Quantum Mechanics with a Hidden Variable!

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Quantum Mechanics with a Hidden Variable!

Postby FrediFizzx » Mon Jun 10, 2019 1:20 pm

Heinera wrote:
Yablon wrote: So you have ferreted out the hidden variable, just as I thought! Congratulations!!! :lol:

Yes, but only because a simple binary hidden variable is so easy to ferret out. So what?

Well, Jay's point is that your hidden variable wasn't hidden after all. But Bell only specified that the outcomes are +/- 1. So each of your A and B's still have outcomes that are +/- 1 no matter what the HV is. I hope you see that now.
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Re: Quantum Mechanics with a Hidden Variable!

Postby Yablon » Mon Jun 10, 2019 1:31 pm

Heinera wrote:
Yablon wrote: So you have ferreted out the hidden variable, just as I thought! Congratulations!!! :lol:

Yes, but only because a simple binary hidden variable is so easy to ferret out. So what?

"So what?" Don't you see? You have disproved yourself by your own contradiction:

You postulate a binary hidden variable. Then you prove that your hidden variable is not hidden because you can make observations which tell you what it is. So your postulate that what you called a hidden variable is really a hidden variable is FALSE. So your "proof" is entirely irrelevant to anything that truly is a hidden variable in the sense of Bell, or in any other sense that makes sense.
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Re: Quantum Mechanics with a Hidden Variable!

Postby FrediFizzx » Mon Jun 10, 2019 1:34 pm

Here is another way to derive the EPR-Bohm correlation for QM based on Jay's eq. (1.11) here.

Image

So there are a few different ways to derive the QM correlation. I like this one because it is a direct calculation of the bra-ket for the singlet with the detection observables.
.
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Re: Quantum Mechanics with a Hidden Variable!

Postby Heinera » Mon Jun 10, 2019 1:38 pm

Yablon wrote:You postulate a binary hidden variable.

I have not postulated a hidden variable. There is a hidden variable postulated in the paper under discussion, but I had nothing to do with it.
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Re: Quantum Mechanics with a Hidden Variable!

Postby Yablon » Mon Jun 10, 2019 1:52 pm

Heinera wrote:
Yablon wrote:You postulate a binary hidden variable.

I have not postulated a hidden variable. There is a hidden variable postulated in the paper under discussion, but I had nothing to do with it.

Oh my God!

Your own supposed "proof," with the values you claim to have obtained added, is below:

Heinera wrote:What? This is of course exactly what I proved. Let me repeat:

takes binary values, let's call them "" and "" respectively.

Then the predicted combinations of outcomes can only be

or


In other words, two.


So what YOU are denoting as a hidden variable in YOUR supposed proof above cannot really be HIDDEN and so you have proven nothing about binary hidden variables in the paper under discussion, or in any other situation. If you cannot see that, or if you do not understand the basics of a proof by contradiction (https://en.wikipedia.org/wiki/Proof_by_contradiction), then I cannot say anything more to help you see that. Sorry. :(

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Re: Quantum Mechanics with a Hidden Variable!

Postby Heinera » Mon Jun 10, 2019 2:08 pm

But this is of course your hidden variable, as presented in the paper. And you agreed in another thread that the hidden variable should include all relevant information that determines the outcomes +1 or -1 for Alice and Bob. Then the conclusion is inevitable: A hidden variable that takes only two values can only produce two combinations. Which is in conflict with the QM predictions.
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Re: Quantum Mechanics with a Hidden Variable!

Postby FrediFizzx » Mon Jun 10, 2019 2:36 pm

Hi Folks,

Just so lurkers don't get confused by Heine's nonsense, Bell only said that A(a, lambda) = +/- 1 and B(b, lambda) = +/- 1. That means for a binary valued HV,

A(a, +1) = +/- 1 and B(b, +1) = +/- 1
A(a, -1) = +/- 1 and B(b, -1) = +/- 1

So you are going to still get all 4 outcome possibilities, + +, - -, + -, and - +. What Bell specified has nothing to do with the 4 outcome possibilities. The outcomes also depend on a and b not just lambda.
.
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Re: Quantum Mechanics with a Hidden Variable!

Postby FrediFizzx » Mon Jun 10, 2019 2:42 pm

FrediFizzx wrote:Here is another way to derive the EPR-Bohm correlation for QM based on Jay's eq. (1.11) here.

Image

So there are a few different ways to derive the QM correlation. I like this one because it is a direct calculation of the bra-ket for the singlet with the detection observables.
.

A reason why we used the Pauli identities for the correlation calculation in the paper here, is that so we could show that the cross products in eq. (10) are in fact pointing opposite of each other thus demonstrating that we in fact have left and right handed singlets.
.
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Re: Quantum Mechanics with a Hidden Variable!

Postby gill1109 » Mon Jun 10, 2019 9:25 pm

Yablon wrote:No matter what else we may or may not know about "hidden variables," including whether local hidden variables do or even can exist in nature, one thing we know is this: if they exist, they are HIDDEN. They can never be detected by human observational equipment, by definition. So, to suggest that some experiment which uses the 2x2=4 combinations Alice's measurement together in some way with Bob's measurement to ferret out the actual value of a hidden variable, is entirely contradicted by the hidden variable being HIDDEN. If you were able to deduce some physical variable of any sort out of Alice's in combination with Bob's , whatever else that physical variable might be, it sure as heck would not be hidden any more. All you would prove is that the variable you deduced was not hidden. You would not have deduced a thing about any variables -- if they exist -- which truly are "hidden."

Sorry Jay, your definition of "hidden" is a common misinterpretation, but it is wrong. There was absolutely no intention in the minds of those who introduced the term hidden variable that such variables *by definition* could not be observed. The only intention was that those are the variables whose "mere" statistical variation is responsible for the statistical variation in outcomes which we do observe. The outcome of a coin toss is determined by initial velocity, initial angular momentum, etc etc etc. The outcome is heads or tails with more or less equal probability and it is only "apparently" random because it was actually determined, ie deterministically generated, through the values at the start of the experiment. Recall statistical mechanics! We can't fix in advance the positions and momenta of those 10^23 particles. We can't know them. They are "hidden variables".
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Re: Quantum Mechanics with a Hidden Variable!

Postby Mikko » Mon Jun 10, 2019 11:44 pm

gill1109 wrote:
Yablon wrote:No matter what else we may or may not know about "hidden variables," including whether local hidden variables do or even can exist in nature, one thing we know is this: if they exist, they are HIDDEN. They can never be detected by human observational equipment, by definition. So, to suggest that some experiment which uses the 2x2=4 combinations Alice's measurement together in some way with Bob's measurement to ferret out the actual value of a hidden variable, is entirely contradicted by the hidden variable being HIDDEN. If you were able to deduce some physical variable of any sort out of Alice's in combination with Bob's , whatever else that physical variable might be, it sure as heck would not be hidden any more. All you would prove is that the variable you deduced was not hidden. You would not have deduced a thing about any variables -- if they exist -- which truly are "hidden."

Sorry Jay, your definition of "hidden" is a common misinterpretation, but it is wrong. There was absolutely no intention in the minds of those who introduced the term hidden variable that such variables *by definition* could not be observed. The only intention was that those are the variables whose "mere" statistical variation is responsible for the statistical variation in outcomes which we do observe. The outcome of a coin toss is determined by initial velocity, initial angular momentum, etc etc etc. The outcome is heads or tails with more or less equal probability and it is only "apparently" random because it was actually determined, ie deterministically generated, through the values at the start of the experiment. Recall statistical mechanics! We can't fix in advance the positions and momenta of those 10^23 particles. We can't know them. They are "hidden variables".

One should also note that there is no "hidden variable" in the EPR paper. In Bell's (1964) response nothing used in the derivation of Bell's inequality is called "hidden" although the term "hidden variable" is otherwise used (without definition).
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Re: Quantum Mechanics with a Hidden Variable!

Postby Joy Christian » Mon Jun 10, 2019 11:53 pm

gill1109 wrote:
There was absolutely no intention in the minds of those who introduced the term hidden variable that such variables *by definition* could not be observed. The only intention was that those are the variables whose "mere" statistical variation is responsible for the statistical variation in outcomes which we do observe.

This is wrong.

It contradicts what John Bell wrote in the opening paragraph of his 1965 paper:

John S. Bell wrote:
These hypothetical `dispersion free' states would be specified not only by the quantum mechanical state vector but also by additional `hidden variables' --- `hidden' because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate.

In other words, if `hidden variables' are observable, then quantum mechanics can be demonstrated to be wrong by appropriate experiments.

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Re: Quantum Mechanics with a Hidden Variable!

Postby Heinera » Tue Jun 11, 2019 3:23 am

Joy Christian wrote:
gill1109 wrote:
There was absolutely no intention in the minds of those who introduced the term hidden variable that such variables *by definition* could not be observed. The only intention was that those are the variables whose "mere" statistical variation is responsible for the statistical variation in outcomes which we do observe.

This is wrong.

It contradicts what John Bell wrote in the opening paragraph of his 1965 paper:

John S. Bell wrote:
These hypothetical `dispersion free' states would be specified not only by the quantum mechanical state vector but also by additional `hidden variables' --- `hidden' because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate.

In other words, if `hidden variables' are observable, then quantum mechanics can be demonstrated to be wrong by appropriate experiments.

***


No, he didn't write "observable", he wrote "could actually be prepared". It means that if we had a mechanism to actually assign definite values to the "hidden" variable in the preparation of the (thought)experiment, QM would be inadequate, because we could then design completely deterministic experiments.
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Re: Quantum Mechanics with a Hidden Variable!

Postby Joy Christian » Tue Jun 11, 2019 3:38 am

Heinera wrote:
No, he didn't write "observable", he wrote "could actually be prepared". It means that if we had a mechanism to actually assign definite values to the "hidden" variable in the preparation of the (thought)experiment, QM would be inadequate, because we could then design completely deterministic experiments.

I disagree. Read Bell's 1965 paper in full to understand what he meant by his words I have quoted.

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Re: Quantum Mechanics with a Hidden Variable!

Postby FrediFizzx » Tue Jun 11, 2019 9:03 am

Hmm... apparently there is some disagreement on what "hidden variable" means exactly. Searching Google is not very helpful either. I suggest that we go with the notion that "hidden" means that the variable can't ever be observable. Though experimenters are very clever and probably could deduce what the variable is indirectly.

Now, in the case of this paper which this thread is about, the variable is for whether the singlet is right handed or left handed. Could an experiment be able to observe the handedness of the individual particles being detected? Assuming the singlet handedness is transferred to the individual particles which is probably a safe assumption to make. Alternately, could the handedness of the singlet be determined before it separated. Probably not.
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Re: Quantum Mechanics with a Hidden Variable!

Postby Mikko » Tue Jun 11, 2019 9:42 am

FrediFizzx wrote:I suggest that we go with the notion that "hidden" means that the variable can't ever be observable.

The concept "can't ever be observable" hardly is useful. Even if some theory predicts that some variable of the theory cannot be observed, it does not exclude the possibility that something not considered in the theory may permit the detection. For example, Bohm's non-local hidden-variable theory is not significantly altered if a way to measure that variable is found. Instead, a more useful concept is "not yet observed".
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Re: Quantum Mechanics with a Hidden Variable!

Postby Yablon » Tue Jun 11, 2019 9:49 am

FrediFizzx wrote:Hmm... apparently there is some disagreement on what "hidden variable" means exactly. Searching Google is not very helpful either. I suggest that we go with the notion that "hidden" means that the variable can't ever be observable.

That is a good place to start, and I certainly come at this from the personal view that "hidden" means "real but not observable" no matter how clever your experiment. But to make that stick as a matter of science not philosophy, the deeper and threshold question, IMHO, is about what constitutes an "element of reality." Because presumably, a "hidden" variable is a "hidden" element of reality, and then we are into what is meant by "hidden," and what gives rise to something becoming "hidden."

This, IMHO, this is where the uncertainty principle of what Richard calls the "conventional dogmas of conventional QM" comes into play, because of how it gives rise to physical quantities which are not "simultaneously observable," leading to both observable and unobservable elements of reality. Which is to say, I believe, personally, that the difficulties many have had with the uncertainty principle over the years stem from not properly recognizing "inability to simultaneously measure" for local systems or single particles as the root source of local hidden variables in the physical world. I am not going to try to shove this opinion of mine down anybody else's throat, but I will try to lay out objective evidence which I hope may convince you also of this view on a scientific, not personal opinion, basis.

Specifically, at bottom, we need to get past my humble opinion, and Richard's humble opinion, and Heine's humble opinion, and Fred's humble opinion, and Mikko's humble opinion, and everybody else's opinion humble or not, and follow the wisdom of EPR that "the elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements." Can everyone at least agree to that?

In sum, can we all start out at least from the same opinion about using this EPR wisdom to identify elements of reality, even if for now we do not necessarily share the same opinion as what those elements of reality will turn out to be?

Jay
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Re: Quantum Mechanics with a Hidden Variable!

Postby Heinera » Tue Jun 11, 2019 10:22 am

The reason Bell called his variable "hidden," I guess, is that if it were in fact observable, QM would be obviously incomplete and his whole paper would be moot. But for his argument (Bell's theorem), the observability (or not) of the variable is irrelevant. What is relevant is that the variable can not be prepared with a definite value, so we should rather call it "uncontrollable" instead of "unobservable".
Last edited by Heinera on Tue Jun 11, 2019 11:08 am, edited 1 time in total.
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Re: Quantum Mechanics with a Hidden Variable!

Postby Joy Christian » Tue Jun 11, 2019 10:40 am

Yablon wrote:Specifically, at bottom, we need to ... follow the wisdom of EPR that "the elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements." Can everyone at least agree to that?

In sum, can we all start out at least from the same opinion about using this EPR wisdom to identify elements of reality, even if for now we do not necessarily share the same opinion as what those elements of reality will turn out to be?

Before we move any further, I want to register my objection to what you have quoted as the wisdom of EPR. Without qualifications, that reads like a Bohr-type anthropocentric point of view. In my view, Einstein was right. He maintained that physical systems have intrinsic properties whether they are observed or not. To be precise about this -- and in support of my Einsteinian point of view -- let me quote the footnote 10 from this GHSZ paper:

https://aapt.scitation.org/doi/10.1119/1.16243

Image
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Re: Quantum Mechanics with a Hidden Variable!

Postby Heinera » Tue Jun 11, 2019 10:51 am

FrediFizzx wrote:Hi Folks,

Just so lurkers don't get confused by Heine's nonsense, Bell only said that A(a, lambda) = +/- 1 and B(b, lambda) = +/- 1. That means for a binary valued HV,

A(a, +1) = +/- 1 and B(b, +1) = +/- 1
A(a, -1) = +/- 1 and B(b, -1) = +/- 1

So you are going to still get all 4 outcome possibilities, + +, - -, + -, and - +. What Bell specified has nothing to do with the 4 outcome possibilities. The outcomes also depend on a and b not just lambda.
.

I specified that for a fixed pair of detector settings, you can only get two combinations of outcomes with a binary HV. For different settings, the two combinations can of course also be different. But this anyway contradicts the QM predictions, where you will observe all four possible combinations for almost any fixed pair of detector settings. (Exceptions are exactly opposite settings, or equal settings.)

It's as simple as this: When you flip a coin, there are only two possible outcomes. Not four.
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Re: Quantum Mechanics with a Hidden Variable!

Postby Yablon » Tue Jun 11, 2019 11:08 am

Joy Christian wrote:
Yablon wrote:Specifically, at bottom, we need to ... follow the wisdom of EPR that "the elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements." Can everyone at least agree to that?

In sum, can we all start out at least from the same opinion about using this EPR wisdom to identify elements of reality, even if for now we do not necessarily share the same opinion as what those elements of reality will turn out to be?

Before we move any further, I want to register my objection to what you have quoted as the wisdom of EPR. Without qualifications, that reads like a Bohr-type anthropocentric point of view. In my view, Einstein was right. He maintained that physical systems have intrinsic properties whether they are observed or not. To be precise about this -- and in support of my Einsteinian point of view -- let me quote the footnote 10 from this GHSZ paper...

Well, I also agree with Einstein "that physical systems have intrinsic properties whether they are observed or not." But by his own terms from EPR for defining reality, this was his philosophical view, and it ought to be confirmed, if possible, "by an appeal to results of experiments and measurements." And I believe that when this is done, these "experiments and measurements" vindicate Einstein's view over the Bohr-type anthropocentric view.

The point here is that if you start with the experiments and measurements themselves, you can prove by scientific method against the anthropocentric view. That is much more powerful than just asserting a view as philosophy, even if it is Einstein's.

Also, to be clear Einstein never for a moment abandoned his belief in scientific method: use experiments to confirm what you say! But that is entirely compatible with his view that physical systems may have properties which are not directly observable. And I did add "directly" to the last sentence, because it is important insofar as some realities are only indirectly observable as a result of statistical outcomes which they cause. Including the statistical correlation outcomes at the heart of this debate.
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