## Bell's theorem refuted!?

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Bell's theorem refuted
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### Bell's theorem refuted!?

:

LATEST NEWS: 20 Dec 2010 - Bell's theorem refuted: Revision 1 now available at http://quantropy.org/12/

Bell's theorem is widely regarded as the most profound discovery of science. To see this, check the net for < "most profound discovery of science" Bell >.

The theorem, it is widely claimed, requires us to abandon one (or maybe both) of two commonsense concepts: realism or locality; fundamental concepts which had Einstein's support. In their place some physicists advocate AAAD (action-at-a-distance) or retro-causality (IMHO an equally bizarre concept).

It follows that a refutation of Bell's theorem would eliminate much extreme metaphysics from physics. It would also re-instate local realism as a valid view of the world; stop Einstein turning in his grave; restore his reputation in this area; put some noses out of joint.

So this thread is NOT for super-sensitive nosies; rather, it is proposed as a safe-haven where serious folk might discuss Bell's theorem refuted based on the essay at http://quantropy.org/8/ -- any discussion of Bell's theorem in its own right being addressed elsewhere, except in so far as it might invalidate or clarify any "refutation" addressed here.

Cheers,

BTR

MAJOR EDIT 1:
I have annotated the subject line with !? as in Chess: The !? serves to indicate my opinion: an interesting move that may not be best. It "may not be best" because it just delays an inevitable defeat; or, AND THIS IS MY HOPE, it may be that there's a better move. The point is: My move is locked-in until this game ends; I am in the game here to learn; I've already learned a lot from earlier moves and replies by others; I seem to learn best from my mistakes; when I'm serious and wrong, that's when I really learn.

Am I serious about refuting Bell's theorem? Yes, I am.

Could I be wrong? Yes, for sure.

I will happily respond to any questions arising out of the latest revised essay: NOW AT http://quantropy.org/12/ .
Last edited by Bell's theorem refuted on Tue Dec 21, 2010 12:15 pm UTC, edited 5 times in total.

Azrael
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### Re: Bell's theorem refuted

We've had several similar threads in various parts of the forums, and those have all devolved into the realm of memorable internet crack pot. Obviously, that needs to be avoided here.

infernovia
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### Re: Bell's theorem refuted

I don't get what your purpose of this thread is. Are you trying to discuss the implications and of Bell's Theorem/experiment or not? And to do that, don't you need an understanding of what that experiment actually did?

Why is it bad that the notion of realism/locality got shattered with the new mechanics? Why is it a bad thing that Einstein did not know everything about science? That Pauli, Bohr, and Heisenberg went further in the field science than Einstein had gone before?

quantropy
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### Re: Bell's theorem refuted

I think I can explain. The OP is finishing off a paper describing a refutation of Bell's theorem, which he plans to post in the Quantropy.org repository (which I run). The repository is set so that you can add a link to a discussion page, but at the moment this needs to be done when the paper is submitted (Sometime I'll get round to making it possible to do so after submission, which would be more logical). Hence the OP decided to start the discussion here before having a link to the paper

Azrael
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### Re: Bell's theorem refuted

Moved to SCIENCE! at the suggestion of a participant.

... let the games begin?

Stacy S.
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### Re: Bell's theorem refuted

I look forward to seeing the paper. I hope the math isn't too difficult. I'm still getting use to the fact that 1/2 = 5/9 for very non-local values of 5/9.

BlackSails
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### Re: Bell's theorem refuted

You cant undo bell's inequality. Its a mathematical thing, having nothing to do with the real world.

Now the experiments showing that our universe does not obey it, that you can do something about, although I wouldnt hold my breath.

And quantropy - what does your website provide that the arxiv does not?

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### Re: Bell's theorem refuted

BlackSails wrote:And quantropy - what does your website provide that the arxiv does not?

Firstly, with arxiv you have to deal with the endorsement system. Whatever they say about it not being peer review, if you want someone who doesn't know you to endorse a paper then that is what it is likely to turn into.

Secondly, with Quantropy there is more of an opportunity for readers to see the context of the paper, with the possibility of links to the author's website, to a discussion of the paper and (hopefully) comments by experts in the field.

Game_boy
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### Re: Bell's theorem refuted

I'm interested to see how a single argument or experiment on this could overturn the many, many experiments confirming non-locality.

(edited)
Last edited by Game_boy on Sun Dec 12, 2010 10:24 am UTC, edited 1 time in total.
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BlackSails
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### Re: Bell's theorem refuted

quantropy wrote:
BlackSails wrote:And quantropy - what does your website provide that the arxiv does not?

Firstly, with arxiv you have to deal with the endorsement system. Whatever they say about it not being peer review, if you want someone who doesn't know you to endorse a paper then that is what it is likely to turn into.

Why is that a problem?

nehpest
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### Re: Bell's theorem refuted

Game_boy wrote:Is it at all related to Frank Tipler, the Omega Point Theory or James Redford?

I hear if you say his name three times, he'll appear in your thread...

BlackSails wrote:Why is that a problem?

Peer review tends to eliminate (or at least point out) unsubstantiated ideas, I suspect is the reason.
Kewangji wrote:Someone told me I need to stop being so arrogant. Like I'd care about their plebeian opinions.

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Simius
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### Re: Bell's theorem refuted

I once followed a course by a teacher who didn't believe in Bell's Theorem. He wrote this paper, among others. It's interesting, though unfortunately not written very clearly. The guy is a bit of a fringe scientist*, but I think that we need those to ask the uncomfortable questions and shake things up a little bit.

Also for a good laugh, take a look through some of the Discussions on the Wikipedia page of Bell's Theorem.

*not to be confused with a pseudoscientist

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### Re: Bell's theorem refuted

If the OP doesn't come back soon to actually start or participate in some of this discussion he or she seems to want, I'm going to lock this thread as irrelevant. (And if it fills up with complete pseudoscientific nonsense, I'll do the same thing. So if someone is proposing that Bell's Theorem is wrong, they had better have the math to back it up.)
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Bell's theorem refuted
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### Re: Bell's theorem refuted

Azrael wrote:We've had several similar threads in various parts of the forums, and those have all devolved into the realm of memorable internet crack pot. Obviously, that needs to be avoided here.

Yes, I understand; thanks for reinforcing the point. That's already a good sign for me.

In my experience, Bell's theorem [BT} does that to most threads. That was why I thought "Serious business" was a good place to begin a serious discussion --

I can assure you that I, for one, will be seeking to be "crack-pot free" in my posts. Unfortunately, I can't give the same assurance re "error-free".

But that is why I am here: To learn of errors and confusions, and then to see if I can correct them.

For those who understand BT, I would say that I am on the side of Einstein (without an error re "elements of physical reality" that's associated with him via EPR) and on the side of Bohr (with an approach that might clarify some of his much-misunderstood or neglected remarks). But don't be scared: I think it is all covered by undergrad maths and logic -- or an obvious mistake -- I'm not up for much more.

My essay, "Bell's theorem refuted in line with Bell's hope and Einstein's ideas" 6-pages, 30+ references, will be delivered today to Quantropy.org.

Thanks again; and my apologies for the delay.
Last edited by Bell's theorem refuted on Sun Dec 12, 2010 8:34 pm UTC, edited 1 time in total.

Bell's theorem refuted
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### Re: Bell's theorem refuted

infernovia wrote:I don't get what your purpose of this thread is. Are you trying to discuss the implications and of Bell's Theorem/experiment or not? And to do that, don't you need an understanding of what that experiment actually did?

Why is it bad that the notion of realism/locality got shattered with the new mechanics? Why is it a bad thing that Einstein did not know everything about science? That Pauli, Bohr, and Heisenberg went further in the field science than Einstein had gone before?

Sorry, No. Not "trying to discuss the implications and of Bell's Theorem/experiment." That's another subject.

I am seeking to have my approach to local-realism, in the context of BT, critiqued; to learn of errors or confusions in my approach.

Bell's theorem refuted
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### Re: Bell's theorem refuted

Game_boy wrote:I'm interested to see how a single argument or experiment on this could overturn the many, many experiments confirming non-locality.

(edited)

As I understand it, BT is a mathematical impossibility theorem, part of a long line of such.

My response is essentially mathematical, being a composite of my understanding of both local realism and its mathematical implications.

Bell's theorem refuted
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### Re: Bell's theorem refuted

gmalivuk wrote:If the OP doesn't come back soon to actually start or participate in some of this discussion he or she seems to want, I'm going to lock this thread as irrelevant. (And if it fills up with complete pseudoscientific nonsense, I'll do the same thing. So if someone is proposing that Bell's Theorem is wrong, they had better have the math to back it up.)

I'm back; see above; apologies for delay.

I suspect that BT is wrong mathematically; we know that it does not agree with relevant experiments.

I suspect that I have identified Bell's error.

I suspect I have some maths that is correct, in the BT context.

I suspect I'm in for some serious and vigorous debate.

I know that that's why I'm here.

infernovia
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### Re: Bell's theorem refuted

Ok, thanks for clearing that up. I was just wondering why it wasn't put in the Science forum, which is a lot better at these things.

Yakk
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### Re: Bell's theorem refuted

BTW, you shouldn't make multiple posts in a row. If you want to respond to more than one person, hit the reply key. Take the contents of the reply window. Cut. Go back, respond to another post. Paste the previous reply-window in (or, do this manually with [ quote ] tags).

...

So this is not an experimental disagreement with the experiments that have supported Bell's Theorem. It is an approach that takes local realism as an axiom, and uses that to disprove Bell's Theorem?

It is known that Bell's Theorem is inconsistent with Local Realism. Is that what your paper covers?

The experimental confirmation of the parts of QM that imply Bell's Theorem (ie, experiments that confirm Bell's Theorem) are the reason why people hold it to be true. All of the "I wish local realism was true" in the world doesn't do anything, unless you can provide explanations for the experiments that confirmed Bell's Theorem, and provide predictions that Bell's Theorem disagrees with that can (at least in theory) be verified.

Other, more theoretical, routes might be building fun models of universes that are not consistent with observations about our universe. Some of these thought experiments are useful (like the one that showed a holographic physics model).
Bell's theorem refuted wrote:I suspect that BT is wrong mathematically; we know that it does not agree with relevant experiments.

Um. As far as I know, we know that BT agrees perfectly with all observations in experiments attempting to refute it. Or am I missing something?
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

Bell's theorem refuted
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### Re: Bell's theorem refuted

infernovia wrote:Ok, thanks for clearing that up. I was just wondering why it wasn't put in the Science forum, which is a lot better at these things.

Thanks for being another reinforcer of my hope for xkcd. For my hope that nonsense and rubbish are removed from threads where the OP indicates serious intentions.

Yakk wrote:BTW, you shouldn't make multiple posts in a row. If you want to respond to more than one person, hit the reply key. Take the contents of the reply window. Cut. Go back, respond to another post. Paste the previous reply-window in (or, do this manually with [ quote ] tags).

...

So this is not an experimental disagreement with the experiments that have supported Bell's Theorem. It is an approach that takes local realism as an axiom, and uses that to disprove Bell's Theorem?

It is known that Bell's Theorem is inconsistent with Local Realism. Is that what your paper covers?

The experimental confirmation of the parts of QM that imply Bell's Theorem (ie, experiments that confirm Bell's Theorem) are the reason why people hold it to be true. All of the "I wish local realism was true" in the world doesn't do anything, unless you can provide explanations for the experiments that confirmed Bell's Theorem, and provide predictions that Bell's Theorem disagrees with that can (at least in theory) be verified.

Other, more theoretical, routes might be building fun models of universes that are not consistent with observations about our universe. Some of these thought experiments are useful (like the one that showed a holographic physics model).

Bell's theorem refuted wrote:I suspect that BT is wrong mathematically; we know that it does not agree with relevant experiments.

Um. As far as I know, we know that BT agrees perfectly with all observations in experiments attempting to refute it. Or am I missing something?

As I understand things: BT was developed in the context of EPR; in the context of quantum entanglement [QE}.

Bell (1964) "In a theory in which parameters are added to QM to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz-invariant."

So I would say that BT is a theorem about other theories.
Last edited by Bell's theorem refuted on Sun Dec 12, 2010 9:22 pm UTC, edited 1 time in total.

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### Re: Bell's theorem refuted

Bell's theorem refuted wrote:Bell's theorem is widely regarded as the most profound discovery of science. To see this, check the net for < "most profound discovery of science" Bell >.

The theorem, it is widely claimed, requires us to abandon one (or maybe both) of two commonsense concepts: realism or locality; fundamental concepts which had Einstein's support. In their place some physicists advocate AAAD (action-at-a-distance) or retro-causality (IMHO an equally bizarre concept).

It follows that a refutation of Bell's theorem would eliminate much extreme metaphysics from physics. It would also re-instate local realism as a valid view of the world; stop Einstein turning in his grave; restore his reputation in this area; put some noses out of joint.

So this thread is NOT for super-sensitive nosies; rather, it is proposed as a safe-haven where serious folk might discuss Bell's theorem refuted; any discussion of Bell's theorem in its own right being addressed elsewhere, except in so far as it might invalidate or clarify any "refutation" addressed here.

Cheers,

BTR

Bell's theorem is correct if quantum mechanics is correct, as Bell's theorem is a mathematical theorem based upon quantum mechanics. Quantum mechanics has been confirmed by every experiment to date.

Per Bell's theorem and special relativity, experiments confirming "nonlocality" are actually confirming the existence of the multiverse. With the multiverse, locality and realism are retained, but counterfactual definiteness is lost, because all possible outcomes consistent with physics really do occur somewhere in the multiverse. (Here "realism" means that our thoughts and conscious observations aren't responsible for quantum mechanical effects, and that causality is never violated.) For the details on that, see the following articles:

Frank J. Tipler, "Does Quantum Nonlocality Exist? Bell's Theorem and the Many-Worlds Interpretation", arXiv:1008.2764, March 30, 2000. http://arxiv.org/abs/quant-ph/0003146

Frank J. Tipler, "Nonlocality as Evidence for a Multiverse Cosmology", arXiv:1008.2764, August 16, 2010. http://arxiv.org/abs/1008.2764

Prof. Frank J. Tipler also points out on pg. 95 of The Physics of Christianity (New York: Doubleday, 2007), "if the other universes and the multiverse do not exist, then quantum mechanics is objectively false. This is not a question of physics. It is a question of mathematics. I give a mathematical proof of [this] in my earlier book ...". For that, see Frank J. Tipler, The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead (New York: Doubleday, 1994), Appendix I: "The Many Worlds Interpretation of Quantum Mechanics", pp. 483-488.

Moreover, there exists only one interpretation of quantum mechanics, and that is the many-worlds interpretation. All other so-called "interpretations" either make no attempt to actually explain quantum phenomena (such as the Statistical interpretation), or they are merely the many-worlds interpretation in denial (such as David Bohm's pilot-wave interpretation).

Anything that acts on reality is real and exists. Quite strange then that quantum phenomena behave exactly as if the other particles in the multiverse exist if in fact they don't exist. If the actual physical nature of the "wave functions" and "pilot waves" are not the other particles in the multiverse, then new physical entities with their own peculiar physics are being invoked: for if these aren't the other particles in the multiverse interacting with the particles in this universe, then we will do well to ask what is their actual physical nature? Pinball flippers, bumpers and ramps? What is their actual physical form, and why do they behave exactly as if the other particles in the multiverse exist?

Furthermore, all wave phenomena are nothing more than particle phenomena: there is no particle-wave duality. A wave is simply a collection of particles interacting with each other. It is the particles that actually exist; the wave is simply an action by particles interacting with each other. We see this with waves through, e.g., liquids: the individual molecules are jostled about via interacting with the other molecules. Likewise, a single photon in this universe behaves as a wave because it's interacting with the ocean of its parallel photons in the multiverse.

See also the leading quantum physicist in the world, Prof. David Deutsch (inventor of the quantum computer, being the first person to mathematically describe the workings of such a device), "Comment on Lockwood", British Journal for the Philosophy of Science, Vol. 47, No. 2 (June 1996), pp. 222-228; also released as "Comment on '"Many Minds" Interpretations of Quantum Mechanics by Michael Lockwood'", 1996. http://web.archive.org/web/200709250520 ... kwood.html

Quantum mechanics is strictly deterministic across the multiverse. If one does away with causation then one also does away with the possibility of explanation, as all explanation is predicated on explicating cause-and-effect relationships. So if by "interpretation" it is meant explanation, then Prof. Deutsch's point in his above paper about there actually only being one known interpretation of quantum mechanics is again found to be inescapable.

And as Prof. Deutsch writes in The Fabric of Reality: The Science of Parallel Universes--and Its Implications (London: Allen Lane The Penguin Press, 1997), Chapter 9: "Quantum Computers", pg. 217:

""
The argument of Chapter 2, applied to *any* interference phenomenon destroys the classical idea that there is only one universe. Logically, the possibility of complex quantum computations adds nothing to a case that is already unanswerable. But it does add psychological impact. With Shor's algorithm, the argument has been writ very large. To those who still cling to a single-universe world view, I issue this challenge: *explain how Shor's algorithm works*. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor's algorithm has factorized a number, using 10^500 or so times the computational resources that can be seen to be present, where was that number factorized? There are only about 10^80 atoms in the entire visible universe. So if the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed?
""

Frank J. Tipler, "Testing Many-Worlds Quantum Theory By Measuring Pattern Convergence Rates", arXiv:0809.4422, September 25, 2008. http://arxiv.org/abs/0809.4422

And most leading physicists do accept the Many-Worlds Interpretation as true. The political scientist L. David Raub conducted a poll of 72 leading quantum cosmologists and other quantum field theorists regarding their view on the truth of the Many-Worlds Interpretation. The possible answers were: (1) "Yes, I think the MWI is true"; (2) "No, I don't accept the MWI"; (3) "Maybe it's true, but I'm not yet convinced"; and (4) "I have no opinion one way or the other". The results of the poll were: 58% said yes; 18% said no; 13% said maybe; and 11% said no opinion. In the "yes" category were Stephen Hawking, Richard Feynman, and Murray Gell-Mann, while the "no" answers included Roger Penrose.
Author of "Jesus Is an Anarchist", SSRN, 2009-10-17 http://ssrn.com/abstract=1337761

Theophysics: God Is the Ultimate Physicist (on Prof. Frank J. Tipler's Omega Point Theory and the quantum gravity TOE) http://theophysics.chimehost.net

Yakk
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### Re: Bell's theorem refuted

Huh? The EPR paradox is about pairs of entangled particles being observed at a remote distance. Bell's Theorem states, roughly, that the predictions of QM are not consistent with "locally real" interpretations. Experiments that attempt to reproduce the EPR thought experiment, which inspired Bell's Theorem, consistently generate what you'd expect to see if the predictions of QM ruled out "locally real" interpretations.

And these experiments pan out. We generate "really weird results" that are exactly what QM implies, and seem to disagree with "locally real" theories of QM.

Bell's Theorem is a mathematical theorem: if (QM is true) then (local reality is false), very roughly. Thus to "disprove the implications of bell's theorem", colloquially, you demonstrate that the predictions of QM in certain situations do not match up with reality, thus demonstrating that we can have local reality.

That, at least, is what I'm meaning when I loosely used the term "disprove bell's theorem". It is true that technically bell's theorem is just a mathematical connection, and real-life experiments won't disprove it. You could also attack the interpretation of bell's theorem (ie, how the mathematics is attached to the interpretation), but that doesn't seem all that viable either.

In short, I'm very confused asto what you are trying to say. I'm no quantum physicist, just a recreational mathematician who enjoys thinking about quantum mechanics. So could someone clarify?
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

++$_ Mo' Money Posts: 2370 Joined: Thu Nov 01, 2007 4:06 am UTC ### Re: Bell's theorem refuted James Redford wrote:"" The argument of Chapter 2, applied to *any* interference phenomenon destroys the classical idea that there is only one universe. Logically, the possibility of complex quantum computations adds nothing to a case that is already unanswerable. But it does add psychological impact. With Shor's algorithm, the argument has been writ very large. To those who still cling to a single-universe world view, I issue this challenge: *explain how Shor's algorithm works*. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor's algorithm has factorized a number, using 10^500 or so times the computational resources that can be seen to be present, where was that number factorized? There are only about 10^80 atoms in the entire visible universe. So if the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed? "" This is a ridiculous argument. If Shor's algorithm actually ever factors a large number (which it has not done yet), then all that will show is that atoms are more complicated than they look. (Alternatively, that the space between the atoms is more complicated than it looks.) It's like saying "There are only about 1012 hard disks in the world. Therefore, how is it possible for us to store more than 1012 bytes of data??? The only possible explanation is that we must be storing some of the data in other universes!!!" BlackSails Posts: 5315 Joined: Thu Dec 20, 2007 5:48 am UTC ### Re: Bell's theorem refuted Shor's algorithm does not work the way you think it does. James Redford Posts: 21 Joined: Sun May 30, 2010 8:24 pm UTC Location: U.S.A. Contact: ### Re: Bell's theorem refuted Yakk wrote:Huh? The EPR paradox is about pairs of entangled particles being observed at a remote distance. Bell's Theorem states, roughly, that the predictions of QM are not consistent with "locally real" interpretations. Experiments that attempt to reproduce the EPR thought experiment, which inspired Bell's Theorem, consistently generate what you'd expect to see if the predictions of QM ruled out "locally real" interpretations. And these experiments pan out. We generate "really weird results" that are exactly what QM implies, and seem to disagree with "locally real" theories of QM. Bell's Theorem is a mathematical theorem: if (QM is true) then (local reality is false), very roughly. Thus to "disprove the implications of bell's theorem", colloquially, you demonstrate that the predictions of QM in certain situations do not match up with reality, thus demonstrating that we can have local reality. That, at least, is what I'm meaning when I loosely used the term "disprove bell's theorem". It is true that technically bell's theorem is just a mathematical connection, and real-life experiments won't disprove it. You could also attack the interpretation of bell's theorem (ie, how the mathematics is attached to the interpretation), but that doesn't seem all that viable either. In short, I'm very confused asto what you are trying to say. I'm no quantum physicist, just a recreational mathematician who enjoys thinking about quantum mechanics. So could someone clarify? Hi, Yakk. That is not what Bell's theorem states. Bell's theorem states that no theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. Bell's theorem requires that every quantum theory must violate either locality or counterfactual definiteness, since local hidden variables cannot be invoked in order to explain quantum mechanical effects. In other words (per Bell's theorem), if causality does not propagate at superluminal speed, then the multiverse must exist. Alternatively, if the multiverse does not exist, then causality must propagate at superluminal speed. Thus, per Bell's theorem, if both quantum mechanics and special relativity are correct, then the multiverse is a logically inescapable result. This is the reason why Stephen Hawking stated that "The many-worlds interpretation is trivially true", and why most leading quantum cosmologists accept the many-worlds interpretation as being true. The only way to avoid the conclusion of the multiverse without rejecting relativity is to assume that quantum mechanics doesn't really apply to everything, which is how Roger Penrose avoids this conclusion. For much more details on these matters, see my previous post above. Author of "Jesus Is an Anarchist", SSRN, 2009-10-17 http://ssrn.com/abstract=1337761 Theophysics: God Is the Ultimate Physicist (on Prof. Frank J. Tipler's Omega Point Theory and the quantum gravity TOE) http://theophysics.chimehost.net ++$_
Mo' Money
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### Re: Bell's theorem refuted

BlackSails wrote:Shor's algorithm does not work the way you think it does.
Are you talking to me or James Redford?

Either way, perhaps you could inform me/him how I/he think/s Shor's algorithm works, since you appear to be an expert on that.

Yakk
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### Re: Bell's theorem refuted

Hi, Yakk. That is not what Bell's theorem states.

Please point out my error. Saying "that isn't right" then repeating a bunch of my post with some extra stuff thrown on does not point out where I made a mistake.

Bell's theorem states that no theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

How, exactly is this not the same thing as:
Bell's Theorem states, roughly, that the predictions of QM are not consistent with "locally real" interpretations.

which is what I said?

For reference, Local realism:
https://secure.wikimedia.org/wikipedia/ ... f_locality

Quoting an entire post, saying "no, that is wrong", isn't helpful. If you could, point out what I said that was wrong, don't just use my post as an excuse to rant. Thanks.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

James Redford
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++$_ wrote: James Redford wrote:"" The argument of Chapter 2, applied to *any* interference phenomenon destroys the classical idea that there is only one universe. Logically, the possibility of complex quantum computations adds nothing to a case that is already unanswerable. But it does add psychological impact. With Shor's algorithm, the argument has been writ very large. To those who still cling to a single-universe world view, I issue this challenge: *explain how Shor's algorithm works*. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor's algorithm has factorized a number, using 10^500 or so times the computational resources that can be seen to be present, where was that number factorized? There are only about 10^80 atoms in the entire visible universe. So if the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed? "" This is a ridiculous argument. If Shor's algorithm actually ever factors a large number (which it has not done yet), then all that will show is that atoms are more complicated than they look. (Alternatively, that the space between the atoms is more complicated than it looks.) It's like saying "There are only about 1012 hard disks in the world. Therefore, how is it possible for us to store more than 1012 bytes of data??? The only possible explanation is that we must be storing some of the data in other universes!!!" Prof. David Deutsch's above passage of "using 10^500 or so times the computational resources that can be seen to be present" I take to mean per the Bekenstein Bound, which is a central theorem of quantum field theory. Author of "Jesus Is an Anarchist", SSRN, 2009-10-17 http://ssrn.com/abstract=1337761 Theophysics: God Is the Ultimate Physicist (on Prof. Frank J. Tipler's Omega Point Theory and the quantum gravity TOE) http://theophysics.chimehost.net gmalivuk GNU Terry Pratchett Posts: 26819 Joined: Wed Feb 28, 2007 6:02 pm UTC Location: Here and There Contact: ### Re: Bell's theorem refuted This thread is about Bell's Theorem, not Frank Tipler. Further repeated posts about the latter will get your posts deleted. Bell's theorem refuted wrote:Sorry, No. Not "trying to discuss the implications and of Bell's Theorem/experiment." That's another subject. No, you do not dictate the terms of discussions here. There's no reasonable way to discuss a proposed refutation of Bell without also talking about the implications of Bell. You can choose not to participate in that aspect of the discussion, but it'll happen in this thread because it's on-topic for this thread. Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true. --- If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome (he/him/his) James Redford Posts: 21 Joined: Sun May 30, 2010 8:24 pm UTC Location: U.S.A. Contact: ### Re: Bell's theorem refuted gmalivuk wrote:This thread is about Bell's Theorem, not Frank Tipler. Further copypasta about the latter will get your posts deleted. Hi, gmalivuk. To whom are you speaking? If you're speaking to me, I didn't copy and paste anything from Prof. Frank J. Tipler. I give quotes of Profs. David Deutsch, Stephen Hawking, and Tipler, but otherwise the rest are my writings. Last edited by James Redford on Sun Dec 12, 2010 11:54 pm UTC, edited 1 time in total. Author of "Jesus Is an Anarchist", SSRN, 2009-10-17 http://ssrn.com/abstract=1337761 Theophysics: God Is the Ultimate Physicist (on Prof. Frank J. Tipler's Omega Point Theory and the quantum gravity TOE) http://theophysics.chimehost.net gmalivuk GNU Terry Pratchett Posts: 26819 Joined: Wed Feb 28, 2007 6:02 pm UTC Location: Here and There Contact: ### Re: Bell's theorem refuted James Redford wrote:Hi, gmalivuk. To whom are you speaking? I'm speaking to the person who always magically shows up in any thread where someone else mentions Tipler's name, and starts posting nonsense which rarely responds directly to what others have said and which almost always includes multiple links to stuff Tipler has written. If you can continue participating in this discussion without going on about Tipler and his multiverse, then you're welcome to stay. Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true. --- If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome (he/him/his) James Redford Posts: 21 Joined: Sun May 30, 2010 8:24 pm UTC Location: U.S.A. Contact: ### Re: Bell's theorem refuted gmalivuk wrote: James Redford wrote:Hi, gmalivuk. To whom are you speaking? I'm speaking to the person who always magically shows up in any thread where someone else mentions Tipler's name, and starts posting nonsense which rarely responds directly to what others have said and which almost always includes multiple links to stuff Tipler has written. If you can continue participating in this discussion without going on about Tipler and his multiverse, then you're welcome to stay. You must mean to say "Tipler and his Omega Point Theorem", which I haven't discussed in this thread. Prof. Frank J. Tipler didn't originate the Many-Worlds Interpretation of quantum mechanics. Rather, it was physicist Hugh Everett III who originated that. Author of "Jesus Is an Anarchist", SSRN, 2009-10-17 http://ssrn.com/abstract=1337761 Theophysics: God Is the Ultimate Physicist (on Prof. Frank J. Tipler's Omega Point Theory and the quantum gravity TOE) http://theophysics.chimehost.net gmalivuk GNU Terry Pratchett Posts: 26819 Joined: Wed Feb 28, 2007 6:02 pm UTC Location: Here and There Contact: ### Re: Bell's theorem refuted I mean to say any further references to anything by Frank Tipler will be removed. If you want to talk about Everett's Many Worlds interpretation, then back up your claims with things Everett wrote, not things Tipler wrote. You can never seem to discuss anything even remotely related to him without going off on a pseudoscientific tangent, which I will not have in this thread. Stick to the topic or stop participating. Edit: because you have been unable to abide by my request three times, and also feel the need to argue with a moderator in-thread about it, I'm kicking you out of this thread entirely. Do not post here again. Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true. --- If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome (he/him/his) Bell's theorem refuted Posts: 24 Joined: Fri Dec 10, 2010 1:53 am UTC ### Re: Bell's theorem refuted My draft essay is up at http://quantropy.org/8/ . 6 pages, 31 references, PDF, 196Kb. Title: Bell's theorem refuted in line with Bell's hope and Einstein's ideas Some typos to be fixed; some short hand proposed for equation (5); some explanations to be improved. Every critical comment or question will be welcomed. Suggestions for improvement will be loved; typo identification too. Final essay will carry acknowledgments of significant correspondence -- there's been a few! A: A big time quantum physicist once said (roughly): If we are to sort out quantum mechanics (QM) we must make all our mistakes ASAP. B: Max Born in his Nobel address, 1954, said: ".. somewhere in our doctrine is a hidden concept, unjustified by experience, which we must eliminate to open up the road." I am pretty sure I'm in A or B. One thing I know for sure: I am here to learn. Let the no-games begin. Please: keep it mostly serious. Thanks. PS: Will attempt to answer every serious question. JWalker Posts: 222 Joined: Sun Nov 23, 2008 1:13 am UTC ### Re: Bell's theorem refuted Bell's theorem is something that often gets thrown around as if it was proof of fundamental non-locality. However, it is not that at all. Bell's theorem merely states an inequality that violated by non-local interactions and not violated by local interactions under several assumptions. Violation of Bell's inequality is not clear-cut evidence of non-locality. In fact, some inherently classical and local systems have been proposed that violate Bell's inequality in a way that non-local systems would (For example: http://arxiv.org/pdf/0812.4506, but there are several others as well). Some well known theoretical physicists have even proposed that Bell's theorem contains an extremely subtle error that allows violation of the inequality by local systems as well (ex: http://arxiv.org/pdf/0904.4259). Furthermore, it has yet to be shown that quantum mechanical processes violate Bell's inequality. There have been experiments performed that seem to suggest the inequality is violated, but as of yet, every one of those experiments suffers from at least one loophole that prevents them from being definitive evidence for non-locality. There are several of these loopholes (one of them is discussed here: http://arxiv.org/pdf/1010.1178) and it is a topic of ongoing research how to overcome them. I suspect it wont be too long before there is a loophole free experiment performed, but there is no guarantee what the outcome will be. The point to all this is that while Bell's theorem is often mistakenly thought of as as a theoretically sound and experimentally confirmed cornerstone of quantum mechanics, it is actually far from either one. I hope the readers of this thread keep that in mind. ++$_
Mo' Money
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### Re: Bell's theorem refuted

My draft essay is up at http://quantropy.org/8/
The problem is that you are assuming what you wanted to show.

The essential mistake here is in Section 3. All the rest is irrelevant, although to some extent the mistake is concealed by confusing writing and choice of notation. Basically, you start out in section 3 by assuming that everything is explicable in terms of hidden variables. That is, if some particle has "hidden variable" [imath]\omega[/imath], the hidden variable's value is in one of two equivalence classes. You give these classes weird names and define them using a strange notation, but I will just call them [imath]A^+[/imath] and [imath]A^-[/imath], where [imath]A^+[/imath] is the set that registers as spin-up in detector A, and [imath]A^-[/imath] the set that registers as spin-down in that detector, and [imath]B^+, B^-[/imath] the equivalents for detector B.

Now, in equations (5a) through (5d) (which, by the way, could be formatted better -- it is general practice to put an equals sign at the beginning of a new line rather than at the end of the previous one), you describe some facts that would have to be true about [imath]A^+, A^-, B^+,[/imath] and [imath]B^-[/imath] because of experimental results. You then state (equation (6)) that if (5a-d) are true, then this is consistent with experimental results. But that begs the question. It does not show anything, because you have not made use of your equivalence classes in equation (6) at all. You have just stated that: IF your equivalence class theory is correct, THEN it is correct. That doesn't mean anything.

Bell's theorem refuted
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### Re: Bell's theorem refuted

++$_ wrote: My draft essay is up at http://quantropy.org/8/ The problem is that you are assuming what you wanted to show. Good start; down to serious business. Thanks! Now: This a serious charge -- in many many fields. So thanks for raising it. BUT am I guilty? I am assuming the validity of local realistic hidden-variables. Bell did the same. I show that they yield results consistent with experiment. Bell did not show this. Is not my approach OK for theoretical physics? Don't we make hypotheses (my assumptions) and show that experiment confirms them? I'm not clear where I've left that well-travelled path. Help, please; and see below. ++$_] "The essential mistake here is in Section 3. All the rest is irrelevant, although to some extent the mistake is concealed by confusing writing and choice of notation[/quote]

I'll deal with the "mistake" below. I am totally open to improvements in my writing and notation ... from any one; so anyone "interested but puzzled" can help me by communicating suggestions and problems.

[quote="++$_ wrote: Basically, you start out in section 3 by assuming that everything is explicable in terms of hidden variables. Yes; as did Bell. And consistent with my long-held beliefs -- which I'd like to correct if they're dumb or wrong. ++$_ wrote: That is, if some particle has "hidden variable" [imath]\omega[/imath], the hidden variable's value is in one of two equivalence classes. You give these classes weird names and define them using a strange notation,

Suggestions for improvement most welcome; from anyone. Yours are in the direction I'm looking at for Revision 1.

++$_ wrote:but I will just call them [imath]A^+[/imath] and [imath]A^-[/imath], where [imath]A^+[/imath] is the set that registers as spin-up in detector A, and [imath]A^-[/imath] the set that registers as spin-down in that detector, and [imath]B^+, B^-[/imath] the equivalents for detector B. Yes, OK; and up to me to do something similar ... so that the notation still covers both spin-half and spin-one conjointly. ++$_ wrote:Now, in equations (5a) through (5d) (which, by the way, could be formatted better -- it is general practice to put an equals sign at the beginning of a new line rather than at the end of the previous one), you describe some facts that would have to be true about [imath]A^+, A^-, B^+,[/imath] and [imath]B^-[/imath] because of experimental results.

Agree re (5), as I indicated in earlier post. But, No. Not because of experimental results (I'm not sure where that idea comes from, but will look and correct it). They are true because of my theory. This truth is "proven" when I show that "the mess" in (5) reduces to the simplicity of (6). That's when I claim my theory is vindicated because it agrees 100% with QM.

++$_ wrote: You then state (equation (6)) that if (5a-d) are true, then this is consistent with experimental results. Yes. ++$_ wrote:But that begs the question. It does not show anything, because you have not made use of your equivalence classes in equation (6) at all. You have just stated that: IF your equivalence class theory is correct, THEN it is correct. That doesn't mean anything.

Are you misspeaking here? The ECs are scattered right throughout (5); (6) shows that my use of everyone of them in (5) is consistent with QM. Is this not how it should be, for theoretical physics?

I will now re-read again my essay in the light of your comments; and maybe comment further.

JWalker wrote:Bell's theorem is something that often gets thrown around as if it was proof of fundamental non-locality. However, it is not that at all. Bell's theorem merely states an inequality that violated by non-local interactions and not violated by local interactions under several assumptions. Violation of Bell's inequality is not clear-cut evidence of non-locality. In fact, some inherently classical and local systems have been proposed that violate Bell's inequality in a way that non-local systems would (For example: http://arxiv.org/pdf/0812.4506, but there are several others as well). Some well known theoretical physicists have even proposed that Bell's theorem contains an extremely subtle error that allows violation of the inequality by local systems as well (ex: http://arxiv.org/pdf/0904.4259).

Furthermore, it has yet to be shown that quantum mechanical processes violate Bell's inequality. There have been experiments performed that seem to suggest the inequality is violated, but as of yet, every one of those experiments suffers from at least one loophole that prevents them from being definitive evidence for non-locality. There are several of these loopholes (one of them is discussed here: http://arxiv.org/pdf/1010.1178) and it is a topic of ongoing research how to overcome them. I suspect it wont be too long before there is a loophole free experiment performed, but there is no guarantee what the outcome will be.

The point to all this is that while Bell's theorem is often mistakenly thought of as as a theoretically sound and experimentally confirmed cornerstone of quantum mechanics, it is actually far from either one. I hope the readers of this thread keep that in mind.

Many thanks for this.

To be clear about my position on these issues: I am confident that improved experiments will prove that the older experiments are correct.

That is: My theory is not based on any appeal to loop-holes. I am seeking, in my theory, to match the results of any related experiment; old or new.

++$_ Mo' Money Posts: 2370 Joined: Thu Nov 01, 2007 4:06 am UTC ### Re: Bell's theorem refuted Agree re (5), as I indicated in earlier post. But, No. Not because of experimental results (I'm not sure where that idea comes from, but will look and correct it). They are true because of my theory. This truth is "proven" when I show that "the mess" in (5) reduces to the simplicity of (6). That's when I claim my theory is vindicated because it agrees 100% with QM. Perhaps it was not clear what I was saying. Everything in (5a)-(5d) is independent of experiment, EXCEPT for the last equality in each one where you say that all the other things are equal to [imath]\cos^2[/imath] of something. Only that last equality depends on experiment (or, if you prefer to think of it this way, on QM theory which is supported by experiment). The particular fact that [imath]\cos^2[/imath] is involved cannot be derived from your theory up to that point, because so far you have created a system of hidden variables and a system of equivalence classes, but nothing to actually say how they are related. Naturally, that part has to come from QM theory and experiments. Are you misspeaking here? The ECs are scattered right throughout (5); (6) shows that my use of everyone of them in (5) is consistent with QM. I don't believe I am misspeaking. I must refer you to the pizza parlor example that I have presented below, which explains why equations (5) can show equation (6) without actually being consistent with QM. Bell's theorem refuted wrote:Now: This a serious charge -- in many many fields. So thanks for raising it. BUT am I guilty? I am assuming the validity of local realistic hidden-variables. Bell did the same. I show that they yield results consistent with experiment. Bell did not show this. Is not my approach OK for theoretical physics? Don't we make hypotheses (my assumptions) and show that experiment confirms them? What Bell actually did was: he assumed the existence of local hidden variables, and then followed a chain of reasoning until he came to a result that contradicted experiments. Now, what you have done is: you assumed the existence of local hidden variables, and then followed a chain of reasoning until you came to a result that does not contradict experiments. Superficially, these seem to be similar logical "moves," but they are actually completely different. Let me illustrate Bell's reasoning first: 1. Assume, for purposes of contradiction, that local realism is true. 2. (Theorem). IF local realism is true, THEN all experimental results must conform to Bell's Inequality. 3. Therefore (from 1 and 2), all experimental results must confirm to Bell's inequality. 4. There exist experimental results that do not conform to Bell's inequality. 5. 3 and 4 are contradictory. 6. Therefore, our assumption (1) must have been false. That is, local realism is false. Now here is (as closely as I can reconstruct it) your reasoning: 1. Assume that local realism is true. 2. IF local realism is true, THEN we can create these equivalence classes of hidden variables. 3. IF these equivalence classes of hidden variables exist, THEN they must satisfy equations (5a) through (5d) (this is because of the experimental data). Now, here is where the reasoning stops making sense to me. One possible way to continue from here would be to construct equivalence classes that actually DO satisfy the equations (5a) through (5d). (However, you will not be able to do this. It is impossible.) If you could do that, then you would have created a hypothesis that is confirmed by experiment; namely, that the behavior of the particles is described by hidden variables in those equivalence classes. However, as you have not created any such equivalence classes (and you won't be able to, because it is impossible), you don't actually have a hypothesis. Let me explain why with an example. I heard this from a quantum physicist. Here is the setup. In my city there is a certain pizza parlor with three kinds of pizzas (pepperoni, cheese, and mushroom). They have a very small oven -- in fact, the oven can only hold up to 2 pizzas. I have observed that if I go into the pizza parlor and order a pizza, fully 3/4 of the time a worker immediately goes over to the oven, opens it, and (without showing me the contents) takes out a pizza of the type I ordered. (This observation plays the role of experiment; or, alternatively, of existing QM theory.) What is going on here? Well, I have a theory which we will call the hidden variable theory of the pizza oven. The theory says that the pizza oven has a "hidden variable"; namely, the pizzas inside the oven. In my theory, this hidden variable can fall into one of 6 mutually exclusive equivalence classes (PP, PM, PC, MM, MC, CC). Which equivalence class is governed by processes unknown to me. I also have experimental evidence. The evidence says that the probability of mushrooms is 3/4. In the hidden variable theory, this means that P(PM or MM or MC) = 3/4. Similarly, the probability of pepperoni is 3/4. That is, P(PP or PM or PC) = 3/4. Finally, P(PC or MC or CC) = 3/4. Now, these three equations I have just given are the equivalent of your equations (5a) through (5d). In my pizza parlor example, there are only 3 different measurements that can be performed, whereas in your case there were more. This is why your equations were slightly more complicated than the ones I have here. From these equations I can easily conclude that P(I get the pizza I ordered) = 3/4, beautifully matching the experimental (or QM-theoretical) predictions. This is the equivalent of your equation (6). From this, should I conclude that I have confirmed (or at least, failed to falsify) the hidden variable theory of the pizza oven? No! In fact, the hidden variable theory of the pizza oven is bogus. If I add my three probability equations together, I find that$P(PP) + P(MM) + P(CC) + 2(P(PM) + P(MC) + P(PC)) = {9 \over 4},$ or, after some algebra, $P(PP) + P(MM) + P(CC) + P(PM) + P(MC) + P(PC) = {9 \over 8} + {1 \over 2}(P(PP) + P(MM) + P(CC)).$ But the left-hand-side of that equation is, in my model, 1. So 1 is equal to 9/8 plus something positive, which is a contradiction. In other words, the hidden variable theory of the pizzas is WRONG, despite the fact that I was able to "deduce" the experimental results from my theory just as you were. JWalker Posts: 222 Joined: Sun Nov 23, 2008 1:13 am UTC ### Re: Bell's theorem refuted ++$_ wrote:Let me explain why with an example. I heard this from a quantum physicist.

Here is the setup. In my city there is a certain pizza parlor with three kinds of pizzas (pepperoni, cheese, and mushroom). They have a very small oven -- in fact, the oven can only hold up to 2 pizzas. I have observed that if I go into the pizza parlor and order a pizza, fully 3/4 of the time a worker immediately goes over to the oven, opens it, and (without showing me the contents) takes out a pizza of the type I ordered. (This observation plays the role of experiment; or, alternatively, of existing QM theory.) What is going on here?

Well, I have a theory which we will call the hidden variable theory of the pizza oven. The theory says that the pizza oven has a "hidden variable"; namely, the pizzas inside the oven. In my theory, this hidden variable can fall into one of 6 mutually exclusive equivalence classes (PP, PM, PC, MM, MC, CC). Which equivalence class is governed by processes unknown to me.

I also have experimental evidence. The evidence says that the probability of mushrooms is 3/4. In the hidden variable theory, this means that P(PM or MM or MC) = 3/4. Similarly, the probability of pepperoni is 3/4. That is, P(PP or PM or PC) = 3/4. Finally, P(PC or MC or CC) = 3/4. Now, these three equations I have just given are the equivalent of your equations (5a) through (5d). In my pizza parlor example, there are only 3 different measurements that can be performed, whereas in your case there were more. This is why your equations were slightly more complicated than the ones I have here.

From these equations I can easily conclude that P(I get the pizza I ordered) = 3/4, beautifully matching the experimental (or QM-theoretical) predictions. This is the equivalent of your equation (6).

From this, should I conclude that I have confirmed (or at least, failed to falsify) the hidden variable theory of the pizza oven? No! In fact, the hidden variable theory of the pizza oven is bogus. If I add my three probability equations together, I find that$P(PP) + P(MM) + P(CC) + 2(P(PM) + P(MC) + P(PC)) = {9 \over 4},$ or, after some algebra,
$P(PP) + P(MM) + P(CC) + P(PM) + P(MC) + P(PC) = {9 \over 8} + {1 \over 2}(P(PP) + P(MM) + P(CC)).$ But the left-hand-side of that equation is, in my model, 1. So 1 is equal to 9/8 plus something positive, which is a contradiction. In other words, the hidden variable theory of the pizzas is WRONG, despite the fact that I was able to "deduce" the experimental results from my theory just as you were.

This is a very beautiful example, thank you for posting it. Not only does it accurately capture the nature of Bell's theorem, it also provides an easy way to demonstrate one of Bell's implicit assumptions. Purely because I find this fascinating, I'll post an explanation of that point. I'll try to keep it as brief as possible.

Lets start with what we know. We know that when we order a pizza, we get the correct one 3/4 of the time. From this we conclude that our conditional probability of ordering a pizza (I'll call our order [imath]O_A[/imath]) and getting that pizza (I'll call our pizza [imath]A[/imath]) is $P(A|O_A)=\frac{3}{4}$
Using Bayes' theorem we can relate this to the probability that pizza A is in the oven, [imath]P(A)[/imath], the probability that we will order pizza A [imath]P(O_A)[/imath], and the probability that given pizza A is in the oven, we will also order it, [imath]P(O_A|A)[/imath]. Note that in general, $P(A|O_A)\neq P(O_A|A)$
This might be the most common mistake people make with probabilities, so I always point it out. Anyways, Bayes' theorem tells us
$P(A|O_A)=\frac{P(O_A|A)P(A)}{P(O_A)}$
It seems reasonable to say that [imath]P(O_A)=\frac{1}{3}[/imath], as there are three pizzas to choose from, and we choose at random. Likewise, it seems reasonable to say [imath]P(A)=\frac{1}{2}[/imath], since our sample space of pizzas A,B and C is AA,AB,AC,BB,BC,CC, half of which contain pizza A. Plugging in to Bayes' theorem, we have
$\frac{3}{4}=\frac{P(O_A|A)(1/2)}{3/4}$
or
$P(O_A|A)=\frac{1}{2}$
That is, if the pizza chef decides to cook pizza A, there is a 50% chance that we will order pizza A. This is actually a strange result, since no matter what the probability of cooking a given pizza is, the best we can do is have [imath]P(O_A|A)=\frac{4}{9}[/imath] and [imath]P(A|O_A)=\frac{2}{3}[/imath]. Thus we conclude that if there are 'hidden variables,' in this case which pizzas are in the oven, we should have
$P(O_A|A)\leq \frac{4}{9}$
This is our 'Bell's inequality' for this case. Clearly, since [imath]P(O_A|A)=\frac{1}{2}[/imath], this inequality is violated. This means that there can be no hidden pizzas in the oven, right?

Well, not quite. The violation of our Bell's inequality, [imath]P(O_A|A)=\frac{1}{2}[/imath], only means that the pizza we order is in the oven more than random chance allows, or in other words, there is some correlation between the two events. There are three ways we can explain this. For one, we could abandon the idea of hidden variables entirely and sacrifice local realism (the most common position). We could also conclude that the pizza chef knew what we were going to order ahead of time (maybe we called ahead). This would be a non-local theory hidden variable theory, since we have action at a distance (phone calls). Finally, we could conclude that one of our assumptions is wrong.

It is this third option that is the basis for many objections to Bell's theorem. I condend that the assumption that we can set [imath]P(A)=\frac{1}{2}[/imath] and [imath]P(O_A)=\frac{1}{3}[/imath] independent of each other implicitly assumes that we do not have a deterministic hidden variable theory*. Simply put, if we are dealing with a deterministic reality, then our choice of order has been pre-determined, as has which pizzas are put in the oven. If this is the case, it is possible that our choice of order is determined by a hidden variable that is [imath]O_A=O(\lambda)[/imath], and likewise the pizzas in the oven are determined by [imath]A=A(\lambda)[/imath]. This hidden variable ([imath]\lambda[/imath]) is what provides the correlation between our order and which pizza is cooked which violates Bell's inequality. Note that this is in fact a local hidden variable theory in the sense that there is no superluminal communication. All that is required is that at some point in the past, the pizza parlor and the customer were inside each others light cones in order to become correlated. As long as neither one spontaneously burst into existence with no cause, this is possible. In this view, nothing travels faster than light, and local realism is preserved.

*If you like, I can provide a more mathematical explanation for this

Please keep in mind that I am not trying to argue that Bell's theorem is wrong, only that it does not exclude all possible local hidden variable theories, but rather a certain subset.

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### Re: Bell's theorem refuted

So, to port your point out of the analogy and back to the real QM situation, you're suggesting the possibility of the world being such that there is, through some unknown hidden-varible-based mechanism, a correlation between the spin configuration of a particle and which test we end up sending the particle through? Or am I misreading?

So, say, the correlation between the horizontal spin and the diagonal spin of a particle is actually less than 1/sqrt(2), to a degree that satisfies Bell's inequality, but it happens that the particles where those spin matches, we're more likely to test those two spins? And for the particles where those spins don't match, we're more likely to run some other test instead? So that the final result of P(spins match|particle tested) is our actual observed (sqrt(2)+2)/4?

I guess it's theoretically possible, in the spontaneous-creation-of-hordes-of-antimatter-wildebeest sense of "possible", but it seems far-fetched... Once you start positing mechanisms by which the Universe starts directly dicking with the experiments, you may as well stop Sciencing altogether. I think this possibility rests in the same category as Descartes's evil demon.

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