Can absence of hidden variables save locality?

[Demystifier]

Let me pose a brain teaser for those who believe that they understand quantum (non)locality, Bell, EPR, as well as logic, very well.

Assume that quantum mechanics is correct (i.e., that future loophole-free experiments will confirm violation of Bell inequalities).

Consider 2 statements, each of which is either true or false:
H: Hidden variables exist.
L: Nature is local.

We have the Bell theorem which, in symbolic notation, can be written as
H => not L ... (1)
i.e., if hidden variables exist then nature is not local.

But we also have the 1935 Einstein-Podolsky-Rosen result
L => H ... (2)
i.e., if nature is local (which they tacitly assumed) then hidden variables exist (i.e., "QM is incomplete"). The implication (2) is equivalent to
not H => not L ... (3)

Now consider (1) and (3) together. Either H or (not H) is true. But in both cases we have (not L). So, irrespective of whether hidden variables do or do not exist, nature is not local.

Is that a correct reasoning? Or if it isn't, where exactly the mistake is?

 

[unusualname]

In the Bell Case, we have H => Not L but this doesn't imply H (is true).

Now you have used different assumptions (EPR) to get Not H => Not L, so the two statements can't be applied simultaneously.

In fact the latter case (EPR) is not even a correct argument, unlike Bell's

 

[Demystifier]

Now you have used different assumptions (EPR) to get Not H => Not L,

What these different assumptions are?

In fact the latter case (EPR) is not even a correct argument

Why not?

 

[unusualname]

What these different assumptions are?

They assume local realism (duh!)

Why not?

because they assume local realism. :-)

 

[Demystifier]

They assume local realism (duh!)

Now you are logically inconsistent. Essentially, you say that they assume L to get Not H => Not L. But that's certainly not true, as should be obvious to anyone trained in classical logic.

because they assume local realism. :-)

There is nothing incorrect with assuming local realism, as long as the only goal is to infer what the logical consequences of that assumption would be.

In short, your objections are logically invalid.

Is there someone with better objections?

 

[unusualname]

the epr paper tries to show that quantum mechanics is not complete since it is not compatible with local realism.

It is an incorrect argument and from that you can not conclude Not H => Not L, like you are trying to.

 

[Demystifier]

the epr paper tries to show that quantum mechanics is not complete since it is not compatible with local realism.

Yes, that's what they try to show (successfully or not), but that's not what I used in my argument. Instead, in my argument I used the following proposition EXTRACTED from their result:

Proposition:
IF local realism is valid, THEN quantum mechanics is not complete.

If you are familiar with the classical logic, you should understand that the validity of that proposition does not depend on whether local realism is valid or not.

Note the difference between that extracted proposition which I use and the original EPR claim which I DON'T use!
EPR - original:
Local realism IS valid, THEREFORE quantum mechanics is not complete.

It is an incorrect argument and from that you can not conclude Not H => Not L, like you are trying to.

The proposition above written in symbolic notation is
L => H
which is equivalent to
Not H => Not L
Therefore, the conclusion Not H => Not L is logically valid.

 

[skippy1729]

H: Hidden variables exist.
L: Nature is local.
R: Observables have a freestanding reality with prexisting values prior to measurement.

L & R -> H

equivalently not H -> not L OR not R.

 

[Demystifier]

Basics of logic

I'm not sure whether unusualname understands what I am saying to him, so let me be more explicit. The expression
A => B
does NOT assume A. That expression does NOT mean "A is true, therefore B is true". Instead, that expression means
"IF A is true, THEN B is true".

 

[unusualname]

No Hidden variables and locality are clearly not incompatible (eg MWI, ensemble interpretation etc), so any argument showing Not H => Not L must be flawed, like the EPR one.

 

[Demystifier]

H: Hidden variables exist.
L: Nature is local.
R: Observables have a freestanding reality with prexisting values prior to measurement.

L & R -> H

equivalently not H -> not L OR not R.

So? Is that supposed to be an objection against my argument?

 

[Demystifier]

No Hidden variables and locality are clearly not incompatible

Are you sure that this is what you wanted to say?

 

[ueit]

Consider 2 statements, each of which is either true or false:
H: Hidden variables exist.
L: Nature is local.

We have the Bell theorem which, in symbolic notation, can be written as
H => not L ... (1)
i.e., if hidden variables exist then nature is not local.

I strongly disagree with this argument. As I stated many times before, Bell's theorem is simply irrelevant to any classical field theory.

Take for example classical electrodynamics. An EPR experiment (and any other quantum experiment) could be reduced to a n-body problem. You describe the whole experiment in terms of position and momenta of charged particles (electrons and nuclei), plug the data into a computer and start the simulation. The theory will then predict both the position/momenta of entangled particles and the detection "choices".

But Bell's theorem asks for those choices to be random, therefore not correlated to the initial position and momenta of the particles. And, predictable, it follows that the classical theory is wrong. Or is it? Can you point out a glaring logical mistake here?

If you keep locality, realism and determinism there is no contradiction with experiments. At the moment you introduce fundamental randomness (because this is the direct implication of free choices) you must also introduce non-locality, as there rely is no way to get distant correlation in a probabilistic universe other than by instantaneous communication.

So, I would say that all quantum experiments are nothing but a reductio ad absurdum for fundamental randomness.

 

[unusualname]

Are you sure that this is what you wanted to say?

Yes, if hidden variables are not assumed that does not mean locality can not be correct, maybe my sentence structure is bad, I mean "No hidden variables" doesn't imply "non-locality", since we have logically consistent models of QM which do not have hidden variables but assume locality (MWI, Ensemble, ...)

 

[Demystifier]

... so any argument showing Not H => Not L must be flawed, like the EPR one.

I'm not saying that it is not flawed. But if it is, I insist on pointing to the precise location (and logically correct explanation) of the mistake. And that requires very deep understanding of Bell and EPR (as well as a solid understanding of logic) which not many physicists have.

 

[skippy1729]

So? Is that supposed to be an objection against my argument?

Yes.

L & NOT H -> NOT R

A different conception of reality is implied.

"What is observed certainly exists, about what is not observed we are still free to make suitable assumptions. This freedom is then used to avoid paradoxes." C. F. Von Weizsacker

 

[unusualname]

I'm not saying that it is not flawed. But if it is, I insist on pointing to the precise location (and logically correct explanation) of the mistake. And that requires very deep understanding of Bell and EPR (as well as a solid understanding of logic) which not many physicists have.

The precise location where the EPR argument goes wrong is their assumption that hidden variables must exist since otherwise QM is wrong. No, QM can be correct with or without hidden variables. It does not require a deep understanding of logic to see this.

 

[DrChinese]

Let me pose a brain teaser for those who believe that they understand quantum (non)locality, Bell, EPR, as well as logic, very well.

Assume that quantum mechanics is correct (i.e., that future loophole-free experiments will confirm violation of Bell inequalities).

Consider 2 statements, each of which is either true or false:
H: Hidden variables exist.
L: Nature is local.

We have the Bell theorem which, in symbolic notation, can be written as
H => not L ... (1)
i.e., if hidden variables exist then nature is not local.

But we also have the 1935 Einstein-Podolsky-Rosen result
L => H ... (2)
i.e., if nature is local (which they tacitly assumed) then hidden variables exist (i.e., "QM is incomplete"). The implication (2) is equivalent to
not H => not L ... (3)

Now consider (1) and (3) together. Either H or (not H) is true. But in both cases we have (not L). So, irrespective of whether hidden variables do or do not exist, nature is not local.

Is that a correct reasoning? Or if it isn't, where exactly the mistake is?

I don't think (3) is a valid true conclusion of EPR. If we call "QM being incomplete" as I and "QM predictions accurate" as QM, then they say QM+L+H -> I. Bell essentially proved that QM -> ~L or ~H (I think your notation is fine on this) which means that QM+L+H cannot all be true.

Therefore I wouldn't agree with the assessment (2) that L -> H. Can you explain further how you obtained that? Maybe I missed something.

 

[Demystifier]

... since we have logically consistent models of QM which do not have hidden variables but assume locality (MWI, Ensemble, ...)

Ah, now I see your point. You are right that, if MWI and Ensemble really are local theories without hidden variables, then my extraction from EPR is wrong. But you haven't explain where exactly the mistake in my extraction from EPR is, which is exactly what I insist on.

 

[Demystifier]

Yes.

L & NOT H -> NOT R

A different conception of reality is implied.

"What is observed certainly exists, about what is not observed we are still free to make suitable assumptions. This freedom is then used to avoid paradoxes." C. F. Von Weizsacker

Sorry, but you still haven't say here what is supposed to be wrong in my argument. Or at least not explicitly.

 

[Demystifier]

The precise location where the EPR argument goes wrong is their assumption that hidden variables must exist since otherwise QM is wrong.

As I explained, I do not use that assumption in my argument.

 

[Demystifier]

Therefore I wouldn't agree with the assessment (2) that L -> H. Can you explain further how you obtained that? Maybe I missed something.

My claim (subject to criticism) is that this is essentially what EPR obtained in 1935, before the theorem of Bell was known. More precisely, they assumed locality (hence L) and then derived incompleteness (hence => H). Are you familiar with the 1935 EPR paper? If not, then you should read it first before attempting to argue on this thread.

 

[Demystifier]

I don't think (3) is a valid true conclusion of EPR. If we call "QM being incomplete" as I and "QM predictions accurate" as QM, then they say QM+L+H -> I.

No, in your notation they say QM+L -> H -> I. H is not their assumption. H is their result obtained from assumptions QM and L.

 

[DrChinese]

Demystifier: I know you see the hidden variables as being a non-local context, but in the present. So your view is contextual although you consider it deterministic (realistic?).

I see them as being part of a context which has both past and future components, otherwise respecting locality (but leading to non-local correlations). But I don't know if that interpretation would be considered any more local or less contextual than yours! And I consider this to be a non-realistic view.

So I think the labels can be misleading if we are not careful.

 

[unusualname]

No, in your notation they say QM+L -> H -> I. H is not their assumption. H is their result obtained from assumptions QM and L.

Yes but H is not deduced correctly, since they are arguing from a 1930s viewpoint where the possibility that QM might be non-real was still considered incredible, so (logically, according to them) it must be incomplete and hence H must be true (wrong!)

Now of course we have grown up and fully understand that QM (and nature) is probabilistic, and the realists are akin to people believing the sun orbits the Earth in times past.

It is not relevant that the EPR argument is mathematically logically correct, it has to have reasonable physics as shown by experiments, I can probably mathematically prove a pot of gold at the end of the rainbow if I am allowed to assume things which are not true (ie. shown to be by experiment) of nature.

 

[skippy1729]

Sorry, but you still haven't say here what is supposed to be wrong in my argument. Or at least not explicitly.

You presupposed a concept of realism in your use of locality. You just proved that local realism is not possible. A failure of local realism implies a failure of locality OR a failure of realism.

 

[zonde]

But we also have the 1935 Einstein-Podolsky-Rosen result
L => H ... (2)
i.e., if nature is local (which they tacitly assumed) then hidden variables exist (i.e., "QM is incomplete"). The implication (2) is equivalent to
not H => not L ... (3)

Now consider (1) and (3) together. Either H or (not H) is true. But in both cases we have (not L). So, irrespective of whether hidden variables do or do not exist, nature is not local.

Is that a correct reasoning? Or if it isn't, where exactly the mistake is?

(2) is incorrect
The correct one is QM+L => H, as you said yourself here:

No, in your notation they say QM+L -> H -> I. H is not their assumption. H is their result obtained from assumptions QM and L.

 

[JesseM]

But we also have the 1935 Einstein-Podolsky-Rosen result
L => H ... (2)
i.e., if nature is local (which they tacitly assumed) then hidden variables exist (i.e., "QM is incomplete").

Only if you adopt their particular version of locality which assumes something akin to Bell's local beables that determine observed experimental outcomes (a non-realist might use a different definition of "locality" that is only concerned with whether the results of observable measurements can allow us to transmit signals FTL, for example). And there are also other hidden assumptions they make, like the assumption that each measurement yields a single unique result, which might be violated in a many-worlds type interpretation--see my post [post=1647627]here[/post] on how MWI advocates argue theirs is a local interpretation, and the simple "toy model" I provided in [post=1557143]this post[/post] showing how if there are multiple copies of each experimenter who observe different outcomes, and no need to decide which copy of an experimenter "over there" is part of the same world as a copy of an experimenter "over here" until there's been time for a signal to pass between them, then you can in principle explain Bell inequality violations in a local way.

 

[Fra]

I agree with skippy and JesseM.

The left side in the EPR implications contains local realism(LR), not just pure locality(L).

(Then of course there are different FORMS of realism. Alot of realism still persists today. The old kind of realism Einstein seeked is less common today, but structural realism as in the reality of the laws of nature irrespective of inference is more common. But I object even to this.)

/Fredrik

 

[zonde]

The left side in the EPR implications contains local realism(LR), not just pure locality(L).

It is very common to ascribe to EPR that it assumes local realism.

But let's look at this definition:
"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity."

In bold there is condition when we can speak about element of physical reality. And the point that a lot of people are missing is that it's a claim of QM that we can predict with certainty values of two non-commuting observables.

So if we assume that we can predict one of the two observables only approximately (i.e. it's contextual) then EPR paradox in that form does not hold any more.