient overall or it will not have fulfilled its supposed purpose as a physical theory. Being able to open the occasional can of paint just isn't enough.
apeiron
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Oct4-11, 09:02 PM
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Quote Quote by wuliheron View Post
Physics isn't mysticism which I'm sure is also quite useful in limited situations. Personally, I always use a screw driver to open cans of paint, but that is not what the screw driver was designed to do and if it did not fulfill its intended purpose people might easily find something else to open their cans of paint. Again, Bohmian mechanics needs to produce unique predictions that can be verified or at least prove itself significantly more efficient overall or it will not have fulfilled its supposed purpose as a physical theory. Being able to open the occasional can of paint just isn't enough.
Sorry, but it seems clear Demystifier understands BM well enough for his support of this interpretation over others to be properly motivated. So you would need to lift your own game to the same level here.

The different interpretations do come with their different unique features - like the quantum equilibrium hypothesis of BM vs the Born rule of rival interpretations. So there are formal differences that can be discussed in terms of their reasonableness, as well as the purely pragmatic differences (such as ease of computation).

I personally think the whole BM approach is ontically "unreasonable" for reasons I just stated. But that just puts a requirement on me to learn more about BM if I want to be so sure about dismissing it.

For instance, the question of how do you square BM with special relativity and Lorentz invariance seems a pretty severe test of it as an ontology. Anyway, much more than annecdotes about screwdrivers and paint tins.
wuliheron
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Oct4-11, 09:57 PM
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What is reasonable is for philosophers, politicians, and theologians to debate. Whether you consider that "lifting your own game to the same level" or lowering it is a question of personal preference and values. Its also popular among professional wrestlers if that's what floats your boat.
ThomasT
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Oct4-11, 10:23 PM
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Quote Quote by Demystifier View Post
And then there is the Bell theorem saying that any hidden variable theory (compatible with QM) MUST be nonlocal.
Yes that's true. But that's because of the modelling constraints (per Bell's formulation) imposed by the local realism requirement. Not necessarily because nature is actually nonlocal. Local realism (per Bell) entails that a LRHV model of quantum entanglement be expressed in terms of the hidden (variable) parameter that determines photon flux at the individual detectors. But we know (or at least can reasonably infer) that the hidden parameter that determines coincidental photon flux is not a variable, that is, whatever the joint polarizer settings are measuring jointly is not varying from entangled pair to entangled pair. Couple this with a 'locality condition' that describes the statistical results at the spatially separated detectors as 'independent' (when in fact a detection at one end or the other alters and severely restricts the sample space at the other end, via the coincidence circuitry), and such a model must necessarily skew the QM expectation values regarding coincidental photon flux (whether nature is local or nonlocal) for most joint polarizer settings (even if it manages to preserve the essential angular dependency between the angular difference of the polarizer settings and the coincidental photon flux).

A fact of the matter is, and Bell showed, that local hidden variable models of individual photon flux are compatible with QM -- from which we can infer that hidden variables are determining, via local transmissions, the results at the individual detectors. The most reasonable assumption is that these hidden variables originated and were emitted (eg., in the 1982 Aspect et al. experiment) during atomic transitions -- with photons entangled in polarization being emitted in opposite directions by the same atom.

It's most reasonable to assume that what the joint polarizers are measuring is a relationship (defined by the conservation of angular momentum) between entangled photons, and that this relationship is produced during the emission process.

We can take polarizer A and put it on the side with polarizer B, and, without changing anything else about the experiment, get the same coincidental photon flux (varying from ~ .5 to ~ 0 times the photon flux at detector A, as the angular difference between the polarizers, now both on the B side, varies from 0 to 90 degrees) as with the polarizers on opposite wings of the setup. But we don't need to invoke nonlocal transmissions between the entangled photons to understand this result. We just have what amounts to a quantum polariscope on the B side, producing results via local transmissions, and unimpeded photons travelling from the emitter to detector A on the A side.

Now, when we move the (A) polarizer from the B side back to the A side, what, essentially, changes? Well, quantitatively, nothing. So why should this (original) setup require a nonlocal explanation/understanding while the one with both polarizers on the same side doesn't?

Anyway, wrt at least some ways of analyzing and interpreting Bell's theorem, it can be said that nonlocality hasn't been demonstrated. Nonlocality might be a relatively easy 'fix' that will give the correct results, but as such it isn't an explanation or understanding of quantum entanglement. And since an 'understanding' of entanglement correlations vis local transmissions and interactions, and relationships due to common causes, makes more sense to me (and isn't necessarily contradicted by Bell's theorem or standard QM) than assuming that nature is nonlocal, then the nonlocality of BM is most unappealing.

I wish it could be otherwise, because I like the general approach, and certain aspects, of BM. But if nature is exclusively local, then BM is, ultimately, just unrealistic (and necessarily contradicts a local understanding of quantum entanglement), as opposed to standard QM which is nonrealistic (and doesn't necessarily contradict a local understanding of quantum entanglement).

And the most perplexing conumdrum is that even if nature is exclusively local, then viable LRHV theories (per Bell) of quantum entanglement are still ruled out.

EDIT: I should note that the archetypal LRHV formulation produces a linear correlation between the angular difference of the polarizer settings and the coincidental photon flux. This seems to be the basis for most Bell inequalities, and would seem to explain why they're significantly violated if one takes into account that this LRHV expectation, this linear correlation, is clearly at odds with the expectation (ie., something approximating a cos2θ dependency) that the optics principles applicable to optical Bell tests indicate should be the case -- and is another consideration which suggests, to me at least, that there's a problem with formulating LRHV models of quantum entanglement which likely has nothing to do with whether nature is local or nonlocal.
skippy1729
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Oct5-11, 02:15 PM
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I have a question for Demystifier or anyone else who knows:

I know that there are theorems stating dBB will produce the same statistical results as QM. Of course, results of individual events cannot be obtained since they are determined by unknown initial conditions. The question is:

Is it possible to solve the dBB equations for some simple physical system for all possible initial conditions then use the ensemble of results to actually construct the statistics?

Any references appreciated.

Skippy
bohm2
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Oct5-11, 08:24 PM
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Quote Quote by apeiron View Post
For instance, the question of how do you square BM with special relativity and Lorentz invariance seems a pretty severe test of it as an ontology.
Do you think in 1000 years down the road assuming we haven't blown each other up, SR will still hold "true" on all scales? I'd be shocked if that was the case. I'm actually shocked that a linguistic ground chimp like us has progressed so much (or so it seems) in some areas (like physics).
apeiron
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Oct5-11, 09:08 PM
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Quote Quote by bohm2 View Post
Do you think in 1000 years down the road assuming we haven't blown each other up, SR will still hold "true" on all scales? I'd be shocked if that was the case. I'm actually shocked that a linguistic ground chimp like us has progressed so much (or so it seems) in some areas (like physics).
Yes, fine, but what reasons do you currently have to doubt SR's validity over all scales - such that you could claim it would be a legitimate surprise if we find it still to be the case in 1000 years?

I am more convinced by the argument that SR as a general relational principle is the route to a proper interpretation of QM, as for example...

http://en.wikipedia.org/wiki/Relatio...ntum_mechanics

Rovelli's approach (like the Fuch's paper you cited) are the kind of current, systems logic, explanations that make sense to me.

BM attempts to shore up a dead paradigm IMO. Time to move on.

Of course you can defend BM if that is your wish. But it would have to be done with arguments not rhetorical flourishes.

So if there is a conflict between BM and SR, then why do you say SR will have to be the one that gives way?
bohm2
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Oct6-11, 01:23 AM
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Quote Quote by apeiron View Post
So if there is a conflict between BM and SR, then why do you say SR will have to be the one that gives way?
The tension is between quantum nonlocality (not just BM) and the locality of Relativity Theory, I think. The experimental tests of Bell's inequality do suggest some form of superluminal information transfer, regardless of interpretation. Such superluminal "influences" don't mean superluminal message tranfer if one uses the Lorentzian interpretation (single preferred frame).
skippy1729
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Oct6-11, 01:57 AM
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Quote Quote by bohm2 View Post
The tension is between quantum nonlocality (not just BM) and the locality of Relativity Theory, I think. The experimental tests of Bell's inequality do suggest some form of superluminal information transfer, regardless of interpretation. Such superluminal "influences" don't mean superluminal message tranfer if one uses the Lorentzian interpretation (single preferred frame).
Superluminal effects are only implied if the quantum state has objective reality not if it is subjective information.

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apeiron
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Oct6-11, 02:18 AM
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Quote Quote by bohm2 View Post
The tension is between quantum nonlocality (not just BM) and the locality of Relativity Theory, I think. The experimental tests of Bell's inequality do suggest some form of superluminal information transfer, regardless of interpretation. Such superluminal "influences" don't mean superluminal message tranfer if one uses the Lorentzian interpretation (single preferred frame).
I was thinking of the fact that BM ontology treats particles as real (existing at some definite place and time) and so assumes that there is indeed a single preferred reference frame.

This seems less an issue for other interpretations that do not insist on anything being fixed in place at some globally shared moment. But then that may be just evading the SR issue rather than answering it.

So everyone has a problem, but BM has it worse! Well, that was my understanding. And a relational approach seems to be about stepping back and accepting SR as a guiding principle. Seek a background independent view.

SR would be emergent rather than fundamental in this view I think. But then I always say everything is emergent anyway. QM says everything is contextual. Relativity says all contexts needs to be constructed. So nothing is certain until it develops.

BM on the other hand is an attempt to hang onto to the underlying certainty of things, the counterfactual definiteness, even when the going gets tough and the evidence suggests time to let go. It is the opposite way of thinking about things.

Having cited Fuchs paper, don't you have anything further to say about its relational ontology?
ThomasT
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Oct6-11, 05:53 AM
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Quote Quote by apeiron
So if there is a conflict between BM and SR, then why do you say SR will have to be the one that gives way?
Quote Quote by bohm2
The tension is between quantum nonlocality (not just BM) and the locality of Relativity Theory, I think.
What tension? What does "quantum nonlocality" refer to? The following statement from [1] gives referents for quantum nonlocality (wrt standard QM) that wouldn't seem to imply any sort of conflict between quantum nonlocality and SR.
Quote Quote by Dmitry V. Stekalov, Yoon-Ho Kim, Yanhua Shih
The conservation laws guarantee the precise value of an observable with respect to the pair (not to the individual subsystems). It is in this sense, we say that the entangled two-photon state of SPDC is nonlocal. Quantum theory does allow a complete description of the precise correlation for the spatially separated subsystems, but no complete description for the physical reality of the subsystems defined by EPR. It is in this sense, we say that quantum mechanical description (theory) of the entangled system is nonlocal.
Quote Quote by bohm2
The experimental tests of Bell's inequality do suggest some form of superluminal information transfer, regardless of interpretation.
How so? As far as I can tell, the inference of existence of FTL depends entirely on how one interprets Bell's theorem.

Quote Quote by skippy1729
Superluminal effects are only implied if the quantum state has objective reality ...
It's not clear what this might mean. It might be true that if one assumes that quantum states have "objective reality", then FTL is implied. I don't see why that should follow, but I don't know. But, how would we be able to ascertain just how closely quantum states approximate/correspond to the reality underlying instrumental behavior? Anyway, from my first introduction to this stuff I was cautioned not to think of quantum states as real states.


[1] Experimental Study of A Photon as A Subsystem of An Entangled Two-Photon State, Phys.Rev. A60 (1999) 2685,
http://arxiv.org/abs/quant-ph/9811060
bohm2
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Oct6-11, 05:56 PM
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Quote Quote by ThomasT View Post
What tension? What does "quantum nonlocality" refer to?
The correlations in the EPR/B experiment strongly suggest that there are non-local influences between distant systems, i.e., systems between which no light signal can travel, and indeed orthodox quantum mechanics and its various interpretations postulate the existence of such non-locality. Yet, the question of whether the EPR/B correlations imply non-locality and the exact nature of this non-locality is a matter of ongoing controversy.

However, satisfying the Lorentz transformations at the level of individual processes is not sufficient for compatibility with Minkowski spacetime; for the Lorentz transformations may also be satisfied at the level of individual processes in theories that postulate a preferred inertial reference frame (Bell 1976). Maudlin suggests that a theory is genuinely relativistic (both in spirit and letter) if it can be formulated without ascribing to spacetime any more, or different intrinsic structure than the relativistic metrics.The question of the compatibility of relativity with quantum mechanics may be presented as follows: Could a quantum theory that does not encounter the measurement problem be relativistic in that sense?

While these arguments challenge the view that the quantum realm as depicted by non-factorizable models for the EPR/B experiment must involve non-locality, they do not show that viable local, non-factorizable models of the EPR/B experiment (i.e., viable models which do not postulate any non-locality) are possible. Indeed, so far none of the attempts to construct local, non-factorisable models for EPR/B experiments has been successful.

http://plato.stanford.edu/entries/qm-action-distance/
ThomasT
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Oct6-11, 11:27 PM
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Quote Quote by Stanford Encyclopedia of Philosophy
The correlations in the EPR/B experiment strongly suggest that there are non-local influences between distant systems, i.e., systems between which no light signal can travel, ...

( ... )

The curious EPR/B correlations strongly suggest the existence of non-local influences between the two measurement events, and indeed orthodox ‘collapse’ quantum mechanics supports this suggestion.
This is, at best, misleading. The correlations in optical Bell tests, without a certain interpretation of Bell's theorem, aren't 'curious' and are pretty much what would be expected via common cause in a universe governed by local causation. That is, the results of these optical tests are in line with established (local) optics principles.

Standard 'uninterpreted' QM doesn't posit a physical 'collapse' of a wave shell in real space and time. It just takes, per known optics, the polarization axis associated with either detection attribute and projects it to the other side so that you get, in the ideal, a cos2θ or a sin2θ dependency (depending on the process used to produce entangled pairs of photons) between the angular difference of the polarizers, θ, and the coincidental photon flux. Which is a result that's in line with established optics principles.

On the other hand, if you place certain (LRHV) restrictions on how a model of quantum entanglement can be formulated, then you get a correlation between θ and coincidental photon flux that in the extreme archetypal formulation of such a (LRHV) model you get a linear correlation between θ and coincidental photon flux. Which is a result that's at odds with established optics principles.

Again, to be clear, entanglement correlations, per se, don't suggest "nonlocal influences between distant systems".

Quote Quote by Standard Encyclopedia of Philosophy
... and indeed orthodox quantum mechanics and its various interpretations postulate the existence of such non-locality.
As far as I'm aware, standard QM doesn't have any postulates involving nonlocality (ie., taking the term "nonlocality" to refer to some FTL physical transmission, or action-at-a-distance between entangled entities).

For clarification of where I'm coming from wrt this, refer to my post #27 in this thread.

And before we go any further it might help to go back to your first question in the OP:

Quote Quote by bohm2
Does the wave function represent the physical state of the system (MW) or merely our information about the system (orthodox interpretation)?
Well, the information about the system is all that's known. There's no way of knowing if it represents anything beyond that (ie., how closely the constructions of QM approximate the reality underlying instrumental behavior).

Thus, the mainstream, standard way of interpreting (or not interpreting, per Peres and Fuchs) QM is that it's a mathematical construction for calculating the probabilities of instrumental behaviors based on what's known about instrumental behavior. In other words, this is all that can be said about what the wave equation and wave functions are. Speculations about nonlocal influences, collapses, etc. aren't testable. Bell's theorem doesn't say that nature is nonlocal, it says that LRHV models of quantum entanglement are impossible. Why they're impossible is still a matter of debate, but, imo, it doesn't have to do with nonlocality in nature.

And without a certain interpretation of Bell, there's nothing to suggest physical nonlocal influences. Paraphrasing Peres and Fuchs: uninterpreted, or standard, QM is essentially local.

Unfortunately, the terms "nonlocal" and "nonlocality" have become part of the technical language and are a source of confusion, because in their technical usage wrt standard QM they don't refer to either FTL transmissions or action-at-a-distance. (See the quoted text from the paper referenced in post #34.)

Hence the conclusion that there's no tension between standard QM and SR.


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