EPR-Bell is proof that we live in a quaternionic 3-sphere

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby FrediFizzx » Wed Oct 26, 2016 2:53 pm

FrediFizzx wrote:
Heinera wrote:Well, if you cannot "predict individual outcomes", but can only "predict the final result of many trials", that is the very definition of probabilistic reasoning.


Show us where the probability is in Joy's model.


It is not that hard. There is a 50-50 chance that the orientation of the particle pair system will either be left or right handed. But does that matter in the correlation calculation? No. The average of the cross-product term vanishes anyways without lambda because a x b = c.

The bottom line is that neither QM nor LHV theories (especially a S^3 theory) can predict individual outcomes for A and B. It is just not possible thus another mistake by Bell. They can only predict the overall correlation result and results for ++, --, +-, and -+.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Wed Oct 26, 2016 9:08 pm

FrediFizzx wrote:The bottom line is that neither QM nor LHV theories (especially a S^3 theory) can predict individual outcomes for A and B. It is just not possible thus another mistake by Bell. They can only predict the overall correlation result and results for ++, --, +-, and -+.

I am not sure what you mean here. What is wrong with these individual outcomes?

Image

They are the predictions of S^3 model, and they are equal to A = +/-1 and B = +/-1. But you are right that quantum mechanics does not predict individual outcomes.

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby FrediFizzx » Wed Oct 26, 2016 9:50 pm

Joy Christian wrote:
FrediFizzx wrote:The bottom line is that neither QM nor LHV theories (especially a S^3 theory) can predict individual outcomes for A and B. It is just not possible thus another mistake by Bell. They can only predict the overall correlation result and results for ++, --, +-, and -+.

I am not sure what you mean here. What is wrong with these individual outcomes?

Image

They are the predictions of S^3 model, and they are equal to A = +/-1 and B = +/-1. But you are right that quantum mechanics does not predict individual outcomes.
***


They for sure predict that the outcomes are +/-1 but I don't think given lambda, that they actually can predict if you get a +1 or -1 individually. I think there is actually another dependency on s_1 and s_2 for the outcomes as I was mentioning before that s_1 can also go to -a and the same for s_2 going to -b. That is really the case in a real EPR-Bohm experiment so just knowing lambda you will not be able to predict the actual outcomes event by event. Assuming that you could even actually know lambda which you probably can't. I don't think that doing for the limit fixes it. I think it really is just . Which still allows you to predict that the outcomes are +/-1 but there is no more BS from Gill about A = lambda and B = -lambda. It is the S^3 correlation calculation that really matters anyways. And the limits drop out of that calculation anyways. They aren't needed for it.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Wed Oct 26, 2016 9:58 pm

FrediFizzx wrote:
Joy Christian wrote:
FrediFizzx wrote:The bottom line is that neither QM nor LHV theories (especially a S^3 theory) can predict individual outcomes for A and B. It is just not possible thus another mistake by Bell. They can only predict the overall correlation result and results for ++, --, +-, and -+.

I am not sure what you mean here. What is wrong with these individual outcomes?

Image

They are the predictions of S^3 model, and they are equal to A = +/-1 and B = +/-1. But you are right that quantum mechanics does not predict individual outcomes.
***


They for sure predict that the outcomes are +/-1 but I don't think given lambda, that they actually can predict if you get a +1 or -1 individually. I think there is actually another dependency on s_1 and s_2 for the outcomes as I was mentioning before that s_1 can also go to -a and the same for s_2 going to -b. That is really the case in a real EPR-Bohm experiment so just knowing lambda you will not be able to predict the actual outcomes event by event. Assuming that you could even actually know lambda which you probably can't. I don't think that doing for the limit fixes it. I think it really is just . Which still allows you to predict that the outcomes are +/-1 but there is no more BS from Gill about A = lambda and B = -lambda. It is the S^3 correlation calculation that really matters anyways. And the limits drop out of that calculation anyways. They aren't needed for it.
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That would make s_1 and s_2 hidden variables and reduce my model to the same old silly model of Bell. The beauty of my model is that the only uncontrollable hidden variable in the model is lambda. And given "a" and lambda, the measurement outcomes A = +/-1 are predicted, individually. That is obvious from the above functions.

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby FrediFizzx » Wed Oct 26, 2016 10:13 pm

Joy Christian wrote:That would make s_1 and s_2 hidden variables and reduce my model to the same old silly model of Bell. The beauty of my model is that the only uncontrollable hidden variable in the model is lambda. And given "a" and lambda, the measurement outcomes A = +/-1 are predicted, individually. That is obvious from the above functions.
***


Didn't you actually have them as variables in your simulations? "s" is the direction vector that is formed upon creation common to both particles and is a real thing. I am not sure that it is a hidden variable so much as just a variable that you don't know the value of. All I can say is that in a real EPR-Bohm experiment, that vector is going to get aligned with a either up or down, + or -. If you know what "s" is then you might be able to predict if it is up or down for a given lambda. But maybe not. And... as I was saying, it doesn't matter for the correlation calculation anyways. Lambda is the only hidden variable in that.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Wed Oct 26, 2016 10:24 pm

FrediFizzx wrote:
Joy Christian wrote:That would make s_1 and s_2 hidden variables and reduce my model to the same old silly model of Bell. The beauty of my model is that the only uncontrollable hidden variable in the model is lambda. And given "a" and lambda, the measurement outcomes A = +/-1 are predicted, individually. That is obvious from the above functions.
***


Didn't you actually have them as variables in your simulations? "s" is the direction vector that is formed upon creation common to both particles and is a real thing. I am not sure that it is a hidden variable so much as just a variable that you don't know the value of. All I can say is that in a real EPR-Bohm experiment, that vector is going to get aligned with a either up or down, + or -. If you know what "s" is then you might be able to predict if it is up or down for a given lambda. But maybe not. And... as I was saying, it doesn't matter for the correlation calculation anyways. Lambda is the only hidden variable in that.
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Yes, I did have "s" as a variable, but that was not for the Clifford algebra model. That was for what you like to call "the complete state theory." It is not based on Clifford algebra per se. It is based on a non-Clifford-algebraic representation of the 3-sphere.

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Wed Oct 26, 2016 10:50 pm

Joy Christian wrote:***
Heinera,

If you know it all, then why don't you prove Bell's "theorem" for us? Here is my challenge again: viewtopic.php?f=6&t=275#p6681. Put up or shut up. 8-)

***

No response from Heinera. In fact, no response from any of the Bell-believers. Not surprisingly, they are unable to prove their theorem without cheating. :)

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby FrediFizzx » Wed Oct 26, 2016 11:41 pm

Joy Christian wrote:
FrediFizzx wrote:
Joy Christian wrote:That would make s_1 and s_2 hidden variables and reduce my model to the same old silly model of Bell. The beauty of my model is that the only uncontrollable hidden variable in the model is lambda. And given "a" and lambda, the measurement outcomes A = +/-1 are predicted, individually. That is obvious from the above functions.
***


Didn't you actually have them as variables in your simulations? "s" is the direction vector that is formed upon creation common to both particles and is a real thing. I am not sure that it is a hidden variable so much as just a variable that you don't know the value of. All I can say is that in a real EPR-Bohm experiment, that vector is going to get aligned with a either up or down, + or -. If you know what "s" is then you might be able to predict if it is up or down for a given lambda. But maybe not. And... as I was saying, it doesn't matter for the correlation calculation anyways. Lambda is the only hidden variable in that.
.

Yes, I did have "s" as a variable, but that was not for the Clifford algebra model. That was for what you like to call "the complete state theory." It is not based on Clifford algebra per se. It is based on a non-Clifford-algebraic representation of the 3-sphere.

***


Well it is still based on S^3. It is a demonstration of why the Clifford GA model works and why the experiments get the results that they do. But in the simulations, can you predict what a single event outcome is given "s" and lambda? It has been awhile since I looked the simulations so I don't remember.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby FrediFizzx » Thu Oct 27, 2016 12:36 am

It all seems pretty straight forward to me,




Then for the correlation calculation since the limits don't matter anyways in it just take them out,



And you know the rest. s_1 and s_2 aren't necessarily hidden variables because the +/- on going to a or b are functions of the polarizers in the detection process. Now Gill or anyone else will have nothing to bitch about any more. But of course they will find something as we know.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby thray » Thu Oct 27, 2016 5:52 am

Richard Gill wrote on Retraction Watch:

"If Christian can fix the problems with his paper he’ll revolutionise physics.

"In fact the main obstacle to rescuing his work is Bell’s theorem, which says that what he is trying to do is impossible. (Bell’s theorem has stood for fifty years. A proof of the theorem adequate to cover Christian’s framework is very easy.)

"To answer your question to me, Jay, unfortunately the a = b question is not the only problem with the present version of his theory. I only emphasised it because the part of the paper where it arises is quite self-contained and contains extremely obvious self-contradictions and errors, involving only elementary algebra and calculus. So any mathematically inclined reader can decide for themselves."

The mathematically inclined reader takes Bell's theorem at face value, not adding ad hoc assumptions and interpretations.

In fact, Joy's mathematics is entirely consistent with relativity as expressed by Einstein: http://www.relativitybook.com/resources ... space.html

Bell's theorem is said to show that quantum configuration space cannot map to physical space without a nonlocal model. To say that physical space = quantum configuration space simply begs the question. Now that Joy has clearly defined physical space, Bell proponents have homework to do. Let's examine that "very easy proof" critically.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Thu Oct 27, 2016 5:58 am

***
Thanks, Tom.

Now that you have quoted Gill's silly and ignorant comments from Retraction Watch, let me also reproduce here my response to his comments:

Joy Christian wrote:
Please note that Gill has not provided a proof for his claim that I assume a = b as I asked him to do after Jay’s suggestion. Instead, Gill now makes several unproven and unprovable statements. He says

“If Christian can fix the problems with his paper he’ll revolutionise physics.”

There are no problems with my paper to be fixed. There is not even a comma misplaced in my paper. As I have already noted above, all the issues raised by Gill and others over the past nine years have been comprehensively addressed and disposed of by me and others. I have provided detailed mathematical refutations of each of the claims made by Gill against my model. Each time he has shifted the goalpost and raised the bar, I have been able to still make the goal and hop over the bar.

Gill now claims that “in fact the main obstacle to rescuing his work is Bell’s theorem, which says that what he is trying to do is impossible. (Bell’s theorem has stood for fifty years. A proof of the theorem adequate to cover Christian’s framework is very easy.)”

In fact, Bell’s theorem remains unproven. What is more, I have comprehensively refuted the unproven claims by Bell independently of my local model presented in the current paper. You can find one of my refutations of Bell’s theorem in the Appendix D of this paper:

https://arxiv.org/abs/1501.03393

This refutation of Bell’s theorem has nothing to do with my physical local model of the EPR-Bohm correlations being discussed here. In addition to the above refutation, some of the participants in this debate are well aware of my open challenge to Bell’s theorem, posted at Fred’s forum, which remains uncontested even today. Thus Bell’s theorem is both refuted as well as remains unproven, and my challenge to Bell’s theorem remains uncontested. The bottom line is that Bell’s so-called theorem is based on some naïve physical assumptions, and thus it is not applicable in the real physical world, as all the experiments done to date in this context have repeatedly demonstrated.

Gill further claims that “…unfortunately the a = b question is not the only problem with the present version of his theory. I only emphasised it because the part of the paper where it arises is quite self-contained and contains extremely obvious self-contradictions and errors, involving only elementary algebra and calculus. So any mathematically inclined reader can decide for themselves.”

This statement is quite objectionable given the fact that all of the claims against my model made by Gill and others have been systematically and comprehensively refuted by me and others. There are no contradictions or errors in my paper, period. It is also interesting to note that if there were “extremely obvious self-contradictions and errors, involving only elementary algebra and calculus”, then the distinguished editors and referees of Annals of Physics were unable to spot a single one of them during their seven-months long rigorous peer review of my paper. In fact Gill’s claims above are simply false, as anyone proficient in Clifford algebra and general relativity can readily see. It is also important to note that Gill is not a physicist. Nor has he ever published a peer-reviewed paper in Clifford algebra or general relativity on which my paper is based. I therefore urge the readers to take his opinions about my paper with a pinch of salt.


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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Thu Oct 27, 2016 7:12 am

***
For the record let me also reproduce here a little technical exchange between me and Richard D. Gill which took place today at Retraction Watch. It vividly exposes Gill's mathematical and logical "prowess." Remember that this man calls himself a mathematician (he has done so on many occasion in this very forum) and holds a professorial position and chairmanship of the statistics department at a very prestigious, well known, and ancient Dutch university. Please do check out his "proof" to judge for yourself. I had challenged him to produce a proof of one of his fallacious claims:

Joy Christian wrote:
The burden of proof is on Gill. He claims that I assume a = b. He has not proved this. I will wait until he produces a proof of his claim. If he cannot produce a proof, then his claim is empty. If he produces a proof, then I will either refute it, or consider revising my paper.

In response to my above challenge Gill produced the following "proof" (the equation numbers refer to those in this paper: https://arxiv.org/pdf/1405.2355.pdf):

Richard D. Gill wrote:
Proof of a = b.

From (54) and (55), A(a, lambda) = -B(b, lambda) = +/-1

Substituting in (67), we find E(a, b) = -1

But according to (75), E(a, b) = – a dot b

a and b are unit vectors. So a dot b = 1 implies that a = b

To those unfamiliar with my paper linked above let me explain how nonsensical and illogical Gill's "proof" really is. First he "proves" that E(a, b) = -1, which is wrong because his argument for it is not only misleading but also violates the conservation of spin angular momentum. But let us go along with it. He is not a physicist after all, so we should be charitable to him. But then he jumps to my equation (75) to conclude E(a, b) = -a dot b. But wait a minute! Didn't he just "prove" E(a, b) = -1 ?

Oh, well. But it gets worse. Not only did he jump from (67) to (75) without attempting to derive it in his own proof (which he absolutely must for his proof to be a proof), but he failed to notice that there is no way to derive E(a, b) = -a dot b without conserving the spin angular momentum, which requires the equality s_1 = s_2. So he derives E(a, b) = -1 by ignoring the conservation of spin angular momentum and then jumps to (75) taking E(a, b) = -a dot b, which cannot be derived without assuming the conservation of spin angular momentum. In other words, he ignores s_1 = s_2 to derive E(a, b) = -1 and then assumes s_1 = s_2 to derive E(a, b) = -a dot b, and then compares the two functions E(a, b) to show contradiction. Please tell me why should we not strip this guy of his lucrative and powerful academic position.

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Thu Oct 27, 2016 9:55 am

***
Well, as I anticipated, Gill didn't understand his mistake even after I explained it to him on Retraction Watch. So here is my second try to explain:

Joy Christian wrote:
My paper is indeed completely correct. But no one is allowed to use two completely different assumptions in the same proof. One cannot have s_1 = s_2 and not have s_1 = s_2 in the same proof. That is what Gill has done in his proof, but he does not seem to recognise that.

E(a, b) = -1 follows if and only if s_1 is not equal to s_2, thus violating the conservation of spin angular momentum.

E(a, b) = -a dot b follows in general if s_1 = s_2 is assumed, as we must do to conserve the spin angular momentum.

Gill mixes up two different assumptions to derive two different correlations, E(a, b) = -1 and E(a, b) = -a dot b, and then compares them to “prove” a = b.

Let me spell this out so that everyone can see the elementary logical flaw in Gill’s “proof.” Let me produce two separate arguments in the manner of Gill to make this clear.

(1) First, let s_1 = s_2. Then my definitions (54) and (55) for A and B, once substituted into (67), immediately gives (72). From (72) then (75) follows giving E(a, b) = -a dot b. This is what is derived in my paper. The key in my derivation is this: Given my definitions and assumptions, (67) immediately and directly gives (72). This step is not understood by Gill. Given my definitions and assumptions, E(a, b) = -1 can only hold in a very special case in which Alice and Bob specifically set a = b. Otherwise E(a, b) = -a dot b necessarily follows.

(2) Now let us drop the assumption of s_1 = s_2, thus violating the conservation of spin angular momentum. In that case my definitions (54) and (55) for A and B, once substituted into (67), do indeed give E(a, b) = -1. The rest of the equations in that case do not add anything, and we end up with a new equation, (75-b), which also gives E(a, b) = -1.

Gill has badly mixed up the cases (1) and (2) above to “prove” a = b. He is not free to compare apples with oranges in this manner to “prove” anything, let alone a = b.

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby thray » Thu Oct 27, 2016 12:54 pm

" ... no one is allowed to use two completely different assumptions in the same proof. One cannot have s_1 = s_2 and not have s_1 = s_2 in the same proof. That is what Gill has done in his proof, but he does not seem to recognise that."

Indeed. This is exactly equivalent to choosing a proposition, and the negation of that proposition, at the same time. A = ~A.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Thu Oct 27, 2016 1:47 pm

thray wrote:" ... no one is allowed to use two completely different assumptions in the same proof. One cannot have s_1 = s_2 and not have s_1 = s_2 in the same proof. That is what Gill has done in his proof, but he does not seem to recognise that."

Indeed. This is exactly equivalent to choosing a proposition, and the negation of that proposition, at the same time. A = ~A.

Thanks, Tom. This is the kind of nonsense we have had to put up with for so many years. Not only from Gill, but also from his entire gang of bullies. Unfortunately Gill is the one who has the political power to block progress in physics. He is the one who blocked the publication of my paper from Nature, Scientific Reports. He is the one who now has my published paper withdrawn from Annals of Physics. He is the one who tried extremely hard to have my other published paper retracted from the International Journal of Theoretical Physics. He is the one who managed to influence FQXi to cut off my only research funding. He is the one who has been writing for years malicious letters about me to my academic superiors (such as to the President of my college in Oxford). And he is able to do all these by choosing propositions, P, and their negations, -P, in his childish logic, as he has been in the endless debates about my work over the past so many years. He is the Prince of the world of physics.

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Fri Oct 28, 2016 12:23 pm

***
There has been some further exchange between me and Richard D. Gill at Retraction Watch:

Joy Christian wrote:
Let me respond to each of the points made by Gill:

Gill: “…there are two quite distinct models in the paper we are discussing.”

This is incorrect. There is only one model — the 3-sphere model: https://arxiv.org/abs/1405.2355 . To be sure, in my paper there are two different representations of the 3-sphere considered, each with some advantages and some disadvantages. Both representations are valuable, and they complement each other quite nicely.

Gill: “They seem to be hardly connected to one another at all.”

This is incorrect. How can there be no connection between two representations of one and the same manifold, namely a 3-sphere? This is why I am sometimes forced to stress that Gill has never published a single peer-reviewed paper in Clifford algebra (which, by the way, he learned from me) or general relativity to understand the physical model presented in my paper.

Gill: “The first model reproduces the quantum correlations, but is non-local – it is Pearle’s detection loophole model.”

This is incorrect, on both counts. Both representations of the 3-sphere model are manifestly local. Gill here makes an empty statement without a proof. And contrary to his claim, the first representation is by no means Pearle’s detection loophole model. His claim makes me suspect whether he has actually read my paper at all. To be sure, I use some of the formal mathematical constructs used by Pearl, but there is no exploitation of a “detection loophole”, or any other “loophole” for that matter, in my local model. There is a one-to-one accounting in the model between the initial (or complete) state (e, s) and the measurement outcomes A and B. So Gill once again makes a false claim without providing a proof for his claim.

Gill: “Christian learnt [Pearle’s model] from me.”

This is incorrect. I did not learn Pearle’s model from Gill. I learnt it from my former Ph.D. adviser, Prof. Abner Shimony, in the mid 1980’s, and few years later from Philip Pearl himself (whom I know personally). And while I am at it, let me also mention that I learnt about Bell’s theorem also from Abner Shimony (the “S” in the Bell-CHSH inequality) while I was his student in the mid 1980’s, and a few years later from John. S. Bell himself (with whom I was also well acquainted, thanks to my mentor Abner Shimony).

Gill: “The second is the crazy model A(a, lambda) = -B(b, lambda) = lambda = +/-1 which is clearly local but which clearly does not reproduce the quantum correlations.”

This is incorrect, on several counts. As anyone can see Gill is confusing the measurement outcomes A and B with the hidden variable lambda when he writes A = +lambda and B = -lambda. Look carefully. That is what he has written, just as he has done many times in the past. This shows that he has not really understood my model. And it is quite extraordinary that he confuses the measurement outcomes A and B with the hidden variable lambda. Also, contrary to his claim, my model evidently reproduces the quantum correlations, as anyone can see by simply studying my paper carefully and investigating the details of the analytical as well as numerical evidence presented therein. But Gill has got one thing right –- my model is indeed manifestly local, as anyone knowledgeable in the subject can readily see.

Gill: “I suggest study of one of the simpler proofs of Bell’s theorem, if you want to understand what Christian is up against.”

I recommend that too. And then, if you think you have understood Bell’s argument, I suggest that you take up my challenge to Bell’s theorem and prove me wrong. Here is my challenge, which is open to anyone, and can be taken anywhere on the Internet, not only at Fred’s forum: viewtopic.php?f=6&t=275#p6681

Gill: “You can’t even define what is a local hidden variables model without using the language of probability theory.”

This is incorrect. John S. Bell, in his famous paper of 1964, used only expectation values, not probabilities, to define a local hidden variables framework, and then produced an explicit analytical local model of his own, without using any unnecessary notion from the probability theory.

Finally, I will not quit participating at RW. I will be here to answer any questions, or respond to any reasonable criticism that I have not addressed already over the past nine years.


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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby thray » Fri Oct 28, 2016 4:44 pm

Gill's statement, "I suggest study of one of the simpler proofs of Bell’s theorem, if you want to understand what Christian is up against" would carry water, if he could come up with a proof not dependent on the proof technique of double negation; i.e., proving the proposition A by showing that A = ~ ~ A (not-not A).

That is a hopeless task, however, if one starts with the implicit assumption A = ~ A.

So Bell-Aspect only proves its own assumptions (which Karl Hess also noted in Einstein was Right!).

Why there is such resistance to Joy's framework (not theory) is surely a case study for sociologists. Statisticians and probabilists own Bell's theorem, because they are so easily convinced by flawed reasoning and proofs that time plays no role in correlations -- and thus discard spacetime as a measure space.

Here Joy specifies a measure space and offers a way to experimentally show that it reproduces quantum correlations exactly. Because it is classical 4-dimension spacetime, though, with no need for entanglement and non-locality, it puts the statisticians and probabilists out of work -- and with them, a whole community of experimenters, theorists, computer scientists and others who have staked their fortunes on quantum entanglement and its expected consequences.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Q-reeus » Fri Oct 28, 2016 7:13 pm

thray wrote:...Because it is classical 4-dimension spacetime,...

Is it? Funny, I was sure Joy actually claims we live in a quaternionic 7-sphere, with a 3-sphere subset capable of explaining only some QM correlations.
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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Joy Christian » Fri Oct 28, 2016 11:38 pm

Q-reeus wrote:
thray wrote:...Because it is classical 4-dimension spacetime,...

Is it? Funny, I was sure Joy actually claims we live in a quaternionic 7-sphere, with a 3-sphere subset capable of explaining only some QM correlations.

Tom is right. The physical spacetime dimensions in my model are only 4. The 7-sphere I employ in my work is not quaternionic but octonionic, with its fibers being the quaternionic 3-spheres. The important point here is that the physical space (minus time) is still 3-dimensional. To be sure the embedding space of octonionic 7-sphere is 8-dimensional, but these are not "extra dimensions" like those in string theory. These are purely algebraic dimensions. They arise because the Clifford algebra of the 3-dimensional physical space happens to be an 8-dimensional vector space: . And this 8-dimensional space is capable of explaining ALL quantum correlations. Unfortunately the dirty, behind-the-scenes shenanigans by the Bell-fanatics have caused me enough financial and intellectual grief to prevent me from completing an important paper clarifying all of these issues. But eventually I hope to complete my paper and settle the question of "extra dimensions" in my model once and for all.

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Re: EPR-Bell is proof that we live in a quaternionic 3-spher

Postby Q-reeus » Sat Oct 29, 2016 12:02 am

Joy Christian wrote:Tom is right. The physical spacetime dimensions in my model are only 4. The 7-sphere I employ in my work is not quaternionic but octonionic, with its fibers being the quaternionic 3-spheres...

I stand corrected there.
Unfortunately the dirty, behind-the-scenes shenanigans by the Bell-fanatics have caused me enough financial and intellectual grief to prevent me from completing an important paper clarifying all of these issues. But eventually I hope to complete my paper and settle the question of "extra dimensions" in my model once and for all.

Sounds like it will be quite a tome. You have at various times agreed that a physically real spatial torsion is responsible for QM correlations being over and above classical ones. Which I find hard to except and hope that paper clearly explains it. For instance, why such torsion exists (source?) and why it seems to effect only the results of Bell-type experiments and otherwise 'invisible'.
Q-reeus
 
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