Local Realistic Hidden Variables Quantum Mechanics (LRHVQM)

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

Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby FrediFizzx » Mon Oct 21, 2019 9:40 am

Heinera wrote:
gill1109 wrote:
Heinera wrote:
FrediFizzx wrote:Well, if you do the product calculation, A*B, you have (+/-1)(+/-1) = (+/-1).
.

Well, that was an extremely rudimentary calculation. It is of course possible to do much better than that, by evaluating the integral
.

Your notation is not very good. If it were true, I would write something like
where is the uniform Haar measure on the sphere .


It's the same, I was just using Bell's notation to avoid unnecessary confusion. Here is the probability density for the uniform (rotationally invariant) distribution on the sphere. (But I forgot a minus in the integrand, corrected now in the quotes above).

There is no doubt the result is correct; see page 161 in Peres for the derivation. It's just the familiar piecewise linear zigzag correlation.

gill1109 wrote:One certainly does have to worry about the sign. The devil is in the details. One also has to worry about Mathematica's precise rules for evaluating mathematical expressions, and how Mathematica interprets multiple occurrences of +/- and -/+


I doubt Mathematica can do this integral without a lot of tweaking, but I haven't checked.


The bottom line is it is nonsense to use the sgn(n.s) for the product calculation just like it is nonsense to use the +/-1's. See Jay's paper for the correct product calculation.
.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Yablon » Mon Oct 21, 2019 9:51 am

Yablon wrote:Image

I was having trouble with tex last evening, which is why I posted an image. I think I have the tex problem fixed, so here are the equations in tex rendering:
(1)
(1) friend corrected
(16) first part
(17) first part
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Heinera » Mon Oct 21, 2019 10:25 am

FrediFizzx wrote:The bottom line is it is nonsense to use the sgn(n.s) for the product calculation just like it is nonsense to use the +/-1's. See Jay's paper for the correct product calculation.
.


I take it you mean that





but Bell's (and everybody else's) definition of correlation, , is nonsense.

Well, then this work has nothing to do with Bell's theorem. Besides, you can of course not pick your own definition of correlation and expect your theory to have anything to do with experiments, because the discrete version of the above integral is how the experimenters are actually computing the empirical correlation in their experiments.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby FrediFizzx » Mon Oct 21, 2019 12:25 pm

Heinera wrote:
FrediFizzx wrote:The bottom line is it is nonsense to use the sgn(n.s) for the product calculation just like it is nonsense to use the +/-1's. See Jay's paper for the correct product calculation.
.


I take it you mean that





but Bell's (and everybody else's) definition of correlation, , is nonsense.

Well, then this work has nothing to do with Bell's theorem. Besides, you can of course not pick your own definition of correlation and expect your theory to have anything to do with experiments, because the discrete version of the above integral is how the experimenters are actually computing the empirical correlation in their experiments.

For QM it is nonsense since QM by itself cannot predict individual outcomes event by event. If you find a local QM correlation derivation that does predict individual outcomes event by event, please let us know.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Heinera » Mon Oct 21, 2019 12:38 pm

FrediFizzx wrote:For QM it is nonsense since QM by itself cannot predict individual outcomes event by event. If you find a local QM correlation derivation that does predict individual outcomes event by event, please let us know.
.

There is no difference here from any other hidden variable theory. That's why Bell called the variable "hidden". The variable cannot be predicted event by event. That's why we have the probability density in the integral above; only the probabilities can be specified in a hidden variable theory.

So I take it you imply something more here: Namely that QM is not a hidden variable theory?
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby FrediFizzx » Mon Oct 21, 2019 2:07 pm

Yablon wrote:
Yablon wrote:Image

I was having trouble with tex last evening, which is why I posted an image. I think I have the tex problem fixed, so here are the equations in tex rendering:
(1)
(1) friend corrected
(16) first part
(17) first part

For me, the outstanding revelation in your derivation is that,



So I think we should just jump to that. Does anyone not agree with that?
.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Yablon » Mon Oct 21, 2019 3:43 pm

FrediFizzx wrote:For me, the outstanding revelation in your derivation is that,



So I think we should just jump to that. Does anyone not agree with that?.

I certainly have no objection. Below, I include the eigenvalue product to which is is equal, in front, just so there is no notation question or other confusion that this is the product of the two eigenvalues for and . And Fred is correct, this is the central mathematical skeleton relation of LRVHQM. There may argument about how we interpret this relation and what we build around it in the way of theory -- not whether it is mathematically correct.



with, with 50% -- 50% probability for each.

Without any interpretation yet, I will assert that this is a mathematically-correct relationship, derived without ambiguity or room for fudge from two Pauli identities for and , using standard eigen-mathematics. Anybody not agree?

Jay
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Yablon » Mon Oct 21, 2019 6:43 pm

Yablon wrote:
FrediFizzx wrote:For me, the outstanding revelation in your derivation is that,



So I think we should just jump to that. Does anyone not agree with that?.

I certainly have no objection. Below, I include the eigenvalue product to which is is equal, in front, just so there is no notation question or other confusion that this is the product of the two eigenvalues for and . And Fred is correct, this is the central mathematical skeleton relation of LRVHQM. There may argument about how we interpret this relation and what we build around it in the way of theory -- not whether it is mathematically correct.



with, with 50% -- 50% probability for each.

Without any interpretation yet, I will assert that this is a mathematically-correct relationship, derived without ambiguity or room for fudge from two Pauli identities for and , using standard eigen-mathematics. Anybody not agree?

Jay

One caveat: This relation holds when s is in the same plane defined by a and b. Or for the component of s which sits in the ab plane. But, the off-plane components are irrelevant to correlations.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby gill1109 » Mon Oct 21, 2019 9:05 pm

Yablon wrote:
FrediFizzx wrote:For me, the outstanding revelation in your derivation is that,



So I think we should just jump to that. Does anyone not agree with that?.

I certainly have no objection. Below, I include the eigenvalue product to which is is equal, in front, just so there is no notation question or other confusion that this is the product of the two eigenvalues for and . And Fred is correct, this is the central mathematical skeleton relation of LRVHQM. There may argument about how we interpret this relation and what we build around it in the way of theory -- not whether it is mathematically correct.

with, with 50% -- 50% probability for each.

Without any interpretation yet, I will assert that this is a mathematically-correct relationship, derived without ambiguity or room for fudge from two Pauli identities for and , using standard eigen-mathematics. Anybody not agree?

Jay

I now understand your notation. "lambda" of a self-adjoint operator stands for "an eigenvalue" of that operator. So technically speaking, it is a many-valued function, there is a spectrum of distinct eigenvalues. On the right-hand side you have something you call "h" which stands for +/1.

I agree that if the one takes either of the two eigenvalues of both of those two operators and multiply them, the result is what is given by the right-hand side either with h = -1 or h = +1.

But you also say "with 50% -- 50% probability for each". If probabilities come out, them probabilities must have gone in. So you have implicitly put a joint probability distribution on the eigenvalues of the two operators you started with. If it is a uniform distribution, each of the four combinations has probability 25%, then the product equals +/-1 with probability half each.

So I can agree with your result but you need to further explain the notation. You are putting a joint probability distribution over the Cartesian product of the spectra of two non-commuting observables. They both depend on an unspecified variable "s". The right-hand side does not depend on "s".

So: you can define everything so that what you say is true but I don't think it has anything whatever to do with physics!

Sorry to be pedantic about notation. As a mathematics professor, it's part of my job description.

PS my revised and extended manuscript "Does Geometric Algebra Provide a Loophole to Bell's Theorem?" is now submitted to a journal, uploaded to viXra, and submitted (but on hold) with arXiv. It can be found on my university home page too, but not specially advertised.

Comments are welcome on the viXra discussion page http://vixra.org/abs/1504.0102 (the discussion forum is run by DISQUS, https://disqus.com/)

Remember the DISQUS rule "You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise, your comment will be deleted as unhelpful."

Actually I am OK with anyone telling me that in their opinion the paper stinks without mentioning any specific "error" but I think in many cases their opinion is already well known. A link to earlier comments is enough.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Joy Christian » Mon Oct 21, 2019 9:38 pm

***
I find the title of your manuscript hilarious. Never heard of any "theorem" having a loophole. It is like asking: "Does blah blah Provide a Loophole to Pythagoras' Theorem?"

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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby gill1109 » Mon Oct 21, 2019 9:43 pm

Joy Christian wrote:I find the title of your manuscript hilarious. Never heard of any "theorem" having a loophole. It is like asking: "Does blah blah Provide a Loophole to Pythagoras' Theorem?"

Excellent! The title of the manuscript does deliberately have a number of different interpretations.

One could argue that the discovery of non-Euclidean geometries provided loopholes to Pythagoras' theorem. In fact, Derek Abbott does just that, in his award-winning paper about the reasonable ineffectiveness of mathematics https://www.semanticscholar.org/paper/The-Reasonable-Ineffectiveness-of-Mathematics-Abbott-Pitici/462d7b6b1ee8243b6aa8897be3cf306239fb43c6
Seriously though, I have heard of many theorems which turned out to have loopholes! Read Imre Lakatos' wonderful book "Proofs and Refutations".
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby FrediFizzx » Tue Oct 22, 2019 6:45 am

Yablon wrote:
Yablon wrote:I certainly have no objection. Below, I include the eigenvalue product to which is is equal, in front, just so there is no notation question or other confusion that this is the product of the two eigenvalues for and . And Fred is correct, this is the central mathematical skeleton relation of LRVHQM. There may argument about how we interpret this relation and what we build around it in the way of theory -- not whether it is mathematically correct.



with, with 50% -- 50% probability for each.

Without any interpretation yet, I will assert that this is a mathematically-correct relationship, derived without ambiguity or room for fudge from two Pauli identities for and , using standard eigen-mathematics. Anybody not agree?

Jay

One caveat: This relation holds when s is in the same plane defined by a and b. Or for the component of s which sits in the ab plane. But, the off-plane components are irrelevant to correlations.

Well, the spin vectors will be in the same plane as a and b after polarization.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Yablon » Tue Oct 22, 2019 9:41 am

gill1109 wrote:
Yablon wrote:. . . Anybody not agree?Jay
I now understand your notation. "lambda" of a self-adjoint operator stands for "an eigenvalue" of that operator. So technically speaking, it is a many-valued function, there is a spectrum of distinct eigenvalues. On the right-hand side you have something you call "h" which stands for +/1.
I agree that if the one takes either of the two eigenvalues of both of those two operators and multiply them, the result is what is given by the right-hand side either with h = -1 or h = +1.

Good, we are on the same page.

The only fine point is that “lambda” here stands for the eigenvalues of the non-adjoint i.e., non-Hermitian operators and . Because each of these is non-adjoint resulting from their Hermitian operator halves being non-commuting with one another, there is an uncertainty relation and a simultaneous measurement limitation associated with each of these, which when we get to the physics, I will argue causes h and also s to become "hidden" variables. But that is by way of preview, no need to discuss at the moment.
gill1109 wrote:But you also say "with 50% -- 50% probability for each". If probabilities come out, them probabilities must have gone in. So you have implicitly put a joint probability distribution on the eigenvalues of the two operators you started with. If it is a uniform distribution, each of the four combinations has probability 25%, then the product equals +/-1 with probability half each.

Yes, and I am glad you caught that (as I would expect from a statistics expert). :) I slightly mis-spoke when I said that the relation

with, with 50% -- 50% probability for each

was derived “using standard eigen-mathematics.” You are correct that whether h = -1 or h = +1 has an a priori 50%-50% probability for , and likewise an independent a priori 50%-50% probability for . So you are correct that there is a 25% probability, a priori, for each one of the four combinations. That is the result of the "standard eigen-mathematics." I do then introduce the hypothesis that if h=+1 for then, jointly, h=+1 for , and similarly for h=-1. That is how I get to the 50%-50% probability.
gill1109 wrote: So I can agree with your result but you need to further explain the notation. You are putting a joint probability distribution over the Cartesian product of the spectra of two non-commuting observables. They both depend on an unspecified variable "s". The right-hand side does not depend on "s"

You make a point which I want to stop to agree with and emphasize: "The right-hand side does not depend on s." In physics language, I would say that means that this expression is invariant with regard to s, and depends only upon a, b and h. This will be become very important when we discuss the physics which builds upon this mathematics.
gill1109 wrote: Sorry to be pedantic about notation. As a mathematics professor, it's part of my job description. . .

You have done your job. :) I think / hope my above clarifications remove any further ambiguity.
gill1109 wrote:So: you can define everything so that what you say is true but I don't think it has anything whatever to do with physics!

Well, you keep saying that you are a mathematician not a physicist, and I take you at your word. So, as a physicist myself, I a glad that an esteemed mathematics professor has agreed with the mathematics of my result, subject to the forgoing clarifications. :-) As I said in the first sentence of https://jayryablon.files.wordpress.com/ ... lrhvqm.pdf which I used to start this thread, it is my present goal to lay out “the mathematical skeleton upon which quantum mechanics as represented through Pauli linear algebra, can, in my humble opinion, be made local and realistic using hidden variables.” When I get to the physics, as I will, I want to make sure that we all have gotten beyond any disagreement regarding the correctness of the underlying mathematics, and have weeded out any ambiguity or miscommunication. Your agreement with my result subject to the foregoing clarifications is encouraging in that direction.

So now we have gone through Q1 through Q3 from my post at viewtopic.php?f=6&t=412&sid=462f446b1d57aeb59ecc271a8b39fd99#p10335, and I believe Richard and I have substantial agreement regarding the mathematics.
----------------------------------
Therefore, I now want to return now to my Q4, which is for you Richard, and for anybody and everybody else:

“Q4: Expressions such as appear regularly in the EPRB literature. When you see such an expression, what does it mean to you, physically?” For example, this expression is in equation (9) of Bell’s original paper at, e.g., https://cds.cern.ch/record/111654/files ... 00_001.pdf, with there being what I call s here. And specifically, don't just make the conclusory statement that it leads to Bell's equation (10) for the classical correlation. What I am asking is this:

When , what is that telling you about the physics of in relation to ? And when , what is that alternatively telling you about the physics of in relation to ? What I am looking for is physics understandings along the lines of "before an observation occurs . . ." and "when an observation occurs . . ." and "after an observation occurs . . ." What is the physics that comes to mind when you see this expression, on its own terms?

Jay
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Joy Christian » Tue Oct 22, 2019 10:24 am

Yablon wrote:
So, as a physicist myself, I am glad that an esteemed mathematics professor has agreed with the mathematics of my result ...

Jay, logically both argumentum ad verecundiam and argumentum ad hominem are equally fallacious arguments. Just because someone has been an "esteemed" professor does not guarantee that they are immune to making silly mistakes or false judgment. The famous cases are the mistakes made by von Neumann and Bell in their respective theorems. Among the lesser mortals, in my over 35 years of experience in academia, I have seen plenty of mistakes made by some of the most esteemed professors I know.

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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Heinera » Tue Oct 22, 2019 11:20 am

Yablon wrote: For example, this expression is in equation (9) of Bell’s original paper at, e.g., https://cds.cern.ch/record/111654/files ... 00_001.pdf, with there being what I call s here. And specifically, don't just make the conclusory statement that it leads to Bell's equation (10) for the classical correlation.
Jay

And why not? The expression(10) is a not very complicated unique solution from equations (9), using only math to get there (i.e., using no disputable physical assumptions). If anyone doubt that, they can of course also try to find the solution using numerical integration (or find someone who can program it for you), which will conclusively confirm equation (10).
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby FrediFizzx » Tue Oct 22, 2019 11:29 am

Yablon wrote: … “Q4: Expressions such as appear regularly in the EPRB literature. When you see such an expression, what does it mean to you, physically?” …

It means absolutely nothing physically really. It is just a math expression to tell what the sign of n.s is. That is why it is nonsense to use it for an EPR-Bohm product calculation just like it is nonsense to do (+/-1)(+/-1) for any physically meaningful calculation.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Yablon » Tue Oct 22, 2019 11:50 am

Heinera wrote:
Yablon wrote: For example, this expression is in equation (9) of Bell’s original paper at, e.g., https://cds.cern.ch/record/111654/files ... 00_001.pdf, with there being what I call s here. And specifically, don't just make the conclusory statement that it leads to Bell's equation (10) for the classical correlation.
Jay

And why not? The expression(10) is a not very complicated unique solution from equations (9), using only math to get there (i.e., using no disputable physical assumptions). If anyone doubt that, they can of course also try to find the solution using numerical integration (or find someone who can program it for you), which will conclusively confirm equation (10).

Why not? Because it is important to understand what the inputs are which lead to that Bell equation (10) output. When someone physically observes , does this mean that when s is oriented in the same hemisphere as a you will detect a +1 correlation 100% of the time? That is, can you use this +1 "click" to say for sure that s was aligned in the same hemisphere as a before detection? Or, can you occasionally register a +1 click even if they were in opposite hemispheres? And in this context, think about how Stern-Gerlach -- often regarded as the paradigmatic experiment of quantum mechanics -- works:

If spins are polarized along the +z axis, and a detector is oriented at an angle down from the +z axis, then the probability of a + click is , while that of a - click is . So, unless there is a 100% alignment between a polarized spin and a detector which picks up that spin, there is always a non-zero probability of a click which originated from the opposite hemisphere.

So again, I want to know how people physically interpret all on its own. This is not a trick question; I just want some straight answers which in part will help me think about this.

Jay
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Joy Christian » Tue Oct 22, 2019 12:09 pm

Yablon wrote:
So again, I want to know how people physically interpret all on its own. This is not a trick question; I just want some straight answers which in part will help me think about this.

For Bell, describes a result of a measurement process, independently of any physical theory. Please see the introduction of his paper.

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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Heinera » Tue Oct 22, 2019 12:22 pm

Yablon wrote: When someone physically observes , does this mean that when s is oriented in the same hemisphere as a you will detect a +1 correlation 100% of the time? That is, can you use this +1 "click" to say for sure that s was aligned in the same hemisphere as a before detection?


Yes, that is what the formula means. If you think something else can happen, then you have to use a different formula.
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Re: Local Realistic Hidden Variables Quantum Mechanics (LRHV

Postby Yablon » Tue Oct 22, 2019 12:59 pm

Heinera wrote:
Yablon wrote: When someone physically observes , does this mean that when s is oriented in the same hemisphere as a you will detect a +1 correlation 100% of the time? That is, can you use this +1 "click" to say for sure that s was aligned in the same hemisphere as a before detection?

Yes, that is what the formula means. If you think something else can happen, then you have to use a different formula.

Well, Heine my friend, you just opened to door to possibly explaining the strong correlation by some physical means other than non-local instantaneous action at a distance!

What describes is a classical experiment in which the hemispheric orientation of the spin axis direction s of a spinning object is detected by a detector oriented toward a. And for such a circumstance, Bell's equation (10) correctly describes the correlation.

But does not describe what happens when we detect spin / angular momentum in quantum mechanics. Therefore, neither will Bell's classical correlation equation (10). The "different" formula would instead have to be based on for + and for , as seen in SG experiments. Then the correlation would be different as well; and in fact we know it is for a singlet.

But it seems that an explanation of this strong correlation based on what we locally observe for quantum spins with SG -- which you effectively admit is not in Bell's (9) if you admit that SG is real-- if it can be done, may be preferable to an explanation which resorts to non-local instantaneous action at a distance.

Jay
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