Detection Loophole, Minimum Rate

[James Jr Tankersley]

James Jr Tankersley

8:46 PM (now) 

to Bell inequalities and quantum foundations

Even though we know how to close the detection loophole with electron spin experiments, photon-based experiments are still being used to test Bell's inequalities, without properly closing the detection loophole (Eberhart requires 72.5% detection, but CHSH simulations modeling Malus law loss at the polarizing beam splitter appears to require detection closer to 100% to close the detection loophole)

A recent paper cites 3 Bell tests in 2015 (2 photon based with ~75% detection rates) as being loophole free. [1]. A recent Nova documentary also cites a recent Vienna photon based experiment [4.1] as being loophole free.

The 2015 Electron spin experiment is loophole free as far as we know (Hensen et al, with 100% detection), but has not been repeated in almost a decade, as far as I can determine, and the published run was apparently only 245 events, with a high probability of being a random chance result [1] (1 in 27) [5].  

If future Electron spin experiments with sufficient trial data refute the tiny trial run above, we appear to have something interesting (but no similar experiments in this many years???)

Eberhart is cited as requiring a minimum of 72.5% detection rate to avoid detection loop hole. (Now achievable with high quality photon detectors)

However, Eberhart's minimum detection must assume a "random distribution" of photon loss, not the "highly selective" loss Malus law causes to photons with real polarities before entering polarizing beam splitters (which very selectively lose photons based on pre-existing photon polarization).[3] 

CHSH simulations of photon with real polarities before hitting polarizing beam splitters, modeling loss using Malus Law calculations, show S violations around 2.2 when detection efficiency is modeled at around 90%[2]. The detection rate needed to close the loophole may need to be closer to 100%, based on the numbers the simulations are providing.

Cheers,

Jim Tankersley

(usually busy with work, but recently inspired by recent events)

[1] LOOPHOLE-FREE BELL TESTS AND THE FALSIFICATION OF LOCAL REALISM, 2018, https://arxiv.org/pdf/1805.09289.pdf, 2018 (accessed 2023-01-22)

[1.1] Discussion, page 8 "Finally, by using highly efficient detectors and testing a version of the CH model, they were able to close the detection loophole (Shalm et al., 2015). The necessary theoretical efficiency for this experiment, which Shalm et al. calculated using the method proposed by Eberhard, was 72.5% (Eberhard, 1993) (Shalm et al., 2015). The actual detector efficiencies used were 74.7 ± 0.3% and 75.6 ± 0.3% as calculated using the method proposed by Klyshko (Klyshko, 1980) (Shalm et al., 2015)."

[2] Testing Bells Theorem, https://sites.google.com/site/physicschecker/unsettled-physics/testing-bells-theorem-paper (access 2023-01-22)

[3] Malus Law, https://byjus.com/jee/malus-law/ (accessed 2023-01-22)

[3.1] "What is Malus Law?

Malus’ law states that the intensity of plane-polarized light that passes through an analyzer varies as the square of the cosine of the angle between the plane of the polarizer and the transmission axes of the analyzer." 

[4] Einstein's Quantum Riddle, https://www.youtube.com/watch?v=068rdc75mHM (accessed 2023-01-22)

[4.1] Dominik Rauch, University of Vienna (43 minute point)

[5] Quantum Entanglement Bell Tests Part 4: Delft – The 1st Loophole-free Bell Test, Karma Penny, https://www.youtube.com/watch?v=9XHJfUeEmns&t=17s (accessed 2023-01-22)

[Chantal Roth]

Thanks James for bringing this up!

The bigger the claim, the greater the amount of evidence required to prove it.

This is about as big as it gets, so I think it is not too much to ask for at least a repeat of some of the currently best experiments (with the issues we saw resolved).

I suggest we add a session to the talks about this topic, because this is too important: until we *really* have a loophole free experiment (that includes all loopholes) that is statistically significant, we cannot simply assume the question has been resolved.

Best wishes,

Chantal

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[Jan-Åke Larsson]

Hi James,
The Eberhard (or CH) inequality requires 66.7% overall efficiency.
Malus' law simulation is only possible up to 50% overall efficiency.

I agree that the Hensen et al experiment has too low number of events.

There are several truly loophole-free experiments nowadays.

We should spend our time on something other than this.

/Jan-Åke

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Jan-Åke Larsson
Professor, Head of Department

Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:512 Please visit us at www.liu.se

[Richard Gill]

There are repeats and *improvements* of the best experiment. I’ve said this several times before, but here I go again (sorry to those who me say this N times before where N is about 10 or so).

Take a look at:

Zhang, W., van Leent, T., Redeker, K. et al.

A device-independent quantum key distribution system for distant users. 

Nature 607, 687–691 (2022). 

https://doi.org/10.1038/s41586-022-04891-y

You can find it on arXiv too.

I extracted the Bell test part of the experiment and took a look at the data here:

See also my

https://arxiv.org/abs/2209.00702

"Optimal statistical analyses of Bell experiments"

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/cac07f58-d9c4-4ea0-8953-7a61b7145f14%40app.fastmail.com.

[Mark Hadley]

Dear Chantal,

I say the claim is that QM makes correct predictions,( and therefore violates Bell's) . And there is a lot of evidence that QM makes correct predictions. And no contrary evidence. 

To argue that the predictions of QM are wrong is the big claim, that needs enormous evidence. There is none. 

The predictions of QM apply to realistic and to loophole free experiments. 

Cheers

Mark

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[Richard Gill]

PS Chantal wants a loophole-free experiment which excludes all loopholes. There are two kinds of loopholes: those which in principle require better experimental procedures including better data processing; and metaphysical loopholes such as the conspiracy aka superdeterminism loophole, which philosophers of science will go on discussing for centuries.

I submit that the Zhang et al experiment of 2022 satisfies Chantal’s criteria as far as experimental imperfections are concerned. Some people might object that the distance between the labs “as the crow flies” is a bit too short, though the distance via glass fibre cable is plenty. Does Chantal demand that the guys in Munich raise the money to buy another lab another 100 meters further from their existing two labs? Does she seriously believe that in the counterfactual world where they had already done this, their experiment would not have been successful?

I’m with Jan-Åke on this: *we* should spend our time on something other than this; the tax-payers of the world deserve that their money is spent on other things; the experimentalists of the world should concentrate their resources on more challenging and interesting work.

On 23 Jan 2023, at 07:26, Chantal Roth <cr...@nobilitas.com> wrote:

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/cac07f58-d9c4-4ea0-8953-7a61b7145f14%40app.fastmail.com.

[Chantal Roth]

Thanks Richard - I have not seen these yet (I was trying to avoid the topic, but... it seems I get drawn in again :-).

In your opinion, which is *the one* experiment that is the most convincing, the one that clearly has no loopholes and is statistically significant? Is it the one you listed below?

(You know, given that people consider all kinds of crazy explanations, including retrocausality, parallel universes, instant communication and so on, I think it is not so crazy to look at these experiments critically :-).

Best wishes,

Chantal

[Richard Gill]

Chantal, my short answer is “yes”. (Why do you think I keep mentioning it all over the place and spent a lot of time looking closely at some of the data?)

These guys are from the Weinfurter group. They did the best of the four loophole free experiments of 2015. They have a lot of routine and expertise, and now they are embedding a Bell test inside more complex experiments intended to demonstrate DIQKD. Alice and Bob each have three settings. Two of them are used for the Bell test, the third for the cryptography application.

On 23 Jan 2023, at 10:10, Chantal Roth <cr...@nobilitas.com> wrote:

Thanks Richard - I have not seen these yet (I was trying to avoid the topic, but... it seems I get drawn in again :-).

In your opinion, which is *the one* experiment that is the most convincing, the one that clearly has no loopholes and is statistically significant? Is it the one you listed below?

(You know, given that people consider all kinds of crazy explanations, including retrocausality, parallel universes, instant communication and so on, I think it is not so crazy to look at these experiments critically :-).

Best wishes,

Chantal

On Mon, Jan 23, 2023, at 9:58 AM, Richard Gill wrote:

There are repeats and *improvements* of the best experiment. I’ve said this several times before, but here I go again (sorry to those who me say this N times before where N is about 10 or so).

Take a look at:

Zhang, W., van Leent, T., Redeker, K. et al.

A device-independent quantum key distribution system for distant users. 

Nature 607, 687–691 (2022). 

https://doi.org/10.1038/s41586-022-04891-y

You can find it on arXiv too.

I extracted the Bell test part of the experiment and took a look at the data here:

Optimized DIQKD rpubs.com <favicon.ico>

[Алексей Никулов]

Dear James,

The controversy about loopholes does not make sense since Bell's
inequalities appeared because of a false understanding by most
physicists of quantum mechanics. It is funny that no one noticed
during many years that the orthodox quantum mechanics cannot predict
the EPR correlation and violation of Bell’s inequalities due to its
well-known principle that the operators can fail to commute only if
they act on the same particle.

Bohm misled Bell by rejecting this principle in order to postulate the
EPR correlation, he has not written that quantum mechanics cannot
predict the EPR correlation if this quantum principle is valid. Bell
misled all physicists since he did not understand that only Bohm’s
quantum mechanics but not the orthodox quantum mechanics can predict
the EPR correlation. Bell misled in particular the authors of the
well-known GHZ theorem [1,2]. These authors used the principle the
operators acting on different particles commute, according to which
quantum mechanics cannot contradict locality, in order to deduce the
GHZ theorem which should prove that quantum mechanics contradicts
locality.

I draw attention to this obvious contradiction in the manuscript
“Physical thinking and the GHZ theorem”. Unfortunately, Editors of
Physical Review A, Annalen der Physik and Annals of Physics rejected
this manuscript without peer review within a few days, from 1 to 3. In
contrast to these Editors, Editors of ‘Foundations of Physics’ did not
reject this manuscript up to now although I submitted it to this
journal July 7 and is considered by a reviewer since August 8. I
assume that my manuscript has not been rejected so far because
Professor Anton Zeilinger is a member of the Advisory Board of
‘Foundations of Physics’. I understand that it is difficult to make a
decision about my manuscript, since on the one hand it is impossible
to deny the mathematical fact that quantum mechanics cannot predict
EPR correlation and violation of Bell inequalities because of its
principle that the operators acting on different particles commute,
and on the other hand it is difficult to admit that many physicists
have been mistaken for many years.

[1] Greenberger, D.M., Horne M.A., Zeilinger, A.: Bell’s Theorem,
Quantum Theory and Conceptions of the Universe, edited by M. Kafatos,
Dordrecht: Kluwer Academic, pp. 73-76, (1989).

[2] Greenberger, D.M., Horne M.A., Shimony A. Zeilinger, A.: Bells
theorem without inequalities. Amer. J. Phys. 58, 1131-1143 (1990).

With best wishes,

Alexey

пн, 23 янв. 2023 г. в 12:09, Richard Gill <gill...@gmail.com>:

> To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/400EBBAD-4CDC-4ED2-BB67-3B4DF6444B81%40gmail.com.

[Chantal Roth]

Richard, (emails crossed...)

Yes, I mean experimental loopholes, that's it. I doubt anyone is asking them to buy another lab... the issues that are left are much less exciting than that.

I am not ready to start "believing" in ideas like retrocausality just yet (or any of the other wild ideas), only because of that (everything else in QM is much clearer and has nothing really weird about it).

Given that there are so many (wild) theories about this, I think it warrants to keep a critical eye on the experimental results. 

Best wishes,

Chantali

[Chantal Roth]

Thanks - here is the link to the supplementary information:

https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-022-04891-y/MediaObjects/41586_2022_4891_MOESM1_ESM.pdf

Do you know if they provide the data as well?

Best wishes,

Chantal

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/065F6016-F164-463C-B2E1-F66EE1F84A55%40gmail.com.

[Richard Gill]

Jim

The Munich experiment involves three parties: Alice, Bob and Charlie. And a sequence of tests of three “aligned” time-slots for the three parties.

Photons go from Alice and Bob’s place to Charlie's where they interfere. Charlie does a measurement there. Of course they may not arrive at all.

So we have three parties with settings a, b, c say, and outcomes x, y, z

Charlie’s setting “c” is fixed

In the experiment one studies the probability distributions p(x, y | a, b, c, z) for a particular z (two clicks of two particular photo detectors).

This is what is called an “event ready” Bell experiment. The special value of z signals when the measurements of Alice and Bob will be used to calculate correlations. Because from the QM point of view, those are occasions on which those atom spins were entangled. 

It’s also called “entanglement swapping”, its a version of quantum teleportation.

The correct analysis of the resulting Bell experiment does not require any belief in QM! You don’t have to “believe” in quantum teleportation, or whatever. It’s the other way round. The results might lead you to agree that it really does seem to exist….

Richard

[James Tankersley Jr]

Thank you, I will study this later this evening.

Also, I just re-read an old paper I wrote and realized I was communicating poorly.  Re-written summary:

... Bell's experiment is a brilliant test to settle the issue (and photon based experiments appear to show that Quantum Theory wins). But computer experiments [20] that model results with LHV (Local Hidden Variable) models, show that photon based experiments have an un-accounted for "selective detect loophole" (requiring close to 100% detection, not the approximately 70% detection rates currently allowed), and Bell CHSH experiments may actually settle the issue in EPRs favor.

[Jan-Åke Larsson]

Hi James,
The Eberhard (or CH) inequality requires 66.7% overall efficiency.
Malus' law simulation is only possible up to 50% overall efficiency.

What is [20]?

I agree that the Hensen et al experiment has too low number of events.

There are several truly loophole-free experiments nowadays.

We should spend our time on something other than this.

/Jan-Åke

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAD%3DV2Ruhy4m-AxBYUMdHOvTTuK%2BS%2BF94FmquGpOVpnYUKsQCUg%40mail.gmail.com.

[James Tankersley Jr]

Will work on this summary more this evening, but I am trying to communicate something similar to below

Bell's experiment is a brilliant test to settle the issue, and computer models show that Bell's inequalities do conclusively detect the difference between QM vs ERP modeled reality.  Computer CHSH experiments [20] with LHV (Local Hidden Variable) models also show that photon loss in polarizing beam splitters using Malus Law distribution, cause a false positive violation of Bell's inequalities at any loss level. This is the "Malus Law Detection Loophole", it is much more strict than the standard detection loophole, and requires CHSH experiments to exclude "Malus Law distribution" photon loss completely.  CHSH experiments using polarizing beam splitters suffer from the "Malus Law Distribution Loophole" and always provide false positive violations of Bell's inequalities. Electron spin tests do not suffer from "Malus Law Detection Loophole" and should be conducted with large data sets to settle the Bell's inequalities test.

[2] Testing Bells Theorem, https://sites.google.com/site/physicschecker/unsettled-physics/testing-bells-theorem-paper (access 2023-01-22)

[Mark Hadley]

Dear Alexey,

You are surely wrong. 

I, and others, can use QM to calculate EPR correlations. It is not difficult. The results are confirmed by experiment. If you make different predictions then you are wrong. If you don't know how to make predictions then read the books and learn. 

Your supposedly well known principle. Is probably wrong, but certainly not part of the axioms of QM that I know. 

An expectation value for an experiment is given by

Tr(\rho A)

 For any state \rho and and observable represented by A

Correlation outcomes are just a special case. For an entangled state rho cannot be factorised, which may be where you are confused. 

This works for anything, including EPR

Cheers

Mark

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[Алексей Никулов]

Dear Mark,

If you do not know about the principle that the operators can fail to
commute only if they act on the same particle, it does not mean that
this principle is not one of the main principles of quantum mechanics.
This principle is used by the authors of the GHZ theorem [1,2] when
they apply the operators of measurements of spin projection in
different directions in any order. The authors of the book [3] write
directly about this in section “6.6 The Greenberger-Horne-Zeilinger
Theorem” : “We know that the three operators Sx(a), Sy(b), and Sy(c)
commute. (This is because each acts on a different particle. Only if
Sx and Sy act on the same particle do they fail to commute.) Thus, we
can apply them to the GHZ state in any order”.

Unfortunately, numerous authors of publications about Bell's
inequalities and participants in the Bell's inequality debate do not
know quantum mechanics, but the perversion of quantum mechanics by
Bohm, or their own fantasies about quantum mechanics. Bohm misled even
Bell. Bell misled all physicists, including to the authors of the GHZ
theorem [1,2], who prove the contradiction of quantum mechanics with
locality with the help of the principle according to which quantum
mechanics cannot contradict locality.

It should be noted that the principle that the operators acting on
different particles commute saves quantum mechanics from predicting
the obvious absurd. Bohm had to abandon this principle in order to
invent the EPR correlation in 1951. As a consequence, the EPR
correlations invented by Bohm logically leads to absurdity, see my
preprint “Logical proof of the absurdity of the EPR correlation”
available at ResearchGate
https://www.researchgate.net/publication/331584709_Logical_proof_of_the_absurdity_of_the_EPR_correlation
.

[1] Greenberger, D.M., Horne M.A., Zeilinger, A.: Bell’s Theorem,
Quantum Theory and Conceptions of the Universe, edited by M. Kafatos,
Dordrecht: Kluwer Academic, pp. 73-76, (1989).

[2] Greenberger, D.M., Horne M.A., Shimony A. Zeilinger, A.: Bells
theorem without inequalities. Amer. J. Phys. 58, 1131-1143 (1990).

[3] G. Greenstein and A. Zajonc, The Quantum Challenge. Modern
Research on the Foundations of Quantum Mechanics, 2nd edn. Jones and
Bartlett, Sudbury, 2006

With best wishes,

Alexey

вт, 24 янв. 2023 г. в 14:29, Mark Hadley <sunshine...@googlemail.com>:

[Richard Gill]

Dear Alexei

I have to say that I think you are talking nonsense. But you already know that that is my opinion.

Moreover we had this discussion many times before and as far as I know no single person supports your opinion.

Maybe you can give a reference to any publication by other authors who support your point of view and have expressed it in different words. So far you are not being very successful in communicating your standpoint. If there is someone else who does understand you, maybe they will be better able to explain your argument to us than you are.

Yours
Richard

Sent from my iPhone

> On 24 Jan 2023, at 17:40, Алексей Никулов <nikulo...@gmail.com> wrote:
>
> Dear Mark,

[Mark Hadley]

Dear Alexey,

You may consider it a fundamental principle. I won't argue that with you. 

But it's a fact that QM can easily be used to calculate EPR correlations and it gives answers confirmed by experiment. 

Are you denying that? Do you have different predictions for EPR outcomes? 

Mark

[Алексей Никулов]

Dear Mark,
According to the postulate of quantum mechanics about the Dirac jump,
only a measured particle should jump “into an eigenstate of the
dynamical variable that is being measured”. Therefore when Alice
measures spin projection of the particle A of the EPR pair

|EPR> = (|A+,B-> + |A-,B+>)/2^0.5 (1)

along the z-axis and observe spin up with the probability of 0.5, only
the particle A should jump into the eigenstate along the z-axis,
whereas the state of the particle B should not change according the
principle of quantum mechanics that the operators can fail to commute
only if they act on the same particle. Therefore Alice will create new
states

|Alice> = |A+z>(|B-> + |B+>)/2^0.5 (2)

according to which Bob will see spin up of the particle B with the
probability of 0.5. Thus, quantum mechanics predicts no correlation
between results of the observations of spin projections in the same
direction of particles in the EPR state (1).

To predict the EPR correlation, it is necessary to postulate that not
only the measured particle A, but also particle B should jump “into an
eigenstate of the dynamical variable that is being measured”. This is
exactly what Bohm did when he claimed about the particles of the EPR
pair that “every component of its spin angular momentum opposite to
that of the other one” and even that ”each atom would continue to have
every component of its spin angular momentum opposite to that of the
other one”, see the section ”The Hypothetical Experiment Einstein,
Rosen and Podolsky” of his book [1].

Bell said in the Introductory remarks “Speakable and unspeakable in
quantum mechanics” at Naples-Amalfi meeting, May 7, 1984 that the
creators of quantum mechanics were sleepwalkers who didn't understand
what they were claiming. That's the smartest thing Bell said. But for
some reason Bell did not understand that Bohm was the same sleepwalker
who did not understand what he was claiming. Bohm was claiming the
following: If Alice directed her analyzer along the z-axis, then not
only her particle, but also Bob's particle should jump into
eigenstates along the z-axis,

|Bohm_z> = |A+z>|B-z> (3z)

but if she directed the analyzer along the x-axis than the both
particles should jump into eigenstates along the x-axis

|Bohm_x> = |A+x>|B-x> (3x)

The expressions (3) predict the EPR correlation along both the z-axis
and the x-axis. They also predict violation of Bell’s inequalities
when the operators of finite rotations of the coordinate system are
used. But here the question arises: "What eigenstates should the
particles jump into if Alice directed her analyzer along the z-axis
and Bob along the x-axis?" Quantum mechanics does not put particles in
front of such an absurd choice due to its principle that the operators
can fail to commute only if they act on the same particle. But quantum
mechanics cannot be used to calculate EPR correlations, contrary to
your confidence, also because of this principle.

Bohm misled himself, Bell, and most physicists because of the illusion
that the EPR correlation could be derived from the law of conservation
of angular momentum. This illusion is misleading for several reasons:
1) in physics there is the law of conservation of angular momentum,
but there is no law of conservation of discrete values of angular
momentum projections; 2) in quantum mechanics, conservation laws are
valid with precision only down to the uncertainty relation; 3) only
what exists can be conserved, whereas not only spin projections of
particles, but even spin states that determine the probabilities of
observations of discrete values of spin projections cannot exist in
the EPR state. Therefore, the EPR correlation can be a consequence
only of a peculiarity of the observer's mind, which can create only
oppositely directed projections of spins, and not the conservation
law.
[1] D. Bohm, Quantum Theory, New York: Prentice-Hall (1951).
With best wishes,
Alexey

вт, 24 янв. 2023 г. в 23:05, Mark Hadley <sunshine...@googlemail.com>:

[Richard Gill]

Alexei, it seems you use different postulates from just about everyone else. That makes communication difficult. Maybe you should write out your postulates in a clear mathematical form.

Richard

Sent from my iPhone

> On 26 Jan 2023, at 10:23, Алексей Никулов <nikulo...@gmail.com> wrote:
>
> Dear Mark,

[Mark Hadley]

Dear Alexey,

What you are saying is simply wrong. And is refuted by experiments 

I've never come across that postulate. It's unnecessary and as you show it is wrong. It may be a good working assumption for systems that are not entangled.

In QM the expected outcome of of an experiment is given by the Trace of the state operator and measurement operator. I'd say that was axiomatic. Try deriving your postulate from the axiom. I think you will find it only follows as a special case.

In EPR the beam is unpolarised. It can be expressed as a classical mixture up/down + down/up The decomposition is not unique. A measurement of one side reveals which of the two it is.

To give another counter example if I split a pair of shoes into two boxes and send one to Alice and the other to Bob. Then they have a 50:50 chance of having a left shoe. As soon as Alice finds a left shoe that changes the probability of Bob having a left shoe. 

Cheers

Mark

[Jan-Åke Larsson]

On 2023-01-26 11:11, 'Mark Hadley' via Bell inequalities and quantum foundations wrote:

Dear Alexey,

What you are saying is simply wrong. And is refuted by experiments 

I've never come across that postulate. It's unnecessary and as you show it is wrong. It may be a good working assumption for systems that are not entangled.

In QM the expected outcome of of an experiment is given by the Trace of the state operator and measurement operator. I'd say that was axiomatic. Try deriving your postulate from the axiom. I think you will find it only follows as a special case.

In EPR the beam is unpolarised. It can be expressed as a classical mixture up/down + down/up The decomposition is not unique. A measurement of one side reveals which of the two it is.

In EPR EACH SINGLE beam is unpolarized. THE TWO-SYSTEM state CANNOT be expressed as a classical mixture up/down+down/up. The decomposition INTO SUPERPOSITIONS is not unique. A measurement of one side projects onto a single vector for the other side.

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[Алексей Никулов]

Dear Mark,
Schrodinger defined in 1935 the EPR (Einstein – Podolsky - Rosen)
correlation as ‘entanglement of our knowledge’: ”Maximal knowledge of
a total system does not necessarily include total knowledge of all its
parts, not even when these are fully separated from each other and at
the moment are not influencing each other at all”. Your example with a
pair of shoes is the example ‘entanglement of our knowledge’. I
consider a similar example in the preprint “Logical proof of the

absurdity of the EPR correlation” available at ResearchGate
https://www.researchgate.net/publication/331584709_Logical_proof_of_the_absurdity_of_the_EPR_correlation
.

Two observers Alice and Bob know that two balls, red and blue, are in
a closed box. Bob takes one ball without looking, and drives away with
it at an arbitrarily long distance. Alice, before she looks at the
remaining ball, knows that Bob will see the blue ball with a
probability of 0.5 and with the same probability of the red ball. Her
knowledge can be described using the expression for the EPR pair

|EPR> = (|A+,B-> + |A-,B+>)/2^0.5 (1)

in which (+) represents the red ball and (-) represents the blue ball.
The knowledge of Alice will change when she will see the red ball, for
example. The new knowledge may be described with the help of the
expression
|Alice> = |A+>|B-> (2)
which means that she will see the red ball with the probability of 1
during the second observation, and Bob will see a blue ball with the
same reliability.

The expression (1) for the EPR pair can be used for the description of
Alice’s knowledge about both balls and spin projections since only two
results can be observed in both cases. But a fundamental difference is
between these cases. We can think that Alice sees a red ball since her
ball was red before her observation. But we cannot think so in the
case of spin projections since spin projections can be measured in
different directions.

To make the essence of the fundamental difference clear even to
schoolchildren, I marked the spin projections in different directions
with different colors in Fig.1 of my preprint “Logical proof of the
absurdity of the EPR correlation”. Even smart schoolchildren should
understand due to Fig.1 that quantum mechanics cannot do without the
Dirac jump because the observable does not exist before observation.
The Dirac jump can provide the perfect correlation between the results
of the first and second measurement of the same dynamical variable,
i.e. spin projections in the same direction. But the Dirac jump cannot
provide the EPR correlation since Dirac postulated in 1930 that only a

measured particle should jump “into an eigenstate of the dynamical
variable that is being measured”.

You wrote that what I was saying is simply wrong. But what exactly is
wrong? Don't you agree that the Dirac jump can provide the perfect
correlation between the results of the first and second measurements
of a single particle, but cannot provide the EPR correlation? I am not
talking about an experiment, but about the fact that quantum mechanics
cannot predict EPR correlation and violation of Bell inequalities. If
you think that there is absolutely reliable experimental evidence for
the violation of Bell's inequalities, then you should conclude that
quantum mechanics is the wrong theory.

With best wishes,
Alexey

чт, 26 янв. 2023 г. в 13:19, 'Jan-Åke Larsson' via Bell inequalities
and quantum foundations <Bell_quantum...@googlegroups.com>:

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