# QM objects do not have properties until measured?

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N88
I would like to learn about and clarify the common statement: "QM objects do not have properties until measured".

"Put a red slip of paper in an envelope and a green one in another. Send one to the other side of the universe. Open one and you automatically know the colour of the other. The systems are correlated - nothing spooky going on. Now it turns out in QM you can do exactly the same thing with particle spins. And you get correlations. Again nothing mysterious. The difference is it has a different kind of statistical correlation
http://www.drchinese.com/Bells_Theorem.htm
It turns out the reason for that different correlation is that in QM objects do not have properties until measured to have them. But what if we insist? Then we find there must be instantaneous communication. But only if we insist." (My emphasis.)

Question: If we did a Bell-test with electron-positron pairs, could we NOT say that each particle in a pair has opposite charge and velocity and that they are correlated by the conservation of angular momentum?

So, it seems, quantum objects have some properties before measurement. What they do not necessarily have is the property measured by each interaction with a detector. That is, in my words, they do not necessarily have spin-up or spin-down before measurement.

So, modifying bhobba's statement: … the different correlation is that QM objects (unlike the red and green slips of paper) do not necessarily have the measured output before measurement. And we find there must be "instantaneous communication" if we insist that they have the measured property (spin-up or spin-down) before measurement.

Is this correct?

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Gold Member
This model concludes instantaneous change of particle state:

1. Initially spin directions for particles A and B are undetermined.
2. A measurement for spin is randomly ± 1 with 50/50 outcome
3. If A measures +1 at direction α then B particle collapses to state with spin direction Φ = Π - α
4. If A measures - 1 at direction α then B particle collapses to state with spin direction Φ = α
5. Later when B measures spin at direction β he gets +1 with probability cos2 (β-Φ)/2
and -1 with probability sin2(β-Φ/2

And in this experimental result, particles having definite spin orientation before measurement is rejected.Consider 3 particles;

1. Particle a is spin + at 0ο and spin - at 45ο
2. Particle a is spin + at 45ο and spin - at 90ο
3. Particle a is spin + at 0ο and spin - at 90ο
Following conservation laws the entangled particle b that is paired with particle a would be expected to be spin + at 45ο and in both cases at 90ο
Then with sin2(θ/2) the probability that an entangled pair will be P++ with θ angle between detectors the inequality:
sin2 (45ο/2) + sin2(45ο/2) ≥ sin2(90ο/2 is violated;
.1464 + .1464 ≥ .5

I question both conclusions in both cases above:

Mentor
the different correlation is that QM objects (unlike the red and green slips of paper) do not necessarily have the measured output before measurement. And we find there must be "instantaneous communication" if we insist that they have the measured property (spin-up or spin-down) before measurement.
Is this correct?
There are some subtleties (that will likely generate a few hundred more posts in this thread), but that's correct enough for most general discussion.

However, there is no substitute for going back to Bell's paper in which he states the assumptions he's making to derive his inequality, because what we really have is "no theory that conforms to Bell's assumptions can match the predictions of QM". Getting from those assumptions to your statement is an extra step that needs to be justified; you have to satisfy yourself that Bell's assumptions are at least as strong as what you mean by "have the measured property" and "instantaneous communication".

For example, Morrobay just used the term "an instantaneous change of state"; presumably you're thinking of that as a form of "communication", but Bell made neither claim - he assumed that the probability distribution of the results of the measurements could be written in a particular form.

bhobba
I would like to learn about and clarify the common statement: "QM objects do not have properties until measured".
It only means that "QM objects usually do not have the measured properties before their measurement", since the measurement setting changes these properties - except in so-called nondemolition measurements.

N88
N88
There are some subtleties (that will likely generate a few hundred more posts in this thread), but that's correct enough for most general discussion.

However, there is no substitute for going back to Bell's paper in which he states the assumptions he's making to derive his inequality, because what we really have is "no theory that conforms to Bell's assumptions can match the predictions of QM". Getting from those assumptions to your statement is an extra step that needs to be justified; you have to satisfy yourself that Bell's assumptions are at least as strong as what you mean by "have the measured property" and "instantaneous communication".

For example, Morrobay just used the term "an instantaneous change of state"; presumably you're thinking of that as a form of "communication", but Bell made neither claim - he assumed that the probability distribution of the results of the measurements could be written in a particular form.

Thank you for directing me to Bell's assumption that the probability distribution of the results of the measurements could be written in a particular form.

Going back to Bell's paper of 1964, and following Professor Neumaier's search for precision on PF, I would like to be very correct for serious QM discussion purposes.

It seems to me that Bell's use of λ is equivalent to "the measured property λ is possessed prior to measurement". So the experimental negation of Bell's inequalities suggests to me (in line with my search for correctness) that "the measured property λ is NOT possessed prior to measurement".

But it is here that other physicists conclude (given the widespread experimental validation of QM): "The world is made up of objects whose existence is dependent on human consciousness."

Here is a Scientific American article in which Bernard d'Espagnat expresses his view: http://www.scientificamerican.com/media/pdf/197911_0158.pdf

I emailed him last night to see if he still adheres to the first statement [EDIT. i.e.: "The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment."] and upon checking my emails this morning I received a reply that he had not departed from it. ...

Professor d'Espagnat's view seems to be closely equivalent to "QM objects do not have properties until measured".

So, modifying bhobba's helpful statement in the OP afresh: … the different correlation is that QM objects (unlike the red and green slips of paper) do not necessarily have the measured output before measurement. But their existence demands that they have other properties prior to measurement, which is neither weird nor spooky.

Is this more correct?

N88
It only means that "QM objects usually do not have the measured properties before their measurement", since the measurement setting changes these properties - except in so-called nondemolition measurements.
Thank you. So seeking to be accurate, in my terms: A QM object need not have a measured property before measurement because the measurement process may change the object's properties.

Would this also be accurate: This is the lesson of Bell's theorem?

So seeking to be accurate, in my terms: A QM object need not have a measured property before measurement because the measurement process may change the object's properties.
A QM object always has uncertain properties (not no properties). For example, the position of a (for simplicity scalar) particle in a beam is not known precisely, but it is known that it is within the confines of the beam. Thus if the beam is in z-direction, one knows (by preparation) the x- and y-coordinates quite well, whereas the z-coordinate is very fuzzy. However (consistent with the Heisenberg uncertainty relations) one knowns the momentum in z-direction quite well. Thus one has good knowledge of a particular complete set of commuting observables.

If you measure a quantum system you change some of its properties through the interaction with the detector. In exchange for it you gain information about the object at the moment of measurement.

This has been known since the early days of quantum mechanics, hence has nothing to do with Bell. Bell's novelty was to study nonlocality in a tractable framework.

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Nugatory and bhobba
Mentor
There are some subtleties (that will likely generate a few hundred more posts in this thread), but that's correct enough for most general discussion.

What was it meatloaf said - you took the words right out of my mouth. It's what I was basically going to say.

I have no doubt those subtleties will emerge as the thread plods along.

Thanks
Bill

Mentor
So, it seems, quantum objects have some properties before measurement. What they do not necessarily have is the property measured by each interaction with a detector. That is, in my words, they do not necessarily have spin-up or spin-down before measurement
Yes - but only if its in an eigenstate of whats being measured.

That's the crux of an improper mixed state becoming a proper mixed state. If its a proper mixed state then it has the property objectively and everything is common-sense sweet. But the 64 million dollar question is - how does that happen. In my interpretation, ignorance ensemble, I simply assume it does - other interpretations explain it - others like me simply throw up their hands. Its the modern version of the so called measurement problem which has morphed a bit in modern times.

Thanks
Bill

ddd123
A QM object always has uncertain properties (not no properties).
Why is the uncertainty of the properties before measurement important here? No properties is usually intended here as no local properties (which can become no properties in some interpretations).

N88
… If you measure a quantum system you change some of its properties through the interaction with the detector. In exchange for it you gain information about the object at the moment of measurement. This has been known since the early days of quantum mechanics, hence has nothing to do with Bell. Bell's novelty was to study nonlocality in a tractable framework. (Emphasis added.)

As I stated above, at #5: It seems to me that Bell's use of λ is equivalent to "the measured property λ is possessed prior to measurement" and true to his focus on locality and EPR "elements of physical reality".

Then you say (and I accept) that the error in this view was known since the early days of QM.

From bhobba's view that I quoted in #1 above: "But what if we insist [that Bell's assumption is worthwhile]? Then we find there must be instantaneous communication. But only if we insist." Which makes good sense to me.

So "instantaneous communication" (nonlocality) enters Bell's work via Bell's use of λ as equivalent to "the measured property λ is possessed prior to measurement". Therefore it does not appear to me that "Bell's novelty was to study nonlocality in a tractable framework." Rather, agreeing with bhobba here, the nonlocality arises if we accept Bell's unrealistic use of λ as equivalent to "the measured property λ is possessed prior to measurement".

the error in this view was known since the early days of QM.
I talked about properties of a quantum system, not about errors is a classical view.

Bell's question is different - he asks whether there is a different, classical theory underlying quantum mechanics and showns that it must have nonlocal laws if his inequalities are violated (which they are according to experiments performed later). Bell's theorem says nothing at all about quantum mechanics - it is a purely classical theorem!

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Why is the uncertainty of the properties before measurement important here?
Because it is the correct description.

Observables with a continuous spectrum can never be known without uncertainty since there are no associated normalized eigenstates!

ddd123
Because it is the correct description.

Observables with a continuous spectrum can never be known without uncertainty since there are no associated normalized eigenstates!

I mean, the change of properties through the interaction with a detector doesn't address the reason behind bell inequalities violation. Or does it?

I mean, the change of properties through the interaction with a detector doesn't address the reason behind bell inequalities violation. Or does it?
Bell inequality violations have nothing at all to do with the measurement problem, hence should be off-topic in this thread. They address a completely different problem - that of local hidden variable theories.

bhobba
Gold Member
From bhobba's view that I quoted in #1 above: "But what if we insist [that Bell's assumption is worthwhile]? Then we find there must be instantaneous communication. But only if we insist." Which makes good sense to me.

So "instantaneous communication" (nonlocality) enters Bell's work via Bell's use of λ as equivalent to "the measured property λ is possessed prior to measurement". Therefore it does not appear to me that "Bell's novelty was to study nonlocality in a tractable framework." Rather, agreeing with bhobba here, the nonlocality arises if we accept Bell's unrealistic use of λ as equivalent to "the measured property λ is possessed prior to measurement".
This is not quite right. Prior to Bell one could imagine that non-locality of QM could be explained by preexisting hidden physical configuration that obeys locality. Bell's work demonstrated that such an explanation is in conflict with predictions of QM.
Maudlin explains this in his article
In other words Bell demonstrated that the only realistic solution to non-locality of QM doesn't work.

This is not quite right. Prior to Bell one could imagine that non-locality of QM could be explained by preexisting hidden physical configuration that obeys locality. Bell's work demonstrated that such an explanation is in conflict with predictions of QM.
Maudlin explains this in his article
In other words Bell demonstrated that the only realistic solution to non-locality of QM doesn't work.
Maudlin is a crackpot whose views are rejected by the vast majority of working physicists. His paper is debunked in this article. He fails to recognize some subtle assumptions that are undoubtedly made in the proof of the theorem.

Maudlin is a crackpot whose views are rejected by the vast majority of working physicists. His paper is debunked in this article. He fails to recognize some subtle assumptions that are undoubtedly made in the proof of the theorem.

Maudlin is not a crackpot. Werner is wrong because if we assume the wave function to be real, the state space is still a simplex. However, if the wave function is real, then collapse is real, and operational QM is nonlocal.

Werner's reference [8] is an article by Wiseman. Wiseman's article supports Maudlin's view. Wiseman shows how Werner's argument and definitions need to be modified to support something like what Werner is trying to get at. But then it turns out that after the appropriate corrections to Werner's view, Werner is talking about something different from Maudlin, and there is nothing wrong with Maudlin's view.

Wiseman and Cavalcanti have a very thorough analysis of all the different routes to the separability criterion: http://arxiv.org/abs/1503.06413. While there are certainly some subtleties to Maudlin's view, it is Maudlin that is essentially correct, and Werner that is essentially wrong.

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Gold Member
He fails to recognize some subtle assumptions that are undoubtedly made in the proof of the theorem.
Bell's theorem is not trivial, as he derives general limits of LHV. But the question about locality of QM becomes much more trivial if you ask very specific question: can there be explanation that obeys locality for particular prediction of QM with specific values. It turns out the answer is "no" and one such a counterexample type argument you can find here. It does not use probability spaces or assumptions about micro world.

Maudlin is not a crackpot. Werner is wrong because if we assume the wave function to be real, the state space is still a simplex. However, if the wave function is real, then collapse is real, and operational QM is nonlocal.
That's what Werner pointed out. You are taking realism for granted. The Bell violations only prove that "locality + realism" is wrong. You need both assumptions. Locality alone isn't enough. Maudlin doesn't recognize this and claims that locality is enough. This is clearly wrong, but instead of admitting is mistake, he is being polemic, which makes him a crackpot.

Werner's reference [8] is an article by Wiseman. Wiseman's article supports Maudlin's view. Wiseman shows how Werner's argument and definitions need to be modified to support something like what Werner is trying to get at. But then it turns out that after the appropriate corrections to Werner's view, Werner is talking about something different from Maudlin, and there is nothing wrong with Maudlin's view.

Wiseman and Cavalcanti have a very thorough analysis of all the different routes to the separability criterion: http://arxiv.org/abs/1503.06413. While there are certainly some subtleties to Maudlin's view, it is Maudlin that is essentially correct, and Werner that is essentially wrong.
Maudlin's view is that no realism assuption needs to be made in the proof of Bell's theorem. This is wrong without any doubt, since the realism assumption can be isolated precisely. It is definitely there and it's crackpottery to doubt that.

Here is another paper, published in the same issue, where the failure of such arguments as Maudlin's is pointed out clearly:
http://iopscience.iop.org/article/10.1088/1751-8113/47/42/424009

Bell's theorem is not trivial, as he derives general limits of LHV. But the question about locality of QM becomes much more trivial if you ask very specific question: can there be explanation that obeys locality for particular prediction of QM with specific values. It turns out the answer is "no" and one such a counterexample type argument you can find here. It does not use probability spaces or assumptions about micro world.
It nevertheless uses assumptions beyond locality. This is adressed in this book.

That's what Werner pointed out. You are taking realism for granted. The Bell violations only prove that "locality + realism" is wrong. You need both assumptions. Locality alone isn't enough. Maudlin doesn't recognize this and claims that locality is enough. This is clearly wrong, but instead of admitting is mistake, he is being polemic, which makes him a crackpot.

No, Werner is wrong. The realism assumption is not equivalent to the state space being a simplex.

Maudlin's view is that no realism assuption needs to be made in the proof of Bell's theorem. This is wrong without any doubt, since the realism assumption can be isolated precisely. It is definitely there and it's crackpottery to doubt that.

That is not Maudlin's view. His view is that realism is a precondition for reality. There is no locality without realism, and this is correct. This of course depends on how one defines locality, but it is true for Maudlin's definition. He sums it up: the world is local. If one wants to define a nonreal world - one can do so, but then the nonreal locality is something else that is not addressed by Bell's theorem. For example, consistent histories does escape the Bell theorem - but consistent histories is not locally causal - the notion of locality in consistent histories is something else.

No, Werner is wrong. The realism assumption is not equivalent to the state space being a simplex.
Mathematically, Bell's theorem requires the assumption of a simplicial state space, whose extremal points are the Dirac measures. Of course, one can state that in simpler terms and say that this means that Bell needs to assume that all random variables are defined on a single probability space. This is what Werner means when he talks about "realism" (in fact, he doesn't use that word at all and rather calls it "classicality") and it is a necessary assumption in every proof of Bell's theorem. No proof exists that doesn't assume this.

That is not Maudlin's view. His view is that realism is a precondition for reality. There is no locality without realism, and this is correct. This of course depends on how one defines locality, but it is true for Maudlin's definition. He sums it up: the world is local.
Maudlin claims that the violation of Bell's inequality proves that the world is non-local. This is false. The world might as well just be non-classical, which is in fact the mainstream position.

If one wants to define a nonreal world - one can do so, but then the nonreal locality is something else that is not addressed by Bell's theorem.
That's right, a non-classical world can still be local. A relation "causes" (##\sim##) one spacetime must satisfy ##x \sim y \Rightarrow x \in I^-(y)## (read: "if ##x## causes ##y##, then ##x## is in the chronological past of ##y##"). Quantum theory can be consistently supplemented with such a relation (a trivial example would be the empty relation, but there are of course non-trivial ones) and thus quantum theory is at least compatible with locality.

For example, consistent histories does escape the Bell theorem - but consistent histories is not locally causal - the notion of locality in consistent histories is something else.
Bell's notion of "local causality" is a misnomer. It should really be called "classical local causality" (see the last paper that I quoted). It is just not a universal criterion for locality and can only be applied to theories, whose state spaces are simplices. So not surprisingly, quantum theory doesn't satisfy it. However, this says nothing about the status of locality in quantum theory.

Mathematically, Bell's theorem requires the assumption of a simplicial state space, whose extremal points are the Dirac measures. Of course, one can state that in simpler terms and say that this means that Bell needs to assume that all random variables are defined on a single probability space. This is what Werner means when he talks about "realism" (in fact, he doesn't use that word at all and rather calls it "classicality") and it is a necessary assumption in every proof of Bell's theorem. No proof exists that doesn't assume this.

But in operational quantum mechanics, which Werner claims to be local, there is wave function collapse. If we take the wave function to be real, then operational quantum mechanics is manifestly nonlocal. The state space in operational quantum mechanics is not a simplex, and that doesn't seem to depend at all on whether one assumes the wave function to be real or not real.

Derek Potter
But in operational quantum mechanics, which Werner claims to be local, there is wave function collapse. If we take the wave function to be real, then operational quantum mechanics is manifestly nonlocal. The state space in operational quantum mechanics is not a simplex, and that doesn't seem to depend at all on whether one assumes the wave function to be real or not real.
If you assume both that the wave function is a classical field on spacetime ("the wave-function is real") and the collapse postulate, then I agree that quantum theory is non-local. However, operationalists usually don't assume the former hypothesis.

If you assume both that the wave function is a classical field on spacetime ("the wave-function is real") and the collapse postulate, then I agree that quantum theory is non-local. However, operationalists usually don't assume the former hypothesis.

Yes, but how does assuming reality of the wave function change the state space from not being a simplex to being a simplex? It seems that in both cases the state space is non-simplicial.

[Just to be clear, I do agree that there is a version of Bell's theorem in which one needs "some form of locality" + "something else".]

Yes, but how does assuming reality of the wave function change the state space from not being a simplex to being a simplex? It seems that in both cases the state space is non-simplicial.
If the wave function is a classical field, then it's state space is the space of classical probability distributions over the phase space. This is a simplex and its extremal points are the Dirac measures that are supported on single points of "definite wavefunction".

Mentz114
If the wave function is a classical field, then it's state space is the space of classical probability distributions over the phase space. This is a simplex and its extremal points are the Dirac measures that are supported on single points of "definite wavefunction".

But mathematically, all the postulates are exactly the same as in "operational quantum mechanics" - or is there any mathematical postulate that is different?

But mathematically, all the postulates are exactly the same as in "operational quantum mechanics" - or is there any mathematical postulate that is different?
Well, there is the additional postulate that "the wave function is real" (i.e. the wave function is a classial field). The state space of classical field theories is a simplex. The remaining postulates then just tell you, which parts of the wave function can be measured. Rather than interpreting the wave function to be a state itself, you interpret the wave function to be a field, which is in some classical state, so the state is not the wave function, but the point (or distribution) in phase space.

Well, there is the additional postulate that "the wave function is real" (i.e. the wave function is a classial field). The state space of classical field theories is a simplex. The remaining postulates then just tell you, which parts of the wave function can be measured. Rather than interpreting the wave function to be a state itself, you interpret the wave function to be a field, which is in some classical state, so the state is not the wave function, but the point (or distribution) in phase space.

What do you mean by phase space? How is the state not the wave function if we take the wave function to be real?

What do you mean by phase space? How is the state not the wave function if we take the wave function to be real?
In standard operationalist quantum theory, the objects of interest are particles for instance (or fields in QFT) and their state is given by a wave function. If you claim that the wave function is real, this is a shift of perspective. The objects of interest aren't the particles anymore, but rather the wave function itself. It is a physical object rather than just a container of information about physical objects ("a state"), so it has a state itself, which contains the information about the physical object called "wave function". This state is an element of a simplex (the space of distributions on phase space, where by phase space I mean classical phase space as in Hamiltonian classical field theory).

Staff Emeritus
But in operational quantum mechanics, which Werner claims to be local, there is wave function collapse. If we take the wave function to be real, then operational quantum mechanics is manifestly nonlocal. The state space in operational quantum mechanics is not a simplex, and that doesn't seem to depend at all on whether one assumes the wave function to be real or not real.

I am puzzled by Werner's argument, although I can't say that I'm 100% certain that he's wrong. But even if Werner is right, his argument is murky enough that it's hyperbole to call someone a "crackpot" for not agreeing with him (as rubi called Maudlin).

It seems to me that in wave function collapse, you can either take the wave function to be something physical, in which case collapse is a nonlocal, physical process. Or you can take the wave function to just reflect our knowledge of the world, in which case the collapse is just updating our knowledge based on new information. The latter takes a "non-realistic" view of the wave function. (Or "non-physical"--I'm not sure what "realism" means). So I can sort-of see that whether collapse is local or not depends on whether you view the wave function realistically.

But the second choice, that the wave function isn't to be taken realistically/physically was exactly what Einstein assumed. He thought that both the probabilistic aspects of quantum and the nonlocal aspects were due to the fact that quantum mechanics was not a fundamental theory, but that the wave function was some kind of statistical summary of a microscopic reality that we don't have a theory for, yet. That was the whole point of the EPR argument, to show that there was some reality that was not being reflected in the wave function.

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entropy1 and AlexCaledin
But even if Werner is right, his argument is murky enough that it's hyperbole to call someone a "crackpot" for not agreeing with him (as rubi called Maudlin).
I'm not calling him a crackpot because I don't agree with him. I'm calling him a crackpot because makes no effort to understand the criticism and rather prefers to respond polemically. If you read Werner's article, you will see that Werner considers Maudlin a crackpot as well. He's just polite enough not say it directly.

In standard operationalist quantum theory, the objects of interest are particles for instance (or fields in QFT) and their state is given by a wave function. If you claim that the wave function is real, this is a shift of perspective. The objects of interest aren't the particles anymore, but rather the wave function itself. It is a physical object rather than just a container of information about physical objects ("a state"), so it has a state itself, which contains the information about the physical object called "wave function". This state is an element of a simplex (the space of distributions on phase space, where by phase space I mean classical phase space as in Hamiltonian classical field theory).

Perhaps. But even if that is true, it doesn't show how operational quantum mechanics is local. Realism is a prerequisite for Maudlin's definition of locality, so at best one has to say that the notion of locality on operational quantum mechanics is empty. One can define another notion of locality, but then it wouldn't contradict Maudlin - it would just be a different definition.

Edit: Regarding state - would Werner's argument work if one were using an operational definition of state, eg. if we consider both classical and quantum states to be just containers of information? Thus for example, if we take the quantum state to be real, the "state" as defined in Eq 12 of https://arxiv.org/abs/quant-ph/0101012 would still not be a simplex, even though the theory is nonlocal.

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But even if that is true, it doesn't show how operational quantum mechanics is local.
I agree with that. My point is however that we can't claim that it is non-local, which is what Maudlin does.

Realism is a prerequisite for Maudlin's definition of locality
I fully agree, but Maudlin denies that he needs to assume realism.

at best one has to say that the notion of locality on operational quantum mechanics is empty. One can define another notion of locality, but then it wouldn't contradict Maudlin - it would just be a different definition.
Well, there is one single notion of locality that applies to all theories that can be formulated on Lorentzian spacetimes (see my post #22 and wikipedia for additional information) and all other notions of locality must be derived from it. Bell's (and Maudlin's) criterion follows from the standard notion plus the assumption of classicality. It's a special case of the general principle.

Gold Member
I'm not calling him a crackpot because I don't agree with him. I'm calling him a crackpot because makes no effort to understand the criticism and rather prefers to respond polemically.
I don't understand the criticism either. Can you explain it?
Can you point out the flaw in this argument of Maudlin:
"if a theory predicts perfect correlations for the outcomes of distant experiments, then either the theory must treat these outcomes as deterministically produced from the prior states of the individual systems or the theory must violate EPR-locality. The argument is extremely simple and straightforward. The perfect correlations mean that one can come to make predictions with certainty about how system S1 will behave on the basis of observing how the other, distant, system S2 behaves. Either those observations of S2 disturbed the physical state of S1 or they did not. If they did, then that violates EPR-locality. If they did not, then S1 must have been physically determined in how it would behave all along. That’s the argument, from beginning to end. (That’s also the point of Bell’s discussion of Bertlmann’s socks.) So preserving EPR-locality in these circumstances requires adopting a deterministic theory. Where, in this argument, does any presupposition about the geometry of the state space play any role? Nowhere."