Commonsense local realism refutes Bell's theorem

[minkwe]

It is impossible to measure a particle more than once. In QM terms, the E(a,b) measurement does not commute with the E(a,c) measurement on the same set of particles.

Don't you find it extremely ironic that you use a QM postulate ("It is impossible to measure a particle more than once") to argue against QM formalism and in favor of LHV models?

I had no idea electrons can be detected more than once in classical physics.

[minkwe]

It is impossible to measure a particle more than once. In QM terms, the E(a,b) measurement does not commute with the E(a,c) measurement on the same set of particles.

Don't you find it extremely ironic that you use a QM postulate ("It is impossible to measure a particle more than once") to argue against QM formalism and in favor of LHV models?

I had no idea electrons can be detected more than once in classical physics.

Besides, who is arguing against QM?

[gill1109]

It is impossible to measure a particle more than once. In QM terms, the E(a,b) measurement does not commute with the E(a,c) measurement on the same set of particles.

Don't you find it extremely ironic that you use a QM postulate ("It is impossible to measure a particle more than once") to argue against QM formalism and in favor of LHV models?

I had no idea electrons can be detected more than once in classical physics.

Michel, in that case, why talk about doing the same measurement several times on the same particles? Whether it is actually possible or actually impossible is totally irrelevant!

When we derive a mathematical inequality starting from some model assumptions, we do not actually measure particles at all. We have a probability distribution rho over a set of values of hidden variables Lambda, and we have two functions A(a, lambda) and B(b, lambda) delivering what the measurement outcomes would be under various settings a, b, .... We are working in a mathematical world (functions, sets, probability theory, expectation values ...).

We can *imagine* a pair of particles with value of the hidden variable lambda, and now one can *write down* A(a, lambda), A(a', lambda), B(b, lambda), B(b', lambda). Calling these four numbers, for short, A, A', B, B' one can now observe that AB + A'B + AB' - A'B' equals minus 2 or plus 2. One can now imagine drawing lambda at random and averaging over all possible values. And so on ...

Einstein, Podolsky and Rosen used quantum mechanics and locality in order to prove realism. The pair of particles each both have a well defined position and a well defined momentum. They don't discuss impossible experiments where several particles are simultaneously measured in several mutually incompatible ways at the same time.

Now if you *do* want to talk about doing several different measurements on the same particle, take a look at Joy Christian's experimental paper, and tell us what you think about it!

http://arxiv.org/abs/0806.3078
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=52#p1898

[gill1109]

Also, below Bell's (1964), equation (13), what is the meaning of "except at a set of points λ of zero probability."

Bell tells us that if you want P in equation (2) to equal -1 when a = b, then it is necessary to have that with probability one (with respect to picking lambda at random with distribution rho), A(a, lambda) = - B(a, lambda).

That's because A and B both only take the values -1 and +1. So A times B is always -1 or +1. If you want it to average to -1 it must essentially always equal -1. If it would equal +1 with positive probability then the average would be larger than -1.

So "with probability one" means exactly what it says. Bell is sayintg that it is possible that A = - B fails for some values of lambda which together only have probability zero. However, if A is different from -B on some set of lambda with positive probability, then the integral of A(a, lambda) times B(a, lambda) would be strictly larger than -1.

It seems to me that those who want to understand Bell's derivations need to have some basic understanding of probability theory and statistics, and some basic "feel" for mathematical thinking. It seems that the literature on the topic is bedevilled by lack of this basic background. How is it possible to train physicists without teaching them probability and statistics? How can physicists use mathematics if they don't appreciate the difference between physical reality and a mathematical model, and don't appreciate the "reality" of mathematical models?

I recommend the standard text-book "Introduction to Mathematical Statistics and Data Analysis" by John A. Rice.

[Heinera]

It is impossible to measure a particle more than once. In QM terms, the E(a,b) measurement does not commute with the E(a,c) measurement on the same set of particles.

Don't you find it extremely ironic that you use a QM postulate ("It is impossible to measure a particle more than once") to argue against QM formalism and in favor of LHV models?

I had no idea electrons can be detected more than once in classical physics.

So, does this mean that you think Bell's theorem is false for electrons, but true for exploding ball fragments (which obviously can be measured twice)?

[gill1109]

Michel, here is the context to Heinera's remark, in case you are not aware of it: from page 4 of http://arxiv.org/abs/0806.3078 by Joy Christian:

Consider a “bomb” made out of a hollow toy ball of diameter, say, three centimeters. The thin hemispherical shells of uniform density that make up the ball are snapped together at their rims in such a manner that a slight increase in temperature would pop the ball open into its two constituents with considerable force [5]. A small lump of density much grater than the density of the ball is attached on the inner surface of each shell at a random location, so that, when the ball pops open, not only would the two shells propagate with equal and opposite linear momenta orthogonal to their common plane, but would also rotate with equal and opposite spin momenta about a random axis in space. The volume of the attached lumps can be as small as a cubic millimeter, whereas their mass can be comparable to the mass of the ball. This will facilitate some 10^6 possible spin directions for the two shells, whose outer surfaces can be decorated with colors to make their rotations easily detectable.

Now consider a large ensemble of such balls, identical in every respect except for the relative locations of the two lumps (affixed randomly on the inner surface of each shell). The balls are then placed over a heater—one at a time—at the center of an EPR-Bohm type setup [6], with the common plane of their shells held perpendicular to the horizontal direction of the setup. Although initially at rest, a slight increase in temperature of each ball will eventually eject its two shells towards the observation stations, situated at a chosen distance in the mutually opposite directions. Instead of selecting the directions a and b for observing spin components, however, one or more contact-less rotational motion sensors—capable of determining the precise direction of rotation—are placed near each of the two stations, interfaced with a computer. These sensors will determine the exact direction of the angular momentum λj (or −λj) for each shell, without disturbing them otherwise, at a designated distance from the center. The interfaced computers can then record this data, in the form of a 3D map of all such directions.

Once the actual directions of the angular momenta for a large ensemble of shells on both sides are fully recorded, the two computers are instructed to randomly choose the reference directions, a for one station and b for the other station—from within their already existing 3D maps of data—and then calculate the corresponding dynamical variables sign (λj · a) and sign ( − λj · b). This “delayed choice” of a and b will guarantee that the conditions of parameter independence and outcome independence are strictly respected within the experiment [2]. It will ensure, for example, that the local outcome sign (λj · a) remains independent not only of the remote parameter b, but also of the remote outcome sign (−λj · b). If in any doubt, the two computers can be located at a sufficiently large distance from each other to ensure local causality while selecting a and b. The correlation function for the bomb fragments can then be calculated using the formula

E(a, b) = 1/N sum_{j = 1}^N {sign (λj · a)} {sign(−λj · b)}, (16)

where N is the number of trials. This result, which would give purely local correlations, should then be compared (in N → ∞ limit) with the predictions (3) and (15).

...

Undoubtedly, there would be many different sources of systematic errors in an experiment such as this. If it is performed carefully enough, however, then—in the light of the discussion above—we believe the experiment will vindicate prediction (15) and refute prediction (3).

(15) is the equation E(a, b) = - a . b
(3) is the equation E(a, b) = int A(lambda) B(lambda) rho(lambda) d lambda

The references are to an earlier paper of Christian [2], a paper and the famous book of Peres [5], and the CHSH paper [6].

[minkwe]

Don't you find it extremely ironic that you use a QM postulate ("It is impossible to measure a particle more than once") to argue against QM formalism and in favor of LHV models?

So, does this mean that you think Bell's theorem is false for electrons, but true for exploding ball fragments (which obviously can be measured twice)?

It means you believe electrons can be measured more than once in classical physics, which is absurd. The suggestion that the impossibility to physically measure an elementary particle more than once is a "postulate" of QM is almost funny in a sad way.

Bell's theorem compares LHV theories with QM predictions. Maybe you also believe LHV theories can never agree with QM predictions for macroscopic exploding ball fragments.

In any case I believe Bells theorem is false for all types of systems. LHV theories can reproduce the QM expectation value for any system, micro- or macroscopic.

[gill1109]

Maybe you also believe LHV theories can never agree with QM predictions for macroscopic exploding ball fragments.
In any case I believe Bells theorem is false for all types of systems. LHV theories can reproduce the QM expectation value for any system, micro- or macroscopic.

What about Christian's predictions for his exploding ball experiment? In which all possible measurements are done at the same time on both "particles".

By the way, according to "Bell's fifth position", your belief is indeed correct: LHV theories can reproduce the QM expectation value for any system, micro- or macroscopic. So far this belief has not been experimentally invalidated. Though not many people take it seriously. Emilios Santos is one exception.

[Heinera]

Don't you find it extremely ironic that you use a QM postulate ("It is impossible to measure a particle more than once") to argue against QM formalism and in favor of LHV models?

So, does this mean that you think Bell's theorem is false for electrons, but true for exploding ball fragments (which obviously can be measured twice)?

It means you believe electrons can be measured more than once in classical physics, which is absurd. The suggestion that the impossibility to physically measure an elementary particle more than once is a "postulate" of QM is almost funny in a sad way.

Bell's theorem compares LHV theories with QM predictions. Maybe you also believe LHV theories can never agree with QM predictions for macroscopic exploding ball fragments.

In any case I believe Bells theorem is false for all types of systems. LHV theories can reproduce the QM expectation value for any system, micro- or macroscopic.

What I believe about electrons is not very relevant; since I certainly believe macroscopic ball fragments can be measured more than once. So how do your objection ("it can only be measured once") apply in that case?

The QM predictions for a macroscopic exploding ball experiment are not the cosine correlations, but exactly the correlations that would come out of a LHV model. So in fact I do agree that a LHV theory agrees with the QM predictions in this case. It is Joy Christian (and you) who thinks we should observe the cosine correlations in his experiment - in conflict with the QM prediction for macroscopic systems.

[minkwe]

What I believe about electrons is not very relevant;

It is relevant, because it demonstrates the persistent misconceptions that prevent you from understanding the points being made by myself or by Watson. For the EPRB experiment being discussed by Watson and Bell, the particles can not be measured more than once, the act of measurement destroys them. That is a physical limitation without any regard for the theory you chose to describe the experiment with.

since I certainly believe macroscopic ball fragments can be measured more than once. So how do your objection ("it can only be measured once") apply in that case?

The inability to measure more than once is not limited to elementary particles. Based on how you perform the experiment, you can easily find that you can not measure even exploding ball fragments more than once. In any case, I believe and have repeatedly stated that ALL quantum correlations can be explained by LHV theories. Please read the former statement again and make sure it sinks in.

So in fact I do agree that a LHV theory agrees with the QM predictions in this case. It is Joy Christian (and you) who thinks we should observe the cosine correlations in his experiment - in conflict with the QM prediction for macroscopic systems.

A bunch of lies, show me where I have ever claimed that a LHV theory and QM will disagree for any experiment. Bell's theorem says LHV will never agree with all the predictions of QM, I have repeated stated that Bell's theorem is false, and all QM correlations will can be explained by LHV. Now you accuse me of claiming that QM will disagree with LHV for macroscopic experiments?! Surely you must know that this is a lie.

Ultimately, the point stands. In the EPRB experiment being discussed by Bell, in his derivation of his original inequalities, the particles can not be measured more than once, therefore Watson's analysis of Bell's original paper is correct. Bell made a fatal error which invalidates his proof. Bell's original highly acclaimed 1964 paper is wrong! I know Gill believes he has rescued Bell's derivation (I don't believe he has or that it can even be rescued) but why would it need to be rescued or strengthened if it was correct and on good footing to begin with?

[gill1109]

Ultimately, the point stands. In the EPRB experiment being discussed by Bell, in his derivation of his original inequalities, the particles can not be measured more than once, therefore Watson's analysis of Bell's original paper is correct. Bell made a fatal error which invalidates his proof. Bell's original highly acclaimed 1964 paper is wrong! I know Gill believes he has rescued Bell's derivation (I don't believe he has or that it can even be rescued) but why would it need to be rescued or strengthened if it was correct and on good footing to begin with?

Bell's derivation does not assume that particles can be measured more than once. Bell shows that the assumption of a local hidden variables theory implies certain limits on correlations which can be observed in Nature, if Nature could be described by such a theory. There is no need to "rescue" his 1964 paper, but there certainly was possibility to remove ambiguities and sharpen the results. Bell's 1980 (?) "Bertlmann" paper already improves and sharpens Bell (1964) in numerous respects.

My own recent work is a further *strengthening* of Bell's. Bell's 1980 results, which improve on those from 1964, are a *corollary* of mine. I derive finite N probability bounds, but Bell only has infinite N limits.

A local hidden variables *theory* implies the mathematical existence, simultaneously, within the theory, of outcomes of different potential measurements. The measurements don't need to be *done*. They aren't *done* within the derivation of the famous inequalities.

[gill1109]

Based on how you perform the experiment, you can easily find that you can not measure even exploding ball fragments more than once.

Perhaps you should read Christian's experimental paper before directly contradicting what he says. Page 4 of http://arxiv.org/abs/0806.3078 by Joy Christian:

Consider a “bomb” made out of a hollow toy ball of diameter, say, three centimeters. The thin hemispherical shells of uniform density that make up the ball are snapped together at their rims in such a manner that a slight increase in temperature would pop the ball open into its two constituents with considerable force [5]. A small lump of density much grater than the density of the ball is attached on the inner surface of each shell at a random location, so that, when the ball pops open, not only would the two shells propagate with equal and opposite linear momenta orthogonal to their common plane, but would also rotate with equal and opposite spin momenta about a random axis in space. The volume of the attached lumps can be as small as a cubic millimeter, whereas their mass can be comparable to the mass of the ball. This will facilitate some 10^6 possible spin directions for the two shells, whose outer surfaces can be decorated with colors to make their rotations easily detectable.

Now consider a large ensemble of such balls, identical in every respect except for the relative locations of the two lumps (affixed randomly on the inner surface of each shell). The balls are then placed over a heater—one at a time—at the center of an EPR-Bohm type setup [6], with the common plane of their shells held perpendicular to the horizontal direction of the setup. Although initially at rest, a slight increase in temperature of each ball will eventually eject its two shells towards the observation stations, situated at a chosen distance in the mutually opposite directions. Instead of selecting the directions a and b for observing spin components, however, one or more contact-less rotational motion sensors—capable of determining the precise direction of rotation—are placed near each of the two stations, interfaced with a computer. These sensors will determine the exact direction of the angular momentum λj (or −λj) for each shell, without disturbing them otherwise, at a designated distance from the center. The interfaced computers can then record this data, in the form of a 3D map of all such directions.

Once the actual directions of the angular momenta for a large ensemble of shells on both sides are fully recorded, the two computers are instructed to randomly choose the reference directions, a for one station and b for the other station—from within their already existing 3D maps of data—and then calculate the corresponding dynamical variables sign (λj · a) and sign ( − λj · b). This “delayed choice” of a and b will guarantee that the conditions of parameter independence and outcome independence are strictly respected within the experiment [2]. It will ensure, for example, that the local outcome sign (λj · a) remains independent not only of the remote parameter b, but also of the remote outcome sign (−λj · b). If in any doubt, the two computers can be located at a sufficiently large distance from each other to ensure local causality while selecting a and b. The correlation function for the bomb fragments can then be calculated using the formula

E(a, b) = 1/N sum_{j = 1}^N {sign (λj · a)} {sign(−λj · b)}, (16)

where N is the number of trials. This result, which would give purely local correlations, should then be compared (in N → ∞ limit) with the predictions (3) and (15).

...

Undoubtedly, there would be many different sources of systematic errors in an experiment such as this. If it is performed carefully enough, however, then—in the light of the discussion above—we believe the experiment will vindicate prediction (15) and refute prediction (3).

(15) is the equation E(a, b) = - a . b
(3) is the equation E(a, b) = int A(lambda) B(lambda) rho(lambda) d lambda

The references are to an earlier paper of Christian [2], a paper and the famous book of Peres [5], and the CHSH paper [6].

[Heinera]

So in fact I do agree that a LHV theory agrees with the QM predictions in this case. It is Joy Christian (and you) who thinks we should observe the cosine correlations in his experiment - in conflict with the QM prediction for macroscopic systems.

A bunch of lies, show me where I have ever claimed that a LHV theory and QM will disagree for any experiment.

What? Don't you claim that a LHV theory will produce the cosine correlations in Joy Christian's experiment? Well, QM disagrees. According to QM, this particular macroscopic experiment reduces to classical mechanics, for which the correlations are easily derived. And they are not the cosine correlations.

[minkwe]

What? Don't you claim that a LHV theory will produce the cosine correlations in Joy Christian's experiment?

I'm sure you will remind me by quoting specifically where I've made any such claims. I claim that whatever the experimental correlations are, they will agree with the QM prediction for the experiment, whatever the experiment is.

Well, QM disagrees. According to QM, this particular macroscopic experiment reduces to classical mechanics, for which the correlations are easily derived. And they are not the cosine correlations.

You claim that the QM prediction for the experiment is not the cosine correlation, Joy claims that it is the cosine correlation, you can attempt to prove him wrong by producing the QM calculation showing that it is not the cosine correlation. What has that got to do with what we are discussing here? This thread is about Watson's paper and the fact that Bell's original paper is wrong. A point you have no argument against.

[minkwe]

There is one and only one interpretation of the QM E(a, b): it stands for the probability two measured spins are equal minus the probability they are unequal.

You say that because you do not yet understand the issue. Every probability can be interpreted as either strongly objective or weakly objective. If I tell you that the probability of heads P(H) is 0.75, you have to decide, unless I tell you which interpretation to use or more information, "strongly objective" or "weakly objective". The strongly objective view is that P(H) is the probability of repeatedly tossing the same coin many times, while the "weakly objective" view is that P(H) is the probability of tossing many different "similar" coins each just one time. Once you pick an interpretation, you must consistently use that interpretation, otherwise you shoot yourself in the foot and drown in paradoxes. The recent discussion involving degrees of freedom, clearly highlight what the issues are when you mix the interpretations willy-nilly.

The set of values E(a,b), E(a,c) and E(b,c) does not tell you which interpretation to use. The "weakly objective" interpretation says the three expectation values represent separate measurements on three different sets of particles, The "strongly objective" view says they represent joint properties of a single set (aka population means). Once you pick one interpretation, you must stick with it. What Bell and later on Gill does is to mix the two interpretations and as a result with end up with the garbage that is Bell's theorem.

Adenier was, ten years ago, in my opinion, badly confused.

Adenier was not confused, then. You are confused now. The truth is timeless. Whether or not the truth is published does not change the fact that it is true. To demonstrate that you are confused, I'll ask you a couple of question, your answers will clearly reveal that it is you who is confused:

The short version of the two questions are: What interpretation does Gill use for the terms in Bell's inequality strongly objective or weakly objective? What interpretation does Gill use for the terms from QM strongly objective or weakly objective?

So we shall see if you are being logically consistent as you answer these questions.

[gill1109]

I take the weakly objective interpretation of E(a, b), both with respect to QM and with respect to a possible LHV theory "behind" QM.

There is one and only one interpretation of the QM E(a, b): it stands for the probability two measured spins are equal minus the probability they are unequal.

You say that because you do not yet understand the issue. Every probability can be interpreted as either strongly objective or weakly objective. If I tell you that the probability of heads P(H) is 0.75, you have to decide, unless I tell you which interpretation to use or more information, "strongly objective" or "weakly objective". The strongly objective view is that P(H) is the probability of repeatedly tossing the same coin many times, while the "weakly objective" view is that P(H) is the probability of tossing many different "similar" coins each just one time. Once you pick an interpretation, you must consistently use that interpretation, otherwise you shoot yourself in the foot and drown in paradoxes. The recent discussion involving degrees of freedom, clearly highlight what the issues are when you mix the interpretations willy-nilly.

The set of values E(a,b), E(a,c) and E(b,c) does not tell you which interpretation to use. The "weakly objective" interpretation says the three expectation values represent separate measurements on three different sets of particles, The "strongly objective" view says they represent joint properties of a single set (aka population means). Once you pick one interpretation, you must stick with it. What Bell and later on Gill does is to mix the two interpretations and as a result with end up with the garbage that is Bell's theorem.

Adenier was, ten years ago, in my opinion, badly confused.

Adenier was not confused, then. You are confused now. The truth is timeless. Whether or not the truth is published does not change the fact that it is true. To demonstrate that you are confused, I'll ask you a couple of question, your answers will clearly reveal that it is you who is confused:

The short version of the two questions are: What interpretation does Gill use for the terms in Bell's inequality strongly objective or weakly objective? What interpretation does Gill use for the terms from QM strongly objective or weakly objective?

So we shall see if you are being logically consistent as you answer these questions.

[minkwe]

Perhaps you should read Christian's experimental paper before directly contradicting what he says. Page 4 of http://arxiv.org/abs/0806.3078 by Joy

Perhaps you do not realize that this thread is about Watson's paper and not Joy's experiment. You can start a new thread for that if you like.

[gill1109]

Perhaps you should read Christian's experimental paper before directly contradicting what he says. Page 4 of http://arxiv.org/abs/0806.3078 by Joy

Perhaps you do not realize that this thread is about Watson's paper and not Joy's experiment. You can start a new thread for that if you like.

There already are several threads on Christian's experiment. We have been asking for your wisdom again and again.

But the fact remains, even on a thread about Watson's paper, it would be wise to read Christian's paper about exploding balls before contradicting what he says about exploding balls.

[minkwe]

The short version of the two questions are: What interpretation does Gill use for the terms in Bell's inequality strongly objective or weakly objective? What interpretation does Gill use for the terms from QM strongly objective or weakly objective?

So we shall see if you are being logically consistent as you answer these questions.

I take the weakly objective interpretation of E(a, b).

There were two questions. Do you answer "weakly objective" for both? Are you sure that is your choice, because you just opened Pandoras box.

[gill1109]

The short version of the two questions are: What interpretation does Gill use for the terms in Bell's inequality strongly objective or weakly objective? What interpretation does Gill use for the terms from QM strongly objective or weakly objective?

So we shall see if you are being logically consistent as you answer these questions.

I take the weakly objective interpretation of E(a, b).

There were two questions. Do you answer "weakly objective for both?"

Yes.

See

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Instrumentalist_interpretation

It's just the usual frequentist interpretation of probability. It works pretty well in science. See "Introduction to mathematical statistics and data analysis" by John A Rice. Excellent text book with practical introduction to probability theory and then to statistics.