What Does the Wave Function Truly Represent?

[bohm2]

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]

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.

skippy

 

[apeiron]

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]

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.

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.

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.

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.

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]

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]

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".

... 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:

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.

 

[Demystifier]

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?

Yes, it's possible.

Any references appreciated.

http://xxx.lanl.gov/abs/1103.1589
http://xxx.lanl.gov/abs/quant-ph/0403034

 

[Demystifier]

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.

Existence at definite place and time has nothing to do with preferred reference frame. After all, classical relativistic particles also exist at definite place and time, and yet it does not involve a preferred reference frame.

To see why BM involves a preferred reference frame, and how that problem can be avoided, see
http://xxx.lanl.gov/abs/1002.3226 [Int. J. Quantum Inf. 9 (2011) 367-377]

 

[bohm2]

Standard 'uninterpreted' QM doesn't posit a physical 'collapse' of a wave shell in real space and time.

This is what I find so difficult to understand about the epistemic view. If one treats the wave function as a mathematical probability wave (an epistemic device to calculate the probability of finding a particle in a particular spatial location) it seems like a very strange sort of probability wave, since it can have "physical" effects like the interference pattern in double-slit experiments. Even the probability density doesn't appear like the classical notion of probability. I'll never understand this and I tried to understand Fuch's arguments but as hard as I tried, I just couldn't follow them.

 

[ThomasT]

Standard 'uninterpreted' QM doesn't posit a physical 'collapse' of a wave shell in real space and time.

This is what I find so difficult to understand about the epistemic view. If one treats the wave function as a mathematical probability wave (an epistemic device to calculate the probability of finding a particle in a particular spatial location) it seems like a very strange sort of probability wave, since it can have "physical" effects like the interference pattern in double-slit experiments.

Well, interacting waves produce interference patterns. That shouldn't seem so strange. And it's good to keep in mind that wave-mechanical QM is based largely on classical wave mechanics.

I don't know exactly how Shroedinger came up with his wave equation, but maybe somebody here does.

You can treat the wave function as a mathematical probability wave because that's all that can be known for sure that it is. However, the fact that it actually works as well as it does seems to suggest that there's some more or less familiar wave mechanics happening in the underlying reality. But that might be misleading. I don't know. Anyway, probability distributions are waves, and the wave functions of QM are probability distributions.

Even the probability density doesn't appear like the classical notion of probability.

From Wiki:
Probability amplitude
Probability density function

I'll never understand this and I tried to understand Fuch's arguments but as hard as I tried, I just couldn't follow them.

I think you'll eventually understand it. And then you can explain it to me.

I don't think I've read the Fuchs article that I think you're referring to. Maybe I'll get to it this afternoon.

 

[bohm2]

I don't know exactly how Shroedinger came up with his wave equation, but maybe somebody here does.

I thought these were some interesting quotes by Schrodinger and others concerning wave function ontology;

Schrodinger started out trying to interpret the wave function realistically. For example, in an early paper on wave mechanics, he writes:

The true mechanical process is realized or represented in a fitting way by the wave processes in q-space, and not by the motion of image points in this space.

Schrodinger considers a two-particle system late in the paper but has only one sentence about the physical representation of the sixdimensional wave function:

The direct interpretation of this wave function of six variables in three-dimensional space meets, at any rate initially, with difficulties of an abstract nature.

Schrodinger wants to interpret the mechanical processes realized or represented by the wave function as taking place in three-dimensional space, but he does not see how this can be done. Lorentz picks up on this problem with multiparticle systems. In 1926, Lorentz wrote a letter to Schrodinger, in which he says:

If I had to choose now between your wave mechanics and the matrix mechanics, I would give the preference to the former, because of its greater intuitive clarity, so long as one only has to deal with the three coordinates x, y, z. If, however, there are more degrees of freedom, then I cannot interpret the waves and vibrations physically, and I must therefore decide in favor of matrix mechanics.

http://spot.colorado.edu/~monton/BradleyMonton/Articles_files/qm%203n%20d%20space%20final.pdf

I'm not sure but it seems this wave is somewhere between a mathematical probability wave and some sort of weird "physical-like" wave existing in 3-N dimensional space? What's interesting, is if you assume a realistic interpretation and try to map the 3-N configuration space into 3-dimensional space, so that the 3-dimensional world is something that emerges from this 3-N configuration space you get more than one set of emergent 3-spaces. That's one reason why Monton argues against treating the 3 N-dimensional space in QM as "fundamental".

 

[apeiron]

Existence at definite place and time has nothing to do with preferred reference frame. After all, classical relativistic particles also exist at definite place and time, and yet it does not involve a preferred reference frame.

To see why BM involves a preferred reference frame, and how that problem can be avoided, see
http://xxx.lanl.gov/abs/1002.3226 [Int. J. Quantum Inf. 9 (2011) 367-377]

Can you briefly explain what is meant by the many-time wave function?

And does this approach really hinge on allowing particles to have velocities greater than c?

I found the paper's insistence on super-determinism and no room for freewill rather too implausible as a motivation. The arguments against experiments to test the ontology - such as systems set up to destroy themselves with retrocausal signals - seem arbitrary.

R: A microscopic object cannot send a message that would contradict its own existence.
O: Why not?
R: First, because I assume that the microscopic object does not have free will, or even
an illusion of free will, to send any message it “wishes”. Second, even if I discard this
assumption, I certainly must assume that the microscopic laws are self-consistent, i.e.,
that such inconsistent systems do not appear as solutions of the mathematical equations
describing the microscopic laws.

But 1) a human with the capacity to choose could choose to set up such an apparatus. Then 2) you only "must" assume this from the particular route to modelling general covariance suggested in the paper.

Then the argument to justify accepting superluminal action...

R: This is like using the following argument on subluminal communication. If communication is subluminal, then there is a Lorentz frame in which the carrier of the message is at rest. If it is at rest in one Lorentz frame, then it is not at rest in any other Lorentz frame. Therefore, there is a preferred Lorentz frame with respect to which the carrier is at rest. Consequently, the principle of relativity is violated.

Wouldn't the real complementary story here have to be the possibility of things "moving slower than rest"?

Relativistic effects arise for matter because they effectively lag behind the natural speed of action/equilibration which is c. They can fall all the way down to the limit which is "rest" in some inertial frame which minimises their "massiveness".

So if it is nonsensical to think a massive particle can go "slower than rest", then by the same argument, it is nosensical to suggest it can go faster than c.

 

[ThomasT]

( ... )
I'm not sure but it seems this wave is somewhere between a mathematical probability wave and some sort of weird "physical-like" wave existing in 3-N dimensional space? What's interesting, is if you assume a realistic interpretation and try to map the 3-N configuration space into 3-dimensional space, so that the 3-dimensional world is something that emerges from this 3-N configuration space you get more than one set of emergent 3-spaces. That's one reason why Monton argues against treating the 3 N-dimensional space in QM as "fundamental".

Thanks. I've got some reading to do. Could take a while. It looks like I'm going to learn more about interpreting wave functions than I ever really wanted to.

Seems like you're making progress, insofar as broadening and deepening your knowledge, in your quest to understand this.

 

[Demystifier]

Can you briefly explain what is meant by the many-time wave function?

Yes, provided that you first tell me why the explanation in the paper is not clear to you.

 

[apeiron]

Yes, provided that you first tell me why the explanation in the paper is not clear to you.

How do you assign a time to individual particles unless you have already defined a reference frame to make those measurements?

 

[Demystifier]

How do you assign a time to individual particles unless you have already defined a reference frame to make those measurements?

Basically, in the same way one does that in classical relativistic mechanics:
First one takes some specific reference frame with coordinates x^\mu, \mu=0,1,2,3.
Then one assigns both time position x^0 and space position x^1, x^2, x^3 of an individual particle.
Finally one writes all equations involving x^\mu in a manifestly covariant form, which provides that physical results will not depend on the choice of reference frame.

For more details see
http://xxx.lanl.gov/abs/1006.1986

 

[Demystifier]

I found the paper's insistence on super-determinism and no room for freewill rather too implausible as a motivation.

Do you know ANY FUNDAMENTAL theory in physics which is compatible with free will? (I don't.)

 

[apeiron]

Do you know ANY FUNDAMENTAL theory in physics which is compatible with free will? (I don't.)

What, not even an "effective freewill"?

 

[apeiron]

First one takes some specific reference frame with coordinates x^\mu, \mu=0,1,2,3.

OK, this can be done for some subset of the universe, but can it be done for the universe as a whole?

Or is this where the further requirement for FTL particle velocities comes in?

 

[ThomasT]

@ Demystifier,

You haven't replied to my post #27 which was in response to your post #19. Do you agree/disagree with it?

Also:

I found the paper's insistence on super-determinism and no room for freewill rather too implausible as a motivation.

Do you know ANY FUNDAMENTAL theory in physics which is compatible with free will? (I don't.)

What, not even an "effective freewill"?

I find the references to 'superdeterminism' and 'free will' to be somewhat off the mark, whether those terms are used in discussions about the compatibility of nonlocality and relativity or the compatibility of LRHV models of quantum entanglement and experimental results.

In Aspect et al. 1982 the analyzer settings are varied randomly and so, apparently, have nothing to do with 'free will'. The term 'superdeterminism' is simply a superfluous extension of the term 'determinism'. Considerations like 'going back in time' make no sense at all to me.

Am I actually missing something here? Or is it possible that none of this is relevant to anything?

 

[Demystifier]

What, not even an "effective freewill"?

Effective free will is the same as illusion of free will, which is consistent with physical laws as discussed in the paper.

 

[Demystifier]

I find the references to 'superdeterminism' and 'free will' to be somewhat off the mark,
...
Am I actually missing something here?

Perhaps you are missing the context, which is the paper mentioned in post #38.

 

[Demystifier]

You haven't replied to my post #27 which was in response to your post #19. Do you agree/disagree with it?

At some points I don't really understand your reasoning, so it's hard to tell wheather I agree or not.

 

[ThomasT]

Perhaps you are missing the context, which is the paper mentioned in post #38.

There's at least two ways to view determinism. Either the universe is evolving and we're part of that evolution, or we're traveling through a static universe. In the case of the former, going back or sending messages back in time is nonsensical because the past refers to spatial configurations that no longer exist. The latter case, on the other hand, suggests that we're somehow distinct from the universe, ie., travelling/evolving in some way separate from it, which seems to be prima facie nonsensical and anyway leads to all sorts of nonsensical stuff.

So, we choose the former view, the view that we're part of an evolving universe, and in that view it's impossible to send messages back in time or to revisit the past, even if we could send messages or transport ourselves instantaneously to any part of the universe.

Properly interpreted, in an evolving universe which we're a part of, there's no frame of reference wrt which even a FTL signal is actually traveling backward in time.

Thus, 'free will' has nothing to do with it. 'Superdeterminism' is a superfluous extension of determinism, because if the universe is evolving deterministically, then free will (in the sense of choices being independent of prior conditions/configurations) is ruled out anyway.

In your paper you say that "By assumption, superluminal signals are inherently quantum phenomena responsible for nonlocal correlations between entangled particles ..." . But this assumption isn't necessary for a certain understanding of the correlations between the angular difference of polarizer settings and coincidental photon flux, and in fact posits the existence of an entirely new class of physical (or nonphysical in the case of instantaneous action-at-a-distance) phenomena for which there's absolutely no physical evidence.

You say that, "The Bell theorem [1] shows that quantum mechanics (QM) is not compatible with local reality.", which isn't precisely correct. Bell's theorem shows that QM is not compatible with LRHV models of quantum entanglement (ie., coincidental photon flux). QM is quite compatible with LRHV models of photon flux at the individual detectors. In general, standard QM is essentially nonrealistic and so is not incompatible with an understanding of quantum entanglement via purely local transmissions and interactions.

You further say that, "This suggests that reality might be nonlocal." . But this isn't at all what's suggested if one looks at the correlations wrt established optics principles, and if one evaluates the meaning of Bell's theorem wrt the formal constraints on LRHV models of entanglement. In this view, LRHV models of entanglement are ruled out even if the universe is evolving strictly in accordance with local determinism.

 

[ThomasT]

At some points I don't really understand your reasoning, so it's hard to tell wheather I agree or not.

Which lines of reasoning in post #27 are unclear? Maybe I can further clarify them.

 

[ThomasT]

@ Demystifier,

You said, "We see that the equation of motion (23) is nonlocal, because the velocity of one particle for some value of s depends on the positions of all other particles for the same value of s." .

Should this be taken to mean that the motional properties of particles are physically determining the motional properties of other particles light years away, or can it be taken to mean that given certain antecedent conditions/configurations and motional properties, then certain things can be deduced about the evolution of a system?

 

[Demystifier]

@ Demystifier,

You said, "We see that the equation of motion (23) is nonlocal, because the velocity of one particle for some value of s depends on the positions of all other particles for the same value of s." .

Should this be taken to mean that the motional properties of particles are physically determining the motional properties of other particles light years away ...

Yes.

 

[bohm2]

Thus, 'free will' has nothing to do with it. 'Superdeterminism' is a superfluous extension of determinism, because if the universe is evolving deterministically, then free will (in the sense of choices being independent of prior conditions/configurations) is ruled out anyway.

I've come across a number of arguments (not just the compatibilist ones) suggesting that determinism is compatible with 'free will'. Others argue that the converse is also true; that is, indeterminism doesn't help the 'free will' cause at all. Carl Hoefer writes:

For reasons that Kant first realized, indeterminism at the microphysical level does not seem to help. The randomness, if any, in microscopic phenomena does not seem to “make room” for free will, but rather only replaces a sufficient physical cause with (at least in part) blind chance. The presumption in favor of upward causation and explanation (from microphysical to macrophysical) that comes with causal completeness is what cuts free agency out of the picture, whether this causation is deterministic or partly random.

http://www2.lse.ac.uk/CPNSS/pdf/DP_withCover_Measurement/Meas-DP%2016%2001.pdf

Carl Hoefer then suggests that:

Physics, particularly 20th century physics, does have one lesson to impart to the free will debate; a lesson about the relationship between time and determinism. Recall that we noticed that the fundamental theories we are familiar with, if they are deterministic at all, are time-symmetrically deterministic. That is, earlier states of the world can be seen as fixing all later states; but equally, later states can be seen as fixing all earlier states. We tend to focus only on the former relationship, but we are not led to do so by the theories themselves.

Nor does 20th (21st) -century physics countenance the idea that there is anything ontologically special about the past, as opposed to the present and the future. In fact, it fails to use these categories in any respect, and teaches that in some senses they are probably illusory.[9] So there is no support in physics for the idea that the past is “fixed” in some way that the present and future are not, or that it has some ontological power to constrain our actions that the present and future do not have. It is not hard to uncover the reasons why we naturally do tend to think of the past as special, and assume that both physical causation and physical explanation work only in the past present/future direction (see the entry on thermodynamic asymmetry in time). But these pragmatic matters have nothing to do with fundamental determinism. If we shake loose from the tendency to see the past as special, when it comes to the relationships of determinism, it may prove possible to think of a deterministic world as one in which each part bears a determining—or partial-determining—relation to other parts, but in which no particular part (i.e., region of space-time) has a special, stronger determining role than any other. Hoefer (2002) uses these considerations to argue in a novel way for the compatiblity of determinism with human free agency.

http://plato.stanford.edu/entries/determinism-causal/#DetHumAct

Personally, I'm unconvinced by any of these arguments (both the pro or anti- free-will arguments) and tend to agree with McGinn that stuff like 'free will' is beyond our cognitive reach. Many humans seem to have this "God-like" complex thinking their cognitive powers have no limits. Consider what an ape's understanding of the universe is compared to ours. They could never understand what we are capable of: science, biology, physics, abstract algebra, etc. We are qualitatively different, so we think. Assume that even our cognitive abilities are only slightly more advanced than an ape's. Of course, from our perspective it doesn't appear that way. Assume reality is extremely complex. The ape's mind might be able to understand/pick up .001% of it. The human mind may have access to about .01% of it. Big improvement but still a miniscule part of all of reality/totality of "true" theories?

 

[ThomasT]

Personally, I'm unconvinced by any of these arguments (both the pro or anti- free-will arguments) and tend to agree with McGinn that stuff like 'free will' is beyond our cognitive reach.

I don't agree with either Hoefer's or McGinn's take on this. Our thoughts and actions are somewhat unique from person to person, but they're not free in the sense that the term 'free' refers to absence of constraints. If the universe is evolving deterministically, then our wills, our thoughts and actions, aren't free.

We assume, for lots of good reasons, that the universe is evolving deterministically, and that we're an inseparable part of that deterministic evolution. That is, there aren't any subsystems of the universe that are isolated from its deterministic evolution.

Anyway, my point was that considerations of free will are irrelevant to interpreting the physical meaning of Bell's theorem.

In my view, the proper interpretation of Bell's theorem provides no basis for assuming the existence of action-at-a-distance 'influences' or FTL propagations.

Wrt your OP, we know that the wave equation and wave function are mathematical constructions which generate probabilities regarding measurement results. Anything else one might want to attribute to them is a matter of speculation, as there's no way to ascertain how they might approximate the reality underlying instrumental behavior.

 

[bohm2]

I don't agree with either Hoefer's or McGinn's take on this. Our thoughts and actions are somewhat unique from person to person, but they're not free in the sense that the term 'free' refers to absence of constraints. If the universe is evolving deterministically, then our wills, our thoughts and actions, aren't free.

I don't think most philosophers/scientists who espouse the compatibility of determinism and free will are arguing against constraints. In fact, they argue that without some constraints to limit options/choices, creativity/theory construction/human behaviour, etc. would be impossible. I'm thinking about Peirce's argument here (e.g. innate property of mind that 'puts a limit upon admissible hypotheses',). The argument, however, is that we are free to choose among those variety of options innately given to us, I think; that is, "we could have done otherwise". That's how I understood "free will" as argued by these authors.