I QM: Interesting View - Get the Inside Scoop

[facenian]

You still lack proof that your LC can be applied to QM. Where is the precise theory-independent definition of LC that contradicts QM?

Equations (7) and (8) in this paper https://arxiv.org/abs/2102.07524

Why are these two equations a precise theory-independent definition of LC?

They are precise because the definition is cast unambiguously in mathematical form. They are theory-independent regarding QM and local hidden variables because they are applicable to both theories independently.
The fact that to obtain QM we have to put \lambda=|\psi\rangle should not be a problem for any student with certain training in abstract reasoning. It means that the expression is general enough to encompass both theories. When the only information is the quantum state and the probabilities are given by the Born rule or the projection postulate we have ordinary QM. When the $\lambda$ variables represent more (or different) of what is contained in QM we no longer have QM.

I see neither an encoding of local nor one of causality. (7) is just a denial of the independence of $a$ and $b$ given $\lambda$, which is obvious when you set $a=b$ - even classically.

Precisely! That encodes the heart of the local causality concept since $a$ and $b$ are space-like determined having an instant influence. QM notoriously fails to pass this criterion.
You don't like it? Perfect, the solution is to change the definition of what locality should mean.
My claim is: if we want our beloved theory to be local, let us make it local but in a coherent way, not by recoursing to denialism nor by merely declaring it local by decree or even worse: uttering tautologies devoid of any sensible meaning like "QM is local because the Bell theorem is the classical result". That is the message of the referenced paper.
PS: there may be other ways to make QM coherently local but my claim is that just declaring it local by definition is not enough because there are reasonable arguments to consider it as implying nonlocal effects therefore those arguments need counter-arguments to justify the locality.

[Moderator's note: Off topic content deleted.]

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

Thread reopened.

 

[Interested_observer]

It is not confusing as a well-defined concept, it is metaphysical and produces confusion. An example of this confusion is the belief that the Bell inequality requires such a hypothesis for its derivation. Another confusion is that determinism implies it. Determinism only means you can predict a result with certainty it does not have to assume its pre-existence, however, EPR assumes the pre-existence by definition. It is not "incorrect"; it is unnecessary and metaphysical because makes an assumption about the existence of what has not been actually measured.
Einstein with his keen insight immediately reacted to this since he did not write the paper.
Unfortunately, the concept is widespread and widely used except perhaps by experts in foundations.

This may be a little off topic, but the way I see it is that the issue, problem, or source of confusion is that Einstein was referring to a SINGLE case of a 2-photon system, whereas nearly everyone else is arguing from an ensemble of identically prepared systems. By the way, how do we KNOW each part of the ensemble is IDENTICALLY prepared? Isn’t that just an assumption based on our current level of knowledge of what we think may occur at the leading edge, or center, or exiting edge of an SG device? Or knowledge of (or maybe lack of consideration of) EXACTLY where the individual electron or ion passes a slit in relation to the slit edges or boundaries and how this may possibly affect different parts of the prepared ensemble?

 

[PeterDonis]

By the way, how do we KNOW each part of the ensemble is IDENTICALLY prepared?

Because we use the same device as a source for the entire ensemble. "Identically prepared" does not mean we know the exact details of each individual particle in the ensemble. It just means, for example, "we prepared a beam of electrons by firing them from a cathode ray tube at such-and-such voltage".

 

[AndreiB]

It is not confusing as a well-defined concept, it is metaphysical and produces confusion. An example of this confusion is the belief that the Bell inequality requires such a hypothesis for its derivation.

This belief is correct, there is no confusion. Bell clearly states this in his paper:

On the Einstein Podolsky Rosen paradox
https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf

"THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics."

So, Bell investigates the only theories that could preserve locality (the hidden-variable ones). His theorem is not to be applied on non-hidden variable theories since those have been proven to be non-local by the EPR argument.

Another confusion is that determinism implies it.

In the context of the EPR argument the "elements of reality", the hidden variables must determine the outcomes. Without such deterministic behavior the perfect correlations cannot be guaranteed. So, determinism in regards to those "elements of reality" is a conclusion of the argument. Locality requires deterministic hidden variables. Of course, you can have non-deterministic hidden variables but those cannot do the job, they are useless.

Determinism only means you can predict a result with certainty it does not have to assume its pre-existence

If you can predict something with certainty without disturbing the system, as EPR specified, that something must preexist. If the measurement at A does not disturb the system at B, the state of B (or its lack of state if you are a non-realist) remains unchanged after that measurement. But QM says that after the A measurement B is in a well-defined spin state. So, it logically folows that even prior the A measurement B was in a well-defined spin state, otherwise the A measurement disturbed B. Really, there is no counter to that. The argument is rock-solid.

EPR assumes the pre-existence by definition.

No, it does not. EPR makes exactly 2 assumptions:

1. The results are always corelated. (this is not even an assumption anymore, it's an experimental fact), and
2. locality (the A measurement does not disturb B)

The pre-existence of the hidden variables are deduced from the above assumptions. It's a conclusion, not a premise.

It is not "incorrect"; it is unnecessary and metaphysical because makes an assumption about the existence of what has not been actually measured.

I agree that EPR made a mistake in including the non-comuting properties in their argument. Such a step was not necessary. The argument works perfectly with only the property that is actually measured. So, if you measure spin UP on Z at A you can deduce that you have spin DOWN on Z at B even before B was measured. There is no point to make any assumptions about the X-spin or Y-spin here.

 

[AndreiB]

it is not a hidden local variable theory, so Bell's theorem doesn't apply.

That means that it contradicts relativity.

Since "the state of the world" in the thermal interpretation is basically the quantum mechanical state, the problem is less to explain the correlations, but to explain why we observe definite measurement outcomes. And that is the measurement problem.

OK, any way you put it, the thermal interpretation does not explain the observed results in an EPR experiment. They are somehow determined by the state but we don't know how.

 

[vanhees71]

This may be a little off topic, but the way I see it is that the issue, problem, or source of confusion is that Einstein was referring to a SINGLE case of a 2-photon system, whereas nearly everyone else is arguing from an ensemble of identically prepared systems. By the way, how do we KNOW each part of the ensemble is IDENTICALLY prepared? Isn’t that just an assumption based on our current level of knowledge of what we think may occur at the leading edge, or center, or exiting edge of an SG device? Or knowledge of (or maybe lack of consideration of) EXACTLY where the individual electron or ion passes a slit in relation to the slit edges or boundaries and how this may possibly affect different parts of the prepared ensemble?

We know this from validating it by measurements. E.g., the preparation of photon pairs in all 4 possible kinds of polarization-Bell states is well established using different kinds of parametric down conversion using birefringent crystals like BBO, and it's well established because the properties of such states predicted by QED are indeed observed with an amazing accuracy.

E.g., one of the seminal papers, which is very well understandable, describing the realization of type-II phase matching

P. G. Kwiat et al, New High-Intensity Source of Polarization-Entangled Photon Pairs, PRL 75, 4337 (1995)
https://doi.org/10.1103/PhysRevLett.75.4337

 

[gentzen]

That means that it contradicts relativity.

The thermal interpretation is just an interpretation, not a modified quantum theory. Therefore, the expectation is that it should not contradict relativity more than quantum (field) theory itself. More generally, there is no reason to expect that it will contradict relativity more than the theory/model that you interpret with its help. And in cases where it currently does (for example because it didn't yet work out exactly what to do with Gauge freedom or renormalization), there is little reason to assume that this could not be fixed.

OK, any way you put it, the thermal interpretation does not explain the observed results in an EPR experiment. They are somehow determined by the state but we don't know how.

Yes, we don't know exactly how the state determines the results. But we can try to workout which parts of the state have a big impact on the results, and which parts only have an extremely small impact on the results. The task is then to show that neither the most exact precision of the state of the particles themselves, nor the state of some atom in a galaxy lightyears away has a significant impact, but that the state of the measurements devices, and other "local" properties of the state indeed has some impact.

 

[A. Neumaier]

They are precise

But they are not a definition from which one could see how they are related to informal notions of causality and locality. Just dropping some formulas does not give them physical contents.

 

[A. Neumaier]

If your "extended object" doesn't determine the results then it must behave like a perfectly rigid object which is impossible in relativity. Which is it?

The extended object is the 2-photon state, That it is not rigid does not matter.

how the "Joint properties" of the 2-photon relate to the observed measurement outcomes? If they strictly determine the outcomes we are in the case of a hidden variable theory. If not, the 2-photon behaves as perfectly rigid rod, violating relativity. Since Neumaier explicitly agreed that space-like events cannot cause each other he should say that what he proposes is a hidden variable approach. However, he claims:

"The thermal interpretation gives a natural, realistic meaning to the standard formalism of quantum mechanics and quantum field theory in a single world, without introducing additional hidden variables."

The variables I introduce are the q-expectations. They are nonlocal for a 2-photon state. They are hidden in the sense of Bell's terminology but not in the more standard sense that quantum mechanics would have to be completed, since q-expectations belong to the standard toolkit of quantum mechanics.

 

[AndreiB]

The thermal interpretation is just an interpretation, not a modified quantum theory. Therefore, the expectation is that it should not contradict relativity more than quantum (field) theory itself. More generally, there is no reason to expect that it will contradict relativity more than the theory/model that you interpret with its help.

I disagree. QM is non-local only if it assumed to be complete (no hidden variables). If one does not make that assumption the theory could be local. So, it's possible that some interpretations conflict with relativity and some other don't. As you specified that the thermal interpretation rejects local hidden variables, it has to be non-local in the sense that space-like events cause each other. This is conflict with relativity.

 

[AndreiB]

The variables I introduce are the q-expectations. They are nonlocal for a 2-photon state.

Are they non-local in the sense that space-like events cause each other?

 

[gentzen]

I disagree. QM is non-local only if it assumed to be complete (no hidden variables). If one does not make that assumption the theory could be local. So, it's possible that some interpretations conflict with relativity and some other don't.

Indeed, it is possible that some interpretations conflict with relativity and some others don't. What I wrote was a reply to your assertion: "That means that it contradicts relativity."

Also note that an interpretation can have non-local aspects without contradicting relativity. For example, the randomness occurring in the Copenhagen interpretation can be non-local. But this sort of non-locality doesn't necessarily contradict relativity. If the non-locality could be used to enable faster than light communication, then the interpretation would clearly contradict relativity.

I admit that there are other ways to contradict relativity. For example, even pilot wave theory doesn't allow faster than light communication. But it has a preferred frame of reference, and you might feel that this contradicts relativity. Fine with me, but then you should be specific about which parts of an interpretation contradict relativity from your point of view.

As you specified that the thermal interpretation rejects local hidden variables, it has to be non-local in the sense that space-like events cause each other. This is conflict with relativity.

Well, space-like events can certainly be correlated with each other. But as long as you cannot clearly distinguish between whether it is event A that causes event B, or event B that causes event A, it remains unclear whether the events A and B really cause each other.

 

[AndreiB]

Also note that an interpretation can have non-local aspects without contradicting relativity. For example, the randomness occurring in the Copenhagen interpretation can be non-local. But this sort of non-locality doesn't necessarily contradict relativity. If the non-locality could be used to enable faster than light communication, then the interpretation would clearly contradict relativity.

The problem is that relativity does not distinguish between space-like events that enable communication and those that don't. Say you measure 10 spins at A: 0010101011. If those spins were not already at B (no local hidden variables) it means that this particular string was teleported instantly at B. This is an explicit faster than light information transfer.

you should be specific about which parts of an interpretation contradict relativity from your point of view.

Given that relativity cannot say if A sent the "signal" 0010101011 and B received it or vice-versa you need to introduce an absolute reference frame, otherwise different accounts would contradict each other. So you are in the same situation as Bohm's theory.

Well, space-like events can certainly be correlated with each other. But as long as you cannot clearly distinguish between whether it is event A that causes event B, or event B that causes event A, it remains unclear whether the events A and B really cause each other.

As long as you assume that there are no local hidden variables we know for a fact that A and B cause each other, it's the only logical conclusion.

 

[vanhees71]

Are they non-local in the sense that space-like events cause each other?

Of course not. Microcausality is implemented in the very construction of all our relativistic QFT models. So there cannot be causal conncections between space-like separated events.

I also don't understand, why one should call correlation functions with more than one spacetime argument "nonlocal". After all the correlations, described by these correlation functions are observed in local experiments with the "registration events" of the outcome at the spacetime arguments of these functions.

 

[A. Neumaier]

Are they non-local in the sense that space-like events cause each other?

The q-expectations of fields are local, and the n-point functions for $n>1$ are nonlocal because they depend on more than one spacetime argument. Bell experiments require for their analysis the 2-point functions.

I also don't understand, why one should call correlation functions with more than one spacetime argument "nonlocal".

For the same reason why the distance to the andromeda nebula is a nonlocal quantity. Anything that depends on more than one spacetime coordinate is necessarily nonlocal.

pilot wave theory doesn't allow faster than light communication.

it is nonrelativistic, hence allows like all nonrelativistic QM instantaneous long distance effect. The probability of a particle prepared in a Gaussian state to be the next moment at Andromeda is nonzero.

This is an explicit faster than light information transfer.

No. B cannot extract any information from the correlations.

 

[vanhees71]

For the same reason why the distance to the andromeda nebula is a nonlocal quantity. Anything that depends on more than one spacetime coordinate is necessarily nonlocal.

Well, the physical meaning of a length between 2 points (non-local) and a correlation function, which describes correlations between two or more local (!) measurements is different.

 

[A. Neumaier]

Well, the physical meaning of a length between 2 points (non-local) and a correlation function, which describes correlations between two or more local (!) measurements is different.

2-point functions are called correlation functions, but in general they do not directly describe measurable correlations. They are just nonlocal mathematical expressions. Only sometimes they can be interpreted in terms of measured correlations.

Independent of this, measured correlations at distinct points are still bilocal since you compute them you need to measure at two points, not only at one.

 

[martinbn]

The distance to Andromeda is not a local quantity, but why would you call it nonlocal! The oposite of local is not always nonlocal, for example it could be global.

 

[gentzen]

The distance to Andromeda is not a local quantity, but why would you call it nonlocal! The oposite of local is not always nonlocal, for example it could be global.

Really? I always thought that the meaning of nonlocal is "not local". If it would mean something else, then I fear I would have to agree with vanhees71 that it is a burned word that should be avoided. Because if it doesn't mean "not local", then everybody will just form his own opinions about what it should mean.

 

[martinbn]

Really? I always thought that the meaning of nonlocal is "not local". If it would mean something else, then I fear I would have to agree with vanhees71 that it is a burned word that should be avoided. Because if it doesn't mean "non local", then everybody will just form his own opinions about what it should mean.

Well, i have seen "the local structure of manifolds..., while the global structure...". And i have never seen "the local structure of manifolds..., while the nonlocal structure...".

 

[gentzen]

Well, i have seen "the local structure of manifolds..., while the global structure...". And i have never seen "the local structure of manifolds..., while the nonlocal structure...".

But this seems consistent with what I said. You don't talk about "the not local structure of manifolds" or "the part of the structure of manifolds which is not local". So "nonlocal" and "not local" seem to mean the same thing, while "global" means something different from "not local", even so it implies "not local".

 

[vanhees71]

2-point functions are called correlation functions, but in general they do not directly describe measurable correlations. They are just nonlocal mathematical expressions. Only sometimes they can be interpreted in terms of measured correlations.

Independent of this, measured correlations at distinct points are still bilocal since you compute them you need to measure at two points, not only at one.

It depends about which two-point functions you are talking. Of course two-point Green's functions or proper vertex functions do not directly descibe observables. I was thinking, however, we are talking about correlation functions referring to measurable quantities like the two-point correlation function of the field intensities for two-photon measurements (see, e.g., Scully&Zubairy, Quantum Optics, Chpt. 21).

 

[A. Neumaier]

Well, i have seen "the local structure of manifolds..., while the global structure...". And i have never seen "the local structure of manifolds..., while the nonlocal structure...".

Global is a very special case of nonlocal, meaning depending on infinitely many points along a curve or a higher-dimensional submanifold.

 

[A. Neumaier]

It depends about which two-point functions you are talking. Of course two-point Green's functions or proper vertex functions do not directly descibe observables. I was thinking, however, we are talking about correlation functions referring to measurable quantities like the two-point correlation function of the field intensities for two-photon measurements (see, e.g., Scully&Zubairy, Quantum Optics, Chpt. 21).

The special case has the same properties as the general case, hence is as bilocal as general 2-point functions. Bilocal is not local, hence nonlocal. Pure time correlations are local.

 

[vanhees71]

Then call it bilocal or multilocal, it's still referring to local events ("clicks of well localized detectors").