Bell’s Theorem Refuted: Bell’s 1964:(15) is False

[Joy Christian]

OK so in flatland we have zero curvature but this nonzero torsion. Am aware that GR can be reformulated as Telleparallel gravity which treats spacetime as spatially flat background but having torsion. In that formulation torsion is still generated by stress-energy-momentum source similar to how curvature is in GR, right? And thus is generally quite nonuniform and negligible in absence of large mass source. So getting back to nominally source-free flatland, what is the source of significant torsion in your picture? Seems to me one has to posit some kind of uniform value that is somehow source-free and an intrinsic property of spacetime. Is that correct? Hard to sensibly imagine this (my limitation no doubt) as the picture I have is; fapp source-free implies uniformity/isotropy thus an all-pervading uniform scalar field with no directionality possible.

Teleparallel gravity is indeed the right picture. The torsion now plays the role of a gravitational force in a Newton-like force equation, which turns out to be equivalent to the geodesic equation of Einstein's theory. Thus one can have torsion even in a source-free situation. It pops up on the right-hand-side of the geodesic equation if we split the "non-flat" connection into a "flat" connection plus torsion, and then bring the torsion on the right-hand-side of the geodesic equation. So we are indeed talking about homogeneous and isotropic scenario, just like in the familiar Friedmann-Robertson-Walker Spacetime. Not really all that hard to imagine.

[Q-reeus]

Teleparallel gravity is indeed the right picture. The torsion now plays the role of a gravitational force in a Newton-like force equation, which turns out to be equivalent to the geodesic equation of Einstein's theory. Thus one can have torsion even in a source-free situation. It pops up on the right-hand-side of the geodesic equation if we split the "non-flat" connection into a "flat" connection plus torsion, and then bring the torsion on the right-hand-side of the geodesic equation. So we are indeed talking about homogeneous and isotropic scenario, just like in the familiar Friedmann-Robertson-Walker Spacetime. Not really all that hard to imagine.

Thanks for your continued responses. Will have to think some more about how source-free torsion works here. And (shudder) maybe thus get round to studying Clifford algebra.

[gill1109]

...The only remaining mystery is why some people are going through such an extraordinary length to not understand this derivation: http://arxiv.org/abs/1405.2355.

Joy - I'm a QM layman in the category of, as Mulder's wall-poster read in the X-files: "I want to believe". However one slices and dices it, the standard QM view of entanglement/non-locality implies magic as literally at the heart of 'reality' - to the extent one's QM interpretation even allows an objective 'reality'.

On the other hand, it's very hard to see how your proposed 'exploding balls' classical experiment would do other than reproduce classical stats. And apart from being not so easy to actualize satisfactorally, one might suspect only elementary particle/particle pairs would really 'feel' the difference between S^3 and R^3 re Bell inequality. Can you point to some feature of S^3 spacetime (or spacetime slice) that admits a fully deterministic, no randomness involved, macroscopic classical physical experiment - mechanical, optical, electrical or whatever, that clearly is contrary to that predicted for normally assumed R^3 spacetime/spacetime slice? If so that should unequivocally settle things.

Indeed the exploding balls experiment exhibits classical statistics, as Christian and Diether's attempts to simulate it have confirmed, and as anyone can figure out for themselves.

I don't think anyone is going to any lengths at all to try to understand http://arxiv.org/abs/1405.2355. I don't think anyone is trying at all. Christian's first works were somehow taken notice of. [comment removed] But the novelty has worn off.

But we are off topic. Where's Gordon? What about Bell's 1964 formula (15)?

[Joy Christian]

I don't think anyone is going to any lengths at all to try to understand http://arxiv.org/abs/1405.2355.

No competent physicist would need much effort to understand the basic physics discussed here. And it is irrelevant what the Gill-types think of my work in any case.

[gill1109]

Gordon, where are you? Help us get back on topic.

[Gordon Watson]

Gordon, where are you? Help us get back on topic.

Richard, rest assured: if I'm not here it's because I'm tied up on other projects; and/or I'm waiting for responses to earlier matters; or I'm writing my resignation. But since you so nicely pleaded; here I am; thanks; me hoping to be more freed up soon.

NOW: Since you and I cannot both be right, you can also rest assured that I won't be leaving here until one or each of us sees the error of our ways.

So, returning to our topic: As I read him, Bell relied on his 1964:(15) to launch "Bell's impossibility theorem" (BIT) -- ie, his claim that Bell 1964:(2) cannot equal Bell 1964:(3). Do you agree with the crucial role of his 1964:(15) here? The whole history of the Bellian canon starts with his (15), right?

So, when I show you a simple refutation of BIT -- call it "Watson 2014e" for now: the correct result for EPRB and Aspect's experiments in a single equation -- then we will be able to take the RHS of Bell's 1964:(3) as output and refute 1964:(15) directly ...

(NB: To be clear here: I mean, of course, a derivation based on the principles of CLR = commonsense local realism.)

… because from observation (as I'm sure you've seen), if we could derive RHS of 1964:(3) from CLR and something like Bell 1964:(2), then 1964:(15) is refuted: independent of any other considerations. Would that be of any help, in so far as changing your mind is concerned.

Now, further, to you as a statistician: Looking at "Bell's integral" in his 1964:(2), what implicit assumption do you see there? NB: This is a very serious question on my part, so please take your time and answer comprehensively; thanks. PS: Do you imagine that the A and B functions that Bell has in his (1) are meant to be the identical functions in "Bell's integral" in his (2)?

Which brings us to this: How come Joy's work has not been laid to rest definitively by you and your many supporters? In a way acceptable to the common man, sort of thing? (Are you waiting for my assistance?) Many experts in the Geometric Algebra (GA) field (including David Hestenes, I believe) have examined Joy's work. Do we have their analyses in print? With mathematical or conceptual objections? Not just blind allegiance to Bell?

I ask because, in my work, spin s may be seen as a symmetry property associated with particles (not with space). So, since GA will certainly be able to reproduce my findings, I'm interested to see if the findings of Joy's critics might relate to particle symmetries -- which might also be an acceptable conclusion from Joy's work? Which might be less controversial to such as you? For we can rest assured that Bell's theorem is experimentally FALSE; hence theoretically FALSE! So it is certain that Joy's work cannot be dismissed on superficial or cult-like grounds alone.

Something to think about: all going back to that erroneous Bell 1964:(15)?

PS: A fan of GA, but not a user: I focus on refuting Bell using simple CLR principles and undergraduate maths; ie, I locate and refute Bell's erroneous assumptions.

With best regards, and thanks again; Gordon

[gill1109]

So, returning to our topic: As I read him, Bell relied on his 1964:(15) to launch "Bell's impossibility theorem" (BIT) -- ie, his claim that Bell 1964:(2) cannot equal Bell 1964:(3). Do you agree with the crucial role of his 1964:(15) here? The whole history of the Bellian canon starts with his (15), right?

Dear Gordon,

This is indeed how it all started. Since then there have been different proofs, and indeed proofs which make less or different assumptions and which get stronger conclusions. But it is fine by me to go back to the original. Even though notation is very old-fashioned, the proof can be made much shorter and sharper, and Bell skates over a number of issues which he later expanded on at length precisely in reaction to critics like you.

Bell's argument is indeed that (2) implies (15) but (3) does not satisfy (15). Hence the model (2) cannot reproduce the quantum correlations predicted in (3).

I suppose you have no problems with the derivation of (15) from (2) and that you have no problems with the QM expression (3).

So it seems you have a problem with

(2) P(a, b) = int d lambda rho(lambda) A(a, lambda) B(b, lambda)

I would like to explain what this formula is supposed to mean by reference to a computer simulation experiment. Suppose we set up a network of three ordinary computers called Source, Station A, and Station B. Station A takes input from Source and from a lab assistant Alice. Station B takes input from Source and from lab assistant B. The input from the source is whatever you like, call it lambda, but it is created using a state of the art pseudo random number generator. We think of each new lambda as being chosen, anew, completely at random, from some fixed set of possible values according to a fixed probability distribution rho(lambda) d lambda.

At the two stations, Alice and Bob (the lab assistants) pick some values of settings a and b just however they like. They don't know anything about the pseudo random number generator. They don't get to see the values of lambda which are sent from source to stations.

Their computers simply evaluate and output some binary output A(a, lambda) and B(b, lambda).

This is repeated lots and lots and lots of times.

If we restrict attention to runs in which Alice and Bob chose a particular pair of settings a and b, and average the product of their outcomes, it would in the long run become very close to P(a, b) = int d lambda rho(lambda) A(a, lambda) B(b, lambda)

Do you believe me so far? This is Probability for Engineers 101 or perhaps Statistics for Engineers 101.

PS [added an hour or so later]: if you would like the computers Station A and Station B to introduce further randomness into the generation of the measurement outcomes, let's suppose that this also uses more pseudo random number generators, just like Source. You can just as well imagine those pseudo random generators as being housed at the source, and you add to the existing "message" from the source to the measurement stations, the next batch of pseudo random numbers which Station A and Station B would use. This way we convert a "stochastic hidden variables model" to a "deterministic hidden variables model". There is no need to invent a new theory for the "stochastic" case.

I don't know what you mean by "common sense local realism" but I think the phrase should mean something like the computer network paradigm which I have just described.

I'm glad that you don't want to allow any loopholes (locality loophole, conspiracy loophole, detection loophole). That allows for a much "cleaner" discussion in which we can focus on the principles. After we have understood the principles, we can start thinking about how well they are reflected in state of the art experiments.

[gill1109]

How come Joy's work has not been laid to rest definitively by you and your many supporters? In a way acceptable to the common man, sort of thing? (Are you waiting for my assistance?) Many experts in the Geometric Algebra (GA) field (including David Hestenes, I believe) have examined Joy's work. Do we have their analyses in print? With mathematical or conceptual objections? Not just blind allegiance to Bell?

Dear Gordon

These are interesting questions but of course they are off topic and whatever I say now may well lead to instant retaliation by Dr. Christian (Oxford) and his supporters on this forum. Who include the forum administrator, so probably I will get into trouble with the admin too.

David Hestenes agrees that Joy's work is fatally flawed. The same holds for every expert in GA who ever looked at it, as far as I know. I checked with everybody who, according to Christian, had checked his work in depth and found if completely correct. Seems that Christian got a rather wrong impression from these guys.

Nobody is waiting for anyone's assistance in laying it to rest because it has been laid to rest, completely.

This is nothing to do with blind allegiance to Bell. Plenty of Bell critics also totally ignore Christian's work. There are two reasons for this: (a) the content, (b) the behaviour of the author in public. Someone who reacts to criticism by shouting obscenities tends to get shunned by the scientific community. Don't take my word for this. Ask Hans de Raedt his opinion.

If you want to lay it to rest in a way acceptable to the common man you will first of all have to choose one of the different versions and then you will have to carefully work through it.

You could for instance choose Christian's one page paper,

http://arxiv.org/abs/1103.1879

which is largely duplicated in the introductory chapter to his book. You could read it carefully and check (a) the conceptual framework and (b) the algebra.

After you have formed your own opinion you could take a look at my analysis

http://arxiv.org/abs/1203.1504

Then you could try to make sense of Christian's refutation of my critique.

http://arxiv.org/abs/1203.2529

Good luck!

I proposed to Christian that we submit his one page paper and my critique thereof jointly to a peer reviewed journal. He declined. His paper is unpublished, mine is too, and probably that is just as well.

I tried to show to Christian supporters that his papers are riddled with logical inconsistencies through the various bets and challenges I offered concerning his experimental paper

http://arxiv.org/abs/0806.3078

Take a look at page 4 and figure out for yourself why no experimenter in their right mind would ever actually do this experiment.

[harry]

Do you believe the following integrals misrepresent what Bell was trying to do?





Note that Bell did not specify a range for his definite integral. So we supply ranges for him, consistent with what he was doing, and with what makes sense, given the thought experiment he had in mind.

Yes, I'm sure that that misrepresents what Bell did, as I and others tried to explain several times. I'll do a last attempt to clarify it:
[..]
Once more, he had no thought experiment in mind!

You are sure I'm misrepresenting Bell but you do not specify how or what. Please state exactly why you believe any of the three expressions I wrote above misrepresent Bell. Can you or can you not elaborate on that point? Have you read Bell's paper? Can you have measurements without having an experiment?

Your expressions suggest a series of thought experiments.
His calculation is not simulating any experiments; the indices on the integrals (n+1 etc) misrepresent what he had in mind. It's more like n=1-∞. That he did not attempt to emulate experiments by his derivation was mentioned before in several ways (also below in that same message on which you commented), so there isn't much else left to say...

There are two ways to go at such a problem:

1. calculate according to theoretical assumptions. As I illustrated, such a calculation doesn't need to simulate an experiment at all.
2. do a simulation of an experiment.

Bell and others had been trying method 2 for a while without success, and many people are continuing that route. However, such simulations cannot prove that a successful simulation using unimagined parameters isn't possible. Therefore Bell next went for option 1. But if I understand it correctly, you and Gordon still think that Bell continued with option 2, just putting the simulation of an experiment in equations instead of in FOR-NEXT loops. But then he could not achieve what he claimed to achieve, as indeed:

You do not realize that it is possible to theorize about experiments. This is what physics is all about. So please state clearly where exactly any of the three expressions above misrepresent Bell, if you can.

To the contrary, I have illustrated how it is possible to theorize about experiments, even without a direct connection with the experimental procedure! And I explained several times that misrepresentation already.

[...] Long running averages of correlations between A and B are reproduced, but the individual outcomes [+1, -1] are never reproduced. It is at this level that this discussion is focused. The factorization that happens inside the integral happens at this level. It is at this level that Gordon's argument about AiAj =/= 1 applies. Do not be fooled that because long running averages of correlations between A and B are conserved means the results of the experiments are reproduced. They are not. You can even take a look at my simulations which have reproducible correlations without the same distributions of lambda and without reproducible individual results.

I don't think that that is what Gordon meant (for him to clarify!), but please give a link to the thread in which your simulations are discussed (it's off-topic here).

Please read this paper: http://arxiv.org/pdf/quant-ph/0604124v2.pdf
[re-arranging:]
If you read the above article, you will understand that even if every lambda encountered for P(a,b) was also encountered for P(b,c) and for P(a,c), you will will not be able to do the factorization unless the sequence of the lambda's is exactly the same. In short, Bell's factorization can only be done if you start with a single spreadsheet with three columns a,b,c and recombine the columns in pairs. If you start with three 6 different columns, even if the same lambdas are in each one in different orders, you must in principle be able to resort them into 3 effective columns for the derivation to proceed. The above paper shows that the resortings required to achieve this are incompatible. In yet other words, the numbers of degrees of freedom for 6 columns is different for 3 columns and that is why the inequality must have a different upper bound for 6 columns, and that is why AiAj =/= 1 as Gordon argues.

That looks interesting, and for Gordon to comment if that is what he was saying in his paper - but I don't find that reasoning in Gordon's paper. Perhaps it's a good "ansatz" to disproving Bell - but not definitive. Back to my illustration: the carpenter can do 10 measurements to reduce measurement error, and still none of them corresponds to my calculation. That doesn't prove that my calculation must be wrong.

[..] And what is the basis of your blatant proclamation that correlation will not be reproduced unless ALL the lambdas come back?

I did not say or "proclaim" that; instead I wrote that "the same effective lambda must come back"... but instead of writing "else no results reoccur", I should have written "else the results will not reproduce". I'll be interested to see the thread in which you demonstrated the contrary, if indeed you did.

[..] The point being made which you apparently have failed to grasp is not about what correlations you get at the end, but what inequalities to compare the correlations you get.

Sorry I cannot parse that sentence!

Thus for example, for the experimental outcomes one must have lambda_2438 = lambda_215, etc, else no results reoccur in contradiction with QM theory (and also in contradiction with experience).

QM does not predict individual results, so you are confusing re-occurrence of lambda with reproducibility of long-running averages. [..]

I did of course not suggest that QM predicts individual results.

[gill1109]

To support Harry in his attempts to convince Michel that Michel is missing something:

Suppose X1, X2, X3, ... are a sequence of drawings from the standard normal distribution.
Suppose Y1, Y2, Y3, ... are a sequence of drawings from the standard normal distribution all with +1 added to them.

Two long sequences of random numbers.

In the long run, the average of the Xi's converges to 0. In the long run, the average of the Yj's converges to 1. The difference between the average of a load of Y's and the average of a load of X's is with large probability close to +1.

Yet the X's can be anything between - infinity and + infinity
The Y's can be anything between -infinity and + infinity

The only thing that we can say for sure about the difference between two averages of sequences of finite length is that it lies between -infinity and + infinity

You'll never see the same value twice, not in either sequence, nor even in the two sequences combined.

The X's might represent measurements done on apples and Y's might represent measurements done on pears.

Michel is saying that we cannot compare the average of X's and the average of Y's because we can't compare apples with pears. But you can compare weights of apples with weights of pears. The prices of apples with the prices of pears.

[Gordon Watson]

So, returning to our topic: As I read him, Bell relied on his 1964:(15) to launch "Bell's impossibility theorem" (BIT) -- ie, his claim that Bell 1964:(2) cannot equal Bell 1964:(3). Do you agree with the crucial role of his 1964:(15) here? The whole history of the Bellian canon starts with his (15), right?

Dear Gordon,

This is indeed how it all started. Since then there have been different proofs, and indeed proofs which make less or different assumptions and which get stronger conclusions. But it is fine by me to go back to the original. Even though notation is very old-fashioned, the proof can be made much shorter and sharper, and Bell skates over a number of issues which he later expanded on at length precisely in reaction to critics like you.

Thanks Richard; but quite seriously: Bell dug his hole deeper -- not better; and struggled (unsuccessfully) to avoid doublespeak re AAD, statistical dependence; etc., as time went on. Please listen to his 1990 talk -- it's online.

Bell's argument is indeed that (2) implies (15) but (3) does not satisfy (15). Hence the model (2) cannot reproduce the quantum correlations predicted in (3).

This is where I asked you, as a statistician, to comment on the implicit assumption that you see in "Bell's integral" -- the one in his (2). Please respond.

I suppose you have no problems with the derivation of (15) from (2) and that you have no problems with the QM expression (3).

Richard; are you drunk on The Netherlands footballing success?

Please, re Bell's silly (15); so easily refuted experimentally too: What is MY topic here, in this thread, again? Please!

Re his (3), no problem at all since I happily derive it almost daily for folks like you. Based on commonsense local realism (CLR), of course.

So it seems you have a problem with

(2) P(a, b) = int d lambda rho(lambda) A(a, lambda) B(b, lambda)

It needs careful handling, so please reply re the implicit assumption that you see therein.

I would like to explain what this formula is supposed to mean by reference to a computer simulation experiment. Suppose we set up a network of three ordinary computers called Source, Station A, and Station B. Station A takes input from Source and from a lab assistant Alice. Station B takes input from Source and from lab assistant B. The input from the source is whatever you like, call it lambda, but it is created using a state of the art pseudo random number generator. We think of each new lambda as being chosen, anew, completely at random, from some fixed set of possible values according to a fixed probability distribution rho(lambda) d lambda.

At the two stations, Alice and Bob (the lab assistants) pick some values of settings a and b just however they like. They don't know anything about the pseudo random number generator. They don't get to see the values of lambda which are sent from source to stations.

Their computers simply evaluate and output some binary output A(a, lambda) and B(b, lambda).

This is repeated lots and lots and lots of times.

If we restrict attention to runs in which Alice and Bob chose a particular pair of settings a and b, and average the product of their outcomes, it would in the long run become very close to P(a, b) = int d lambda rho(lambda) A(a, lambda) B(b, lambda)

Do you believe me so far? This is Probability for Engineers 101 or perhaps Statistics for Engineers 101.

Richard; thanks, but with respect: When we settle the World-Cup by computer, I'll switch my studies from real-life to gaming. Until then, I trust that you are happy to deal with the real world and real experiments? Knowing, as you do, that two correlated footballs have nothing like the correlations associated with two entangled particles?

PS [added an hour or so later]: if you would like the computers Station A and Station B to introduce further randomness into the generation of the measurement outcomes, let's suppose that this also uses more pseudo random number generators, just like Source. You can just as well imagine those pseudo random generators as being housed at the source, and you add to the existing "message" from the source to the measurement stations, the next batch of pseudo random numbers which Station A and Station B would use. This way we convert a "stochastic hidden variables model" to a "deterministic hidden variables model". There is no need to invent a new theory for the "stochastic" case.

I don't know what you mean by "common sense local realism" but I think the phrase should mean something like the computer network paradigm which I have just described.

"Commonsense local realism (CLR) is the fusion of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively)." Do you sense any problems here? Any that might prevent you too adopting CLR [ pronounced clear ] as a working philosophy?

I'm glad that you don't want to allow any loopholes (locality loophole, conspiracy loophole, detection loophole). That allows for a much "cleaner" discussion in which we can focus on the principles. After we have understood the principles, we can start thinking about how well they are reflected in state of the art experiments.

Why the need for state-of-the-art experiments? Under CLR, there are NO loopholes to be closed. We predict the correct results (just like QM) but without collapse or any need for FTL or AAD or nonlocality. Surely Aspect, and Bell himself (when introspective), convinced you of that?

So, Richard, seriously, how about we quit the word games and let our maths do the talking. I moved first, in my essay. Your move next, in reply, via some maths?

With best regards; Gordon

[Gordon Watson]

Harry, I'm happy to respond to your questions but that is made difficult when they are scattered through varying long texts to others.

If you would post them here (maybe one question per post), then I believe that will be best for us all.

PS: In your last post, re minkwe, you seem to be mentioning that Carpenter mate of yours again. Did you reply to my analysis re your experiment? (My apologies if I missed it.)

If not, I'm a bit surprised that you are still using it? That is, I thought the Carpenter could readily replace the coincidence-detector/integrator in any Bell-test. In other words, IMHO, your experiment seemed to be no answer to the problem that you sought to address.

With best regards; Gordon

[Gordon Watson]

Gill, re Joy's work:

You write,

"David Hestenes agrees that Joy's work is fatally flawed. The same holds for every expert in GA who ever looked at it, as far as I know."

Could you please provide the sources for these comments? Hestenes essay is where? The others that you definitively know of, too, please?

Thanks.

[harry]

Harry, I'm happy to respond to your questions but that is made difficult when they are scattered through varying long texts to others. [..]
PS: In your last post, re minkwe, you seem to be mentioning that Carpenter mate of yours again. Did you reply to my analysis re your experiment? (My apologies if I missed it.) [..]
With best regards; Gordon

Hi Gordon,
I replied first to minkwe and next to you on p.14 (=in the sequence of replies to my earlier reply to you).

[Ben6993]

Hi Richard. In your sampling example, you are averaging the u.n.d.s as if they were on a straightforward and linear interval scale. If these values are part of the hidden variables then they could be the vector directions of particles, say, with the spin being taken care of by an ignored second element of the hidden variable. So you are taking the vector part of a spinor and averaging it without a care in the world. This is worse than Lord's fictional professor performing interval statistics on nominal 'football' numbers in his private locked study.

Yes, you can average them, but what does it mean? In QM one cannot work out the effect of rotations without using Pauli matrices, or the like. It is not physically meaningful to average spinors on a linear interval scale. Isn't that what you are doing?

My concerns about the issue are:
1. in explaining the 'missing' data which is suggested not really to be missing ... but why is it not present?
2. in needing to add the four correlations using higher dimensions instead of normal algebra. Is that what has happened? [trusting this will not lead to flaming ... ]
3. ok, electrons have 4pi symmetry but photons have 2pi symmetry. So what are the implications of Joy's paper, if any, on Bell's Theorem, for photons? (NB yes I know you say this issue is not just about physics, but I am only here for the physics.)
4. Does space have a single dimensionality/spinorial property? And does that apply to everything in it? Size/distance seems to matter for particle interactions eg QCD v QED, so why should macroscopic behave the same as microscopic.
5. What effect does the higgsfield have on the hidden variables? Or, equivalently, what effect if any does zitterbewegung have on the hidden variables for electrons/positrons during time of flight?

[gill1109]

Hi Richard. In your sampling example, you are averaging the u.n.d.s as if they were on a straightforward and linear interval scale. If these values are part of the hidden variables then they could be the vector directions of particles, say, with the spin being taken care of by an ignored second element of the hidden variable. So you are taking the vector part of a spinor and averaging it without a care in the world. This is worse than Lord's fictional professor performing interval statistics on nominal 'football' numbers in his private locked study.

Yes, you can average them, but what does it mean? In QM one cannot work out the effect of rotations without using Pauli matrices, or the like. It is not physically meaningful to average spinors on a linear interval scale. Isn't that what you are doing?

No that is not what I am doing. The quantum mechanical prediction for P(a, b) is computed using a weird formula involving Pauli matrices, but it is supposed to predict the long run average of the product of measurements of spin in directions a and b on pairs of particles in the given state.

You want to create a completely new bridge between quantum formalism and laboratory experiments? Well be my guest, but sorry, along with the mathematical framework of conventional QM there is also a minimalistic conventional set of interpretation rules. A standard bridge between theory and experiment. You want to build a new bridge? Are you saying that every experiment done so far which seems to confirm QM was actually analysed in the wrong way because experimenters have been using the wrong bridge between theory and experiment for the last 90 years?

[gill1109]

Gill, re Joy's work:

You write,

"David Hestenes agrees that Joy's work is fatally flawed. The same holds for every expert in GA who ever looked at it, as far as I know."

Could you please provide the sources for these comments? Hestenes essay is where? The others that you definitively know of, too, please?

Thanks.

David Hestenes sent me an email. I also corresponded with Azhar Iqbal and Manfried Faber. In private I could quote to you from their messages.

I also corresponded with Lucien Hardy. Not a GA expert, but a close personal friend of Christian and a pretty smart guy. He has never spoken out in public in support of Christian. He easily could do and he's famous enough that he can say in public just what he thinks.

You could also write to these guys yourself. You could also ask yourself why so far no single peer reviewed publication has taken Christian's work further. There are plenty of Bell critics out there who (a) can do geometric algebra and (b) publish in peer reviewed journals and speak at international conferences.

By the way, the kind of GA which Christian is using is pretty easy stuff... Computer scientists use it to program virtual reality. It's cute, it's powerful, but it's not rocket science. (Christian's version of GA, on the other hand, is voodoo).

[gill1109]

Richard; thanks, but with respect: When we settle the World-Cup by computer, I'll switch my studies from real-life to gaming. Until then, I trust that you are happy to deal with the real world and real experiments? Knowing, as you do, that two correlated footballs have nothing like the correlations associated with two entangled particles?
***
So, Richard, seriously, how about we quit the word games and let our maths do the talking. I moved first, in my essay. Your move next, in reply, via some maths?

Too bad Gordon, you've had my very serious and careful reply. You can take it seriously or you can forget it, just as you like.

If you want to see some maths read my paper http://arxiv.org/abs/1207.5103. Theorem 1 is rather relevant to this discussion.

[Ben6993]

Hi Richard. I need to take that slower.

QM uses Pauli matrices to get the a.b result.
Joy used geometric algebra to get the a.b result.
Bell's Theorem uses ordinary algebra?

[gill1109]

Hi Richard. I need to take that slower.

QM uses Pauli matrices to get the a.b result.
Joy used geometric algebra to get the a.b result.
Bell's Theorem uses ordinary algebra?

Ben, I think you need to study Bertlman's socks. Find out what the whole point of the exercise was.

Joy uses geometric algebra, together with a new definition of correlation, and together with some magic sign switches, to get the a.b result. Read my paper http://arxiv.org/abs/1203.1504

Bell uses elementary probability theory to show that a local hidden variables theory cannot reproduce the a.b result.