## 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!

Heinera wrote:
FrediFizzx wrote:Yeah, I know. He also must think it should be possible to get around the fact that at each detector spin up or spin down is 50-50. It's not possible. The correlation is simply because the two spin 1/2 particles are from a singlet with zero spin. That is really all there is to it.
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In Quantum Mechanics, that is really all there is to it. For local realists, it is a quagmire, since the same assumption in that setting only produces the triangle correlation.

Not a quagmire at all since we have Joy's classical local-realistic model that gives exactly the same predictions as QM. And... guess what? It also is a perfect demonstration of how the QM correlation is obtained in a local manner. Now, for me QM is simply about real probability factors for real physical events. Call it "The Realistic Interpretation of Quantum Mechanics". All the other nonsense should be driven out of QM. It's junk physics pure and simple as that. "Shut up and calculate" was the right approach. The math works, but many of the interpretations are just complete trash.
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### Re: Quantum Mechanics with a Hidden Variable!

FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:Yeah, I know. He also must think it should be possible to get around the fact that at each detector spin up or spin down is 50-50. It's not possible. The correlation is simply because the two spin 1/2 particles are from a singlet with zero spin. That is really all there is to it.
.

In Quantum Mechanics, that is really all there is to it. For local realists, it is a quagmire, since the same assumption in that setting only produces the triangle correlation.

Not a quagmire at all since we have Joy's classical local-realistic model that gives exactly the same predictions as QM. And... guess what? It also is a perfect demonstration of how the QM correlation is obtained in a local manner. Now, for me QM is simply about real probability factors for real physical events. Call it "The Realistic Interpretation of Quantum Mechanics". All the other nonsense should be driven out of QM. It's junk physics pure and simple as that. "Shut up and calculate" was the right approach. The math works, but many of the interpretations are just complete trash.
.

Joy, Fred,

1: I prepare n sets of EPRB kits -- EPRB$_{i}$. i = 1, 2, ..., n; n large -- and send one kit to each of n couples, Alice$_{i}$ and Bob$_{i}$.

2: The pre-set detector settings are such that the angle (a$_{i}$, b$_{i}$) is identical in all kits and equal to (a,b). BUT no two vector products a$_{i}$xb$_{i}$ are the same.

3. Each couple send me a single result in the form $A_{i}B_{i} = \pm1$ and a$_{i}$xb$_{i}$.

4. I calculate the expectation over the n digits: E(a,b) = - cos(a,b).

5. What do I do with the n different a$_{i}$xb$_{i}$?

Thanks
Gordon Watson

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### Re: Quantum Mechanics with a Hidden Variable!

Are you talking about the cross product of a and b or the dot product?
FrediFizzx
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### Re: Quantum Mechanics with a Hidden Variable!

Heine brought up "counterfactual definiteness." I have a question about how people would define this. Specifcally:

Can anybody write down a good, concise definition of "counterfactual definiteness" entirely using other EPRB concepts in combination, including "elements of reality," "hidden variables," "observability," "simultaneous measurement" (or lack thereof), and "predict with certainty"?

Or, does "counterfactual definiteness" need its own definition because it adds something which is more than just a combination of the above EPRB concepts?

Also, separate question, what would people say are the primary concepts needed to discuss EPRB, whittled down and sifted to avoid redundancy? Obviously, the ones named above, as well as "locality" and "completeness."

I am soon heading toward starting a new thread dealing entirely with definitions, because EPRB physics seems to have more unique term definitions than any other areas of physics I have encountered, and because there is a lot of disagreement about meanings of these definitions. I feel sometimes like we are doing law here in the sense of arguing about words and definitions, as much as science. This is why I always like to clarify using mathematics to accompany and provide examples for these words, as much as possible.

Jay
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### Re: Quantum Mechanics with a Hidden Variable!

FrediFizzx wrote:Are you talking about the cross product of a and b or the dot product?

The n different a$_{i}$xb$_{i}$ are cross-products.
Gordon Watson

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### Re: Quantum Mechanics with a Hidden Variable!

Gordon Watson wrote:
FrediFizzx wrote:Are you talking about the cross product of a and b or the dot product?

The n different a$_{i}$xb$_{i}$ are cross-products.

Where did the cross products come from? Because as far as I can tell, those cross products don't physically exist. They are mathematical artifacts.
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### Re: Quantum Mechanics with a Hidden Variable!

Yablon wrote:Heine brought up "counterfactual definiteness." I have a question about how people would define this. Specifcally:
Can anybody write down a good, concise definition of "counterfactual definiteness" entirely using other EPRB concepts in combination, including "elements of reality," "hidden variables," "observability," "simultaneous measurement" (or lack thereof), and "predict with certainty"?

It means that for a given particle, the model should be able to produce an outcome for any possible hypothetical detector setting, not only for the one Alice actually chooses.

Another way of saying this is that if the model can be turned in to an event-by-event simulation with exogenous detector settings and it always produces an outcome, it will be counterfactually definite.

It is also required for the definition of locality, since "local" in Bell's sense means that Alice's outcome for a given particle should be the same no matter what setting Bob chooses, which involve hypothetical settings on Bob's side.

QM is really a theory about infinite ensembles of identically prepared experiments. But to define a hidden variable theory, you will sooner or later have to start talking about individual particles.
Heinera

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### Re: Quantum Mechanics with a Hidden Variable!

Heinera wrote:
Yablon wrote:Heine brought up "counterfactual definiteness." I have a question about how people would define this. Specifcally:
Can anybody write down a good, concise definition of "counterfactual definiteness" entirely using other EPRB concepts in combination, including "elements of reality," "hidden variables," "observability," "simultaneous measurement" (or lack thereof), and "predict with certainty"?

It means that for a given particle, the model should be able to produce an outcome for any possible hypothetical detector setting, not only for the one Alice actually chooses.

Another way of saying this is that if the model can be turned in to an event-by-event simulation with exogenous detector settings and it always produces an outcome, it will be counterfactually definite.

It is also required for the definition of locality, since "local" in Bell's sense means that Alice's outcome for a given particle should be the same no matter what setting Bob chooses, which involve hypothetical settings on Bob's side.

QM is really a theory about infinite ensembles of identically prepared experiments. But to define a hidden variable theory, you will sooner or later have to start talking about individual particles.

Heinera: It means that for a given particle, the model should be able to produce outcomes for all possible hypothetical detector settings.

It is good that you use the words "the model". I think that counterfactual definiteness is a property of mathematical-physical *models* of reality. It is not supposed to be a property of reality.

I do think that people who want to talk now about notions of counterfactual definiteness should study the standard modern texts such as Pearl's magisterial work on causality or various popularised versions thereof. Take a look too at https://en.wikipedia.org/wiki/Causality and https://en.wikipedia.org/wiki/Counterfactual_definiteness
gill1109
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### Re: Quantum Mechanics with a Hidden Variable!

gill1109 wrote:It is good that you use the words "the model". I think that counterfactual definiteness is a property of mathematical-physical *models* of reality. It is not supposed to be a property of reality.

Exactly.
Heinera

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### Re: Quantum Mechanics with a Hidden Variable!

FrediFizzx wrote:
Gordon Watson wrote:
FrediFizzx wrote:Are you talking about the cross product of a and b or the dot product?

The n different a$_{i}$xb$_{i}$ are cross-products.

Where did the cross products come from? Because as far as I can tell, those cross products don't physically exist. They are mathematical artifacts.

For example, see this comment -- after the reduction of eqn (8) to (12) -- in your 5 June 2019 essay with Joy and Jay:

" ... where we have used the Pauli identities, and the cross products terms reduce to zero because of the rotational invariance of the singlet state. It is easy to see from the cross product terms that we indeed have left and right handed components as they are pointing in opposite directions." [My emphasis.]

NB: in my thought-experiment, no two cross-products are the same. So, in addition to seeking an explanation of my experiment in your latest terms, the further question arises: How do you "reduce them -- my cross-products -- to zero".

Thanks.
Gordon Watson

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### Re: Quantum Mechanics with a Hidden Variable!

Gordon Watson wrote:
FrediFizzx wrote:
Gordon Watson wrote:
FrediFizzx wrote:Are you talking about the cross product of a and b or the dot product?

The n different a$_{i}$xb$_{i}$ are cross-products.

Where did the cross products come from? Because as far as I can tell, those cross products don't physically exist. They are mathematical artifacts.

For example, see this comment -- after the reduction of eqn (8) to (12) -- in your 5 June 2019 essay with Joy and Jay:

" ... where we have used the Pauli identities, and the cross products terms reduce to zero because of the rotational invariance of the singlet state. It is easy to see from the cross product terms that we indeed have left and right handed components as they are pointing in opposite directions." [My emphasis.]

NB: in my thought-experiment, no two cross-products are the same. So, in addition to seeking an explanation of my experiment in your latest terms, the further question arises: How do you "reduce them -- my cross-products -- to zero".

Thanks.

Oh, because it is a singlet state. So a x b = c and any individual observable is zero. See eq. (3). What you actually have is $i{\boldsymbol \sigma}\cdot {\bf c}$. If you do the following calculation by hand, you will see that the cross product components cancel out anyways in the step from (A2) to (A3).
FrediFizzx
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### Re: Quantum Mechanics with a Hidden Variable!

Heinera wrote:...
QM is really a theory about infinite ensembles of identically prepared experiments. But to define a hidden variable theory, you will sooner or later have to start talking about individual particles.

Both sentences are complete nonsense. QM is about real probability factors for real physical events. And that is it; shut up and calculate! That kills the second sentence.
FrediFizzx
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### Re: Quantum Mechanics with a Hidden Variable!

FrediFizzx wrote:
Heinera wrote:...
QM is really a theory about infinite ensembles of identically prepared experiments. But to define a hidden variable theory, you will sooner or later have to start talking about individual particles.

Both sentences are complete nonsense. QM is about real probability factors for real physical events. And that is it; shut up and calculate! That kills the second sentence.

I agree that QM is about real probability factors for real physical events. We know how to calculate. Sometimes there are different routes to calculating the same thing, but the answer is always the same, so it doesn't matter (cf. Schrödinger's cat, Wigner's friend, and the most recent Frauchiger-Renner paradox).

So what is the purpose of this forum?

Are there faster, easier ways to calculate? That would be nice. But it's already nice that there are different routes to calculating the same thing because then one can be smart and choose the fastest, easiest way. Having to have an "interpretation" of QM is an unnecessary luxury, maybe even a hindrance. Why try to retro-fit naïve classical intuition about the world when all we really have are the formulas? We just need to gain *abstract* mathematical intuition with which to faster manipulate the formulas. If Christian's theory makes you "feel good" then take it on board. Does it change the ways we do quantum mechanical calculations? Does it change the predictions?
gill1109
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### Re: Quantum Mechanics with a Hidden Variable!

Joy's model changes the bogus interpretations of QM a lot. That coupled with

viewtopic.php?f=6&t=380

changes the bogus interpretations even more. That is one of the purposes of this forum. To get people to see the real truth about Nature.
.
FrediFizzx
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### Re: Quantum Mechanics with a Hidden Variable!

FrediFizzx wrote:Joy's model changes the bogus interpretations of QM a lot. That coupled with

viewtopic.php?f=6&t=380

changes the bogus interpretations even more. That is one of the purposes of this forum. To get people to see the real truth about Nature.
.

Joy gives an account of a model which reproduces the singlet correlations. Other experiments have actually, it seems, realised quite different quantum states, and violated apparently different inequalities. For instance, the famous 2015 experiments at Vienna and at Boulder, Colorado (NIST) seem to have created the polarization state

$(1/\sqrt{1 + r^2})(|\,\text{vertical}~\text{horizontal}> + r |\,\text{horizontal}~\text{vertical}>)$

with r approximately equal to 0.70. The experiment at Delft and the 2016 experiment in Munich both use "entanglement swapping", whereby photons travel *from* the two measurement stations A, B *to* a central location S where a kind of "controlling" measurement is taken of the two photons which (sometimes) arrive there almost simultaneously, interfere in an interfering beam-splitter, and are measured by two photo-detectors. This effectively "entangles" the spins which were already present at Alice and Bob's labs, and which are also measured at roughly the same time. CHSH style data now results by post-selection, keeping the measurement settings and outcomes at A and B, conditional on the two outcomes at S, on those occasions when there *are* two outcomes, one in each channel, at S. In Delft the result was a CHSH value of about 2.4 (about half way between 2 and 2 sqrt 2)
gill1109
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### Re: Quantum Mechanics with a Hidden Variable!

gill1109 wrote:
FrediFizzx wrote:Joy's model changes the bogus interpretations of QM a lot. That coupled with

viewtopic.php?f=6&t=380

changes the bogus interpretations even more. That is one of the purposes of this forum. To get people to see the real truth about Nature.
.

Joy gives an account of a model which reproduces the singlet correlations. Other experiments have actually, it seems, realised quite different quantum states, and violated apparently different inequalities. For instance, the famous 2015 experiments at Vienna and at Boulder, Colorado (NIST) seem to have created the polarization state

$(1/\sqrt{1 + r^2})(|\,\text{vertical}~\text{horizontal}> + r |\,\text{horizontal}~\text{vertical}>)$

with r approximately equal to 0.70. The experiment at Delft and the 2016 experiment in Munich both use "entanglement swapping", whereby photons travel *from* the two measurement stations A, B *to* a central location S where a kind of "controlling" measurement is taken of the two photons which (sometimes) arrive there almost simultaneously, interfere in an interfering beam-splitter, and are measured by two photo-detectors. This effectively "entangles" the spins which were already present at Alice and Bob's labs, and which are also measured at roughly the same time. CHSH style data now results by post-selection, keeping the measurement settings and outcomes at A and B, conditional on the two outcomes at S, on those occasions when there *are* two outcomes, one in each channel, at S. In Delft the result was a CHSH value of about 2.4 (about half way between 2 and 2 sqrt 2)

This is all completely irrelevant. It is one of the standard tricks of obfuscation and distraction from what has been achieved by my local-realistic model: https://arxiv.org/abs/1806.02392.

The question answered by my model is quite simple. EPR argued that if we assume locality and reality then quantum mechanics is incomplete. Bell claimed that no local-realistic model can reproduce the strong correlations E(a, b) = -a.b for the rotationally invariant singlet state, thereby undermining the EPR argument. But I have demonstrated that Bell was wrong and we can indeed reproduce the strong correlation local-realistically. Therefore the original EPR argument is correct after all and Bell did not undermine it. Consequently, the upshot of my model is that quantum mechanics is incomplete, as EPR have concluded. That is all there is to it. All the rest is obfuscation and distraction, because if the quantum mechanical description of just one state, namely of the singlet state, is incomplete, then quantum mechanics is an incomplete theory, period. The whole Bell industry is thus just smoke and mirror to fool the taxpayers.

***
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### Re: Quantum Mechanics with a Hidden Variable!

Dear Joy

I am not putting out smoke and mirrors here. I am just pointing out that there are more strong correlations out there than the singlet correlations.

Your main point is absolutely valid - if your initial novel model for the singlet correlations is correct, then the usual Bell EPRB story is destroyed.

In the heart of the RSOS paper, in Section 3.1, you take care of the bipartite singlet correlations. Then in Section 3.2 you show how this argument can in principle be extended to arbitrary (multipartite) quantum correlations.

Your paper does already cover, in some generality, other states and other setups. I'm pointing out that it might be worth your while to go into the specifics, some time. Moreover there are some further features of modern experiments which I believe you haven't dealt with yet.

We have two "new" types of experiment:

(1) the Vienna and NIST experiment with not fully entangled Eberhard states and detection rate just exceeding 66.7%;

(2) the Delft and Munich experiments with three parties (A, B and S; particles travel from A to S and from B to S, there are measurements at all three locations, and post-selection on the outcome at S. S is now a sink, not a source!)

I don't think the RSOS paper takes account of imperfect detection and I don't think it deals with post-selection. It should be easy to extend in these directions.
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### Re: Quantum Mechanics with a Hidden Variable!

gill1109 wrote:We have two "new" types of experiment:

(1) the Vienna and NIST experiment with not fully entangled Eberhard states and detection rate just exceeding 66.7%;

(2) the Delft and Munich experiments with three parties (A, B and S; particles travel from A to S and from B to S, there are measurements at all three locations, and post-selection on the outcome at S. S is now a sink, not a source!)

I don't think the RSOS paper takes account of imperfect detection and I don't think it deals with post-selection. It should be easy to extend in these directions.

These are interesting experiments. The question of imperfect detection is also experimentally important. But these issues are not relevant for the advancement of my theoretical model.

***
Joy Christian
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### Re: Quantum Mechanics with a Hidden Variable!

Joy Christian wrote:
gill1109 wrote:We have two "new" types of experiment:

(1) the Vienna and NIST experiment with not fully entangled Eberhard states and detection rate just exceeding 66.7%;

(2) the Delft and Munich experiments with three parties (A, B and S; particles travel from A to S and from B to S, there are measurements at all three locations, and post-selection on the outcome at S. S is now a sink, not a source!)

I don't think the RSOS paper takes account of imperfect detection and I don't think it deals with post-selection. It should be easy to extend in these directions.

These are interesting experiments. The question of imperfect detection is also experimentally important. But these issues are not relevant for the advancement of my theoretical model.

***

People still tend think in terms of "loopholes" like as if loopholes could prove that QM is wrong. The math of QM is a bit restrictive by mostly OK. It is the freakin' bogus interpretations that really stink QM up to no end. I blame Bohr and Heisenberg for the bad smell.
.
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### Re: Quantum Mechanics with a Hidden Variable!

FrediFizzx wrote:
Gordon Watson wrote:
FrediFizzx wrote:
Gordon Watson wrote:The n different a$_{i}$xb$_{i}$ are cross-products.

Where did the cross products come from? Because as far as I can tell, those cross products don't physically exist. They are mathematical artifacts.

For example, see this comment -- after the reduction of eqn (8) to (12) -- in your 5 June 2019 essay with Joy and Jay:

" ... where we have used the Pauli identities, and the cross products terms reduce to zero because of the rotational invariance of the singlet state. It is easy to see from the cross product terms that we indeed have left and right handed components as they are pointing in opposite directions." [My emphasis.]

NB: in my thought-experiment, no two cross-products are the same. So, in addition to seeking an explanation of my experiment in your latest terms, the further question arises: How do you "reduce them -- my cross-products -- to zero".

Thanks.

Oh, because it is a singlet state. So a x b = c and any individual observable is zero. See eq. (3). What you actually have is $i{\boldsymbol \sigma}\cdot {\bf c}$. If you do the following calculation by hand, you will see that the cross product components cancel out anyways in the step from (A2) to (A3).

Thanks for this, Fred. And though the above calculation is now included in v.3 of the Joy, Fred, Jay paper: it does not, in my view, remove the difficulty.

In my view you should have no reference to cross-products at all: which means, I suppose, no need for chirality??

nb: a constant in my experiment is the angle (a,b) between the detector settings: but with no two detector settings [Alice$_i$ with $a_i$, Bob$_i$ with $b_i$, etc.] being the same.

So your use of identical settings is not allowed in analyzing my experiment: its whole point being that cross-products have no place in such analysis.

Instead, let's use that constant angle (a,b). Then, in a fairly conventional notation, we can use the Probability Law that applies. That is, the extension of Malus' Law -- c.1810 -- the extension we find by analyzing the experiment*** in accord with Einstein-classicality and true-local realism:

$E(a,b)=P(A^+B^+)-P(A^+B^-)-P(A^-B^+)+P(A^-B^-).\;\;(1)$

So

$E(a,b)=[sin^2((a,b)/2)-cos^2((a,b)/2)-cos^2((a,b)/2)+sin^2((a,b)/2)]/2.\;\;(2)$

So

$E(a,b)=-a.b.\;QED\;\;(3)$

Thus a straight-forward result in line with the classicality that Einstein argued for -- according to Bell (2004:86) -- a classicality that I support.

*** The same Law is confirmed experimentally in Aspect (2004) with spin s = 1.

Thanks again; Gordon
Gordon Watson

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