Has further work been done building on J Christian's model?

[gill1109]

The point is that the parallelized 3-sphere character of space will only reveal itself in special cases macroscopically. It really has never been properly tested. There should be a test done somehow or the other.

Well, why does Joy think it might manifest itself in an experiment with exploding ping-pong balls (an experiment initially put forward by Peres in order to explain why we would *not* see quantum entanglement there)? And why does Joy's original description of the experiment contain the instructions that the spins of the two hemispheres, say u and v, as two directions in real 3-D space, will be determined by computer image processing of the results of a battery of video cameras ... so that the sign of the inner products a^T u and b^T v are simultaneously determined for all a and for all b in S^2? If we restrict attention to the two pairs of CHSH directions for a and for b, and do N runs, we obtain the Nx4 spreadsheet which was discussed seriously by several persons in another thread, though others exhibited strange rowdy behaviour reminiscent of the lower house of the British parliament.

I don't see how any amount of precise instructions by Joy to David Wineland on how to set up the spins of the two ping-pong ball halves in the singlet state is going to help here. What is the quantum mechanical joint state of the spins of two separated macroscopic objects? How do you engineer it to be the singlet state? (It is already a tough order in the quantum physics lab). As far as I understand, the very definition of "macroscopic" is that quantum superpositions cannot be observed (think about sad experimental cats, for instance).

[FrediFizzx]

What is the quantum mechanical joint state of the spins of two separated macroscopic objects?

How can there be a quantum mechanical joint state of macroscopic objects such as the exploding ball? You really do need to learn some physics. Quantum mechanics has nothing to do with it.

[Joy Christian]

What is the quantum mechanical joint state of the spins of two separated macroscopic objects?

How can there be a quantum mechanical joint state of macroscopic objects such as the exploding ball? You really do need to learn some physics. Quantum mechanics has nothing to do with it.

No need to start learning physics from scratch. All he has to do is read my paper---not even the long ones, just this short one: http://arxiv.org/abs/0806.3078

[gill1109]

What is the quantum mechanical joint state of the spins of two separated macroscopic objects?

How can there be a quantum mechanical joint state of macroscopic objects such as the exploding ball? You really do need to learn some physics. Quantum mechanics has nothing to do with it.

OK, then what is the singlet state of two separated macroscopic objects? (Joy's words, not mine.)

[Joy Christian]

OK, then what is the singlet state of two separated macroscopic objects? (Joy's words, not mine.)

The answer is already given to you by Mikko. It means that the initial spin angular momentum of the total or composite system is zero: .

[gill1109]

Here we are talking about classical spin angular momentum? OK. The ball is initially at rest and then explodes into two halves. No angular momentum is dissipated to the environment (the gasses coming free by the explosion do not take away much angular momentum with them).

We don't want interaction with the environment, so that could be a good reason to do the experiment in a vacuum.

[Joy Christian]

Here we are talking about classical spin angular momentum? OK. The ball is initially at rest and then explodes into two halves. No angular momentum is dissipated to the environment (the gasses coming free by the explosion do not take away much angular momentum with them).

We don't want interaction with the environment, so that could be a good reason to do the experiment in a vacuum.

Yes. Total absence of air and gravity would be ideal. But as Fred notes, experimenters are very clever people. They may be able to compensate for the effects of air and gravity. More importantly, my description of the proposed experiment is merely to get the basic idea of how it can be done in principle. In practice the system involved would most likely not be an exploding Ping-Pong ball, but something entirely different. Something like two large Bucky balls, joined by a tiny chemical bond.

[Heinera]

Here we are talking about classical spin angular momentum? OK. The ball is initially at rest and then explodes into two halves. No angular momentum is dissipated to the environment (the gasses coming free by the explosion do not take away much angular momentum with them).

We don't want interaction with the environment, so that could be a good reason to do the experiment in a vacuum.

Yes. Total absence of air and gravity would be ideal. But as Fred notes, experimenters are very clever people. They may be able to compensate for the effects of air and gravity. More importantly, my description of the proposed experiment is merely to get the basic idea of how it can be done in principle. In practice the system involved would most likely not be an exploding Ping-Pong ball, but something entirely different. Something like two large Bucky balls, joined by a tiny chemical bond.

Hm....the Buckminsterfullerenes are still small enough to exhibit quantum behaviour, so the experiment would have to use something considerably larger.

[gill1109]

Here we are talking about classical spin angular momentum? OK. The ball is initially at rest and then explodes into two halves. No angular momentum is dissipated to the environment (the gasses coming free by the explosion do not take away much angular momentum with them).

We don't want interaction with the environment, so that could be a good reason to do the experiment in a vacuum.

Yes. Total absence of air and gravity would be ideal. But as Fred notes, experimenters are very clever people. They may be able to compensate for the effects of air and gravity. More importantly, my description of the proposed experiment is merely to get the basic idea of how it can be done in principle. In practice the system involved would most likely not be an exploding Ping-Pong ball, but something entirely different. Something like two large Bucky balls, joined by a tiny chemical bond.

Hm....the Buckminsterfullerenes are still small enough to exhibit quantum behaviour, so the experiment would have to use something considerably larger.

Yes. Already, the two-slit experiment was done with Bucky balls.

Joy's claim is that classical physical systems can exhibit the singlet correlations. He claims he has a classical local hidden variables model which does so, using the S^3 property of physical space. The experiment should exhibit the singlet correlations with macroscopic objects which we usually succesfully describe by classical mechanics. That's what his experiment paper claims. Have two hemispherical halves of a small ball fly apart, rotating in equal and opposite directions. Observe their spatial coordinates and orientiations through a battery of video cameras and so that their directions of spin, relative to measurement directions a and a', and relative to directions b and b', could all be determined simultaneously.

Later Joy insisted that we would only actually calculate A(a, lambda) *or* A(a', lambda), not both of them, but he makes clear that we should compute lambda using image reconstruction software from the video films, and A(a, lambda) is just the sign of a^T lambda

[Joy Christian]

Yes. Already, the two-slit experiment was done with Bucky balls.

I said "something like two large Bucky balls, joined by a tiny chemical bond." One can even make a "chemical bond" out of two ping pong balls. Then the spherical symmetries of the flying halves can be retained, resolving many practical issues.

Joy's claim is that classical physical systems can exhibit the singlet correlations.

Correct, but not any old classical systems. Only those which are in relative rotations with respect to each other.

He claims he has a classical local hidden variables model which does so, using the S^3 property of physical space.

Yes, I do.

The experiment should exhibit the singlet correlations with macroscopic objects which we usually succesfully describe by classical mechanics.

The latter half of your sentence is incorrect. In particular, Peres's calculation of his experiment is incorrect. His calculation is done using the symmetry group SO(3), whereas the experimental scenario he describes demands the symmetry group SU(2). This is elementary classical mechanics, and Peres gets it spectacularly wrong.

You can find the correct calculation in this as well as this paper.

That's what his experiment paper claims. Have two hemispherical halves of a small ball fly apart, rotating in equal and opposite directions. Observe their spatial coordinates and orientations through a battery of video cameras and so that their directions of spin, relative to measurement directions a and a', and relative to directions b and b', could all be determined simultaneously.

Yes, determined simultaneously, but not used simultaneously. It is very clearly discussed in the first paper above that the calculation must be done according to equation (16). I am not interested in how anyone else does the calculation but Nature. I have described how Nature does the calculation in the above papers.

Later Joy insisted that we would only actually calculate A(a, lambda) *or* A(a', lambda), not both of them, but he makes clear that we should compute lambda using image reconstruction software from the video films, and A(a, lambda) is just the sign of a^T lambda.

There was, and there is, no "Later". The first paper exists since 2008. Your misinterpretation of what is written in it is not going to change anything.

You can calculate both A(a, lambda) and A(a', lambda) if you want, but cannot add A(a, lambda) and A(a', lambda), or subtract them, in the computation of the correlation. The four correlations must be calculated separately, as specified in equation (16) of the first paper:

**********************************************************************************

For the record, let me repeat that equation (16) of my attached
experimental paper describes exactly how the expectation values
E(a, b), E(a', b), E(a, b'), and E(a', b') are to be computed in my
proposed experiment. Four separate sums are to be calculated as
follows

E(a, b) = 1/N Sum_j A_j B_j ,

E(a, b') = 1/N Sum_j A_j B'_j ,

E(a', b) = 1/N Sum_j A'_j B_j ,

and

E(a', b') = 1/N Sum_j A'_j B'_j .

It is a matter of indifference whether N here is chosen to be the same
or different for each of the four alternatives.

The experimental procedure described in my paper is unambiguous.

**********************************************************************************

[gill1109]

You can calculate both A(a, lambda) and A(a', lambda) if you want, but cannot add A(a, lambda) and A(a', lambda), or subtract them, in the computation of the correlation. The four correlations must be calculated separately, as specified in equation (16) of the first paper:

Excellent!

We are going to add and subtract four correlations each computed on a disjoint subset of the runs.

The runs belonging to the pair a, b are a random sample of all N runs, of size about N/4.
The runs belonging to the pair a, b' are a disjoint random sample of all N runs, of size about N/4.
The runs belonging to the pair a', b are a disjoint random sample of all N runs, of size about N/4.
The runs belonging to the pair a', b' are a disjoint random sample of all N runs, of size about N/4.

[Joy Christian]

You can calculate both A(a, lambda) and A(a', lambda) if you want, but cannot add A(a, lambda) and A(a', lambda), or subtract them, in the computation of the correlation. The four correlations must be calculated separately, as specified in equation (16) of the first paper:

Excellent!

We are going to add and subtract four correlations each computed on a disjoint subset of the runs.

The runs belonging to the pair a, b are a random sample of all N runs, of size about N/4.
The runs belonging to the pair a, b' are a disjoint random sample of all N runs, of size about N/4.
The runs belonging to the pair a', b are a disjoint random sample of all N runs, of size about N/4.
The runs belonging to the pair a', b' are a disjoint random sample of all N runs, of size about N/4.

Incorrect. Please read the description of my proposed experiment and other comments in my previous post. I am not interested in your version of the calculation.

[gill1109]

You can calculate both A(a, lambda) and A(a', lambda) if you want, but cannot add A(a, lambda) and A(a', lambda), or subtract them, in the computation of the correlation. The four correlations must be calculated separately, as specified in equation (16) of the first paper:

Excellent!

We are going to add and subtract four correlations each computed on a disjoint subset of the runs.

The runs belonging to the pair a, b are a random sample of all N runs, of size about N/4.
The runs belonging to the pair a, b' are a disjoint random sample of all N runs, of size about N/4.
The runs belonging to the pair a', b are a disjoint random sample of all N runs, of size about N/4.
The runs belonging to the pair a', b' are a disjoint random sample of all N runs, of size about N/4.

Incorrect. Please read the description of my proposed experiment and other comments in my previous post. I am not interested in your version of the calculation.

Our notations differ, but our descriptions are fully in agreement.

We agreed that for each run, Alice and Bob's measurement settings would be determined by coin tosses supplied by me. Each of Alice's coin toss outcomes determines whether she measures in direction a or a'; each of Bob's determines whether he measures in direction b or b'.

So if there are a total of N runs (that's my "N"), then in about a quarter of them, we'll get an outcome for A and B; in about a quarter, we'll get an outcome for A and B'; and so on. Those four numbers each approximately equal to my N divided by 4, are your N's (a possibly different one for each pair of settings, as you yourself say).

Your "N" is different from my "N". We have four sets of runs, each of size N11, N12, N21, N22 say. These four numbers are what you call "N". My "N" is their sum. N11, N12, N21, and N22 will be approximately equal to one another. My N is about four times each of your four N's.

We are going to perform your calculation, exactly as you describe it.

[Joy Christian]

Our notations differ, but our descriptions are fully in agreement.

No, they are not. Please read the paper where I have described the experiment. All actual spin directions are measured, for all of the N runs. The a's and b's need not be supplied at all during the experiment. Once all actual spins are recorded, the data is stored on a computer. We can then calculate E(a, b) etc., for each pair (a, b), using all of the data, over all of N. There is no N/4 or Nx4 in my description. I believe we have a fundamentally different understanding of the calculations involved.

[gill1109]

Dear Joy

Please make up your mind. Are the four correlations computed on the same set of N runs, or on four different sets of runs (of similar but possibly slightly different sizes?)

I know that your original paper stipulated the former. In that case there is no need to do the experiment since simple algebra shows me that you will certainly lose, as Han Geurdes perceptively also noticed (he warned you very firmly against it!). In fact, from the N runs we could generate that famous Nx4 spreadsheet! You forbid me to add and subtract within the rows. I don't have to do that, in order to deduce that the addition and subtraction of four correlations will result in agreement with CHSH inequality. You can't forbid a Gedankenexperiment.

If however in the n'th run Alice and Bob each choose one of two settings at random, as in a real CHSH experiment, then four disjoint subsets of runs are created. I asked for a CHSH style experiment, and you agreed.

Now it is no longer certain that I'll win, but as long as N is large the chance that I'll win is very close to 1. Now I need some simple probability theory as well as the earlier performed simple algebra in order to work out how large N should be in order that my chance of losing is acceptably small relative to the amount I can bet.

[FrediFizzx]

Richard, it is simple. Joy is not going to fall for you "rigging the game" with your phony CHSH.

[gill1109]

Richard, it is simple. Joy is not going to fall for you "rigging the game" with your phony CHSH.

The problem is not a so-called phoney CHSH Fred; I am afraid that I suspect that the problem is Bell's theorem. However Joy believes he has proven a counter-example so he believes the theorem is not true. So he should be OK then, right?

I am not rigging any game. I'm asking for a standard CHSH experiment, and Joy has agreed with that in principle. I would say that John S. Bell brilliantly "rigged" CHSH so that it would effectively discriminate between quantum mechanics on the one hand, and local realism (local hidden variables) on the other. Joy "knows" that Bell was wrong. Great, and now we are going to put that to the test.

We are now settling little details of interpretation. In my opinion, different writings of Joy's are not consistent with one another. Taken together, they are ambiguous. So together with three adjudicators we are going to draw up a definitive CHSH-style protocol which we all five agree on, and from then on, Joy and I will be bound by the three adjudicators' interpretation of what we five have previously drawn up in writing, and signed in agreement.

I suggest you now take a look at section 4 of Joy's experimental paper arXiv:1211.0784

There Joy asks for N runs and he wants all four correlations calculated in the usual way, except that for each of the correlations he uses the same N runs. So apparently when we have done the n'th exploding ball run, n=1, ..., N, we can write down any spin measurement outcome for any possible direction for either of the two hemispheres. And moreover, he tells the experimenter to do that for *many different directions* on the basis of the same set of N runs.

But maybe I misread him.

Now actually I wanted a regular CHSH type experiment in which, for the n'th run, Alice and Bob each supply a new coin toss outcome to decide whether they want to measure in directions a or a', and in directions b or b', where these four directions have been decided in advance. So the way I see it, there will be approximately N/4 runs available for each of four setting pairs only: (a,b), (a,b'), (a',b), (a',b').

I'm perfectly happy with either arrangement!

Joy's arrangement: I believe that I win with probabilty 1, see "Fact 2" of Section 2 of my paper. My arrangement: I believe that I win with large probability, see Theorem 1 of Section 2 of my paper. Joy, Michel, Fred and no doubt others, believe that theoretical developments starting from considering an Nx4 spreadsheet are irrelevant. I believe they are mistaken.

Either way, we are going to end up calculating four correlations in conventional fashion. We will surely be able to agree in advance, how to determine which runs are to be used for which correlation. There are two options on the table at the moment. Anyone have any alternative suggestions?

So it's not clear to me, Fred, whether you are against any kind of CHSH type experiment in principle, which seemed to be Han Geurdes' position, of if you simply have a different CHSH protocol in mind from what other people have used in the past.

[minkwe]

Bell's theorem says a locally realistic theory can not reproduce the quantum correlations. The important question then is can Joy's model reproduce the quantum correlations. It has done so in theory. The experiment will show that a locally realistic macroscopic system can also produce the correlations. I have to agree with Han Geurdes. Nobody needs to talk about any Nx4 spreadsheet or any CHSH. There is an experiment in which particles are produced in pairs and measured in pairs with outcomes +1/-1. The only relevant question as far as Bell's theorem is concerned is whether such a locally realistic macroscopic experiment can reproduce the quantum correlations. If it does, case closed. CHSH and Nx4 spreadsheets are just red-herrings here and an opportunity for rigging.

Any one who disagrees with this would have to explain why it is not enough for a locally realistic macroscopic experiment to reproduce the QM correlations. Why shouldn't that be sufficient to destroy Bell's theorem? Apart from any CHSH or Nx4 spreadhseet discussion.

[gill1109]

Bell's theorem says a locally realistic theory can not reproduce the quantum correlations. The important question then is can Joy's model reproduce the quantum correlations. It has done so in theory. The experiment will show that a locally realistic macroscopic system can also produce the correlations. I have to agree with Han Geurdes. Nobody needs to talk about any Nx4 spreadsheet or any CHSH. There is an experiment in which particles are produced in pairs and measured in pairs with outcomes +1/-1. The only relevant question as far as Bell's theorem is concerned is whether such a locally realistic macroscopic experiment can reproduce the quantum correlations. If it does, case closed. CHSH and Nx4 spreadsheets are just red-herrings here and an opportunity for rigging.

Any one who disagrees with this would have to explain why it is not enough for a locally realistic macroscopic experiment to reproduce the QM correlations. Why shouldn't that be sufficient to destroy Bell's theorem? Apart from any CHSH or Nx4 spreadhseet discussion.

Well actually the experts disagree about the "theory" part. A whole lot of experts claim to have found serious errors. A small number of people have cited Joy approvingly but without actually building on his theory.

There is no Nx4 spreadsheet in the experiment which Joy and I are planning. There will be CHSH since we are making a bet and we need an absolutely unambiguous criterion for who has won. So we will be looking at just four correlations, the usual four pairs rho(a, b), rho(a, b'), rho(a', b), rho(a', b'). If they are all close to +/- 0.707 (three positive and one negative, or three negative and one positive) then Joy will have won the bet. Of course he's welcome to use the experiment to exhibit the whole cosine curve if he wants to. I am just interested in four points on it. If they're good, then I'll pay up.

There will be no rigging of anything. The only thing which I insist on, is that for each of N runs, Alice chooses between setting a and setting a' by tossing a fair coin, and Bob similarly chooses between b and b'.

[gill1109]

You can calculate both A(a, lambda) and A(a', lambda) if you want, but cannot add A(a, lambda) and A(a', lambda), or subtract them, in the computation of the correlation. The four correlations must be calculated separately, as specified in equation (16) of the first paper:

**********************************************************************************

For the record, let me repeat that equation (16) of my attached
experimental paper describes exactly how the expectation values
E(a, b), E(a', b), E(a, b'), and E(a', b') are to be computed in my
proposed experiment. Four separate sums are to be calculated as
follows

E(a, b) = 1/N Sum_j A_j B_j ,

E(a, b') = 1/N Sum_j A_j B'_j ,

E(a', b) = 1/N Sum_j A'_j B_j ,

and

E(a', b') = 1/N Sum_j A'_j B'_j .

It is a matter of indifference whether N here is chosen to be the same
or different for each of the four alternatives.

The experimental procedure described in my paper is unambiguous.

Pretty unambiguous. It's OK to do N runs. It's OK to calculate A_j and A'_j and B_j and B'j for each of the N runs. This provides us with 4N numbers +/-1.

I'm just not allowed to put them into an Nx4 spreadsheet together, OK, I won't, I promise!!! (It was only a Gedankenexperiment by silly me, I am so sorry for having mentioned my private thoughts).

I must sum products, divide by N, then I have four correlations. I will add three of the correlations and subtract the fourth. That's OK.

I think I'm going to win my bet. Someone please help Joy ...