Joy Christian's disproof of Bell

[Gordon Watson]

Ok, noted and done.

Thank you vanesch.

Can you also fix each page header?

It would give PF a better look if its page-headers were error-free.

 

[JesseM]

The relationship between the polarizers isn't a local fact, and the relationship between the photons isn't a local fact.

No, but both involve a statistical correlation between a collection local facts. Clearly the assumption of local realism does not rule out the existence of such correlations between local facts, and whether you call them "relationships between local facts" or "relationships between relationships", we could find the same kind of relationships in classical electromagnetism which is a local realist theory, do you disagree?

Wrt the polarizers this relationship just refers to their angular difference ( θ). Wrt the photons, things aren't so simple. What the polarizers are jointly physically measuring during any coincidence interval is the relationship between two optical disturbances emitted by the same atom -- a relationship that's expressed vis the applicable conservation law.

And couldn't we find relationships between two electromagnetic waves generated by the same source in classical electromagnetism?

What the experiment is correlating to θ is the rate of generation of identical detection attributes. The joint detection attribute, (A,B), is also not a local fact. E(A,B) isn't, effectively, determined by local hidden variables.

But E(A,B) for any joint detection attributes we could come up with in a classical EM experiment would be determined solely by local variables in the region of each measurement, do you disagree?

It almost sounds like you're arguing that by the very nature of the experiment Bell's assumptions about local realist are wrong, but that clearly isn't the case, if you did the same type of experiment but the statistical results were a little different, then it might be fully explainable by a local realist theory just as would be true for an experiment in classical EM.

Wrt the two photon scenarios, the hidden variable, λ, is typically taken to refer to the optical vector of the polarizer-incident photons.

No it isn't, this is an idea I've seen you refer to before, but if you think this is the way physicists conceive of it then that's a misconception. The hidden variable is sometimes imagined to be, not any sort of "vector", but simply a function that assigns a + or - to every possible detection angle in advance...but one of the points of Bell's proof is that it requires no understanding of what the local hidden variables would actually be or exactly how they would determine the measurement results.

It's just an empirical observation that photons emitted by the same atom are correlated in this way, but it doesn't tell you, for example, whether they are correlated because they were each assigned identical hidden variables at the moment they were created and they just carried the variables with them as they traveled, or whether the fact that they were created together gives them an FTL connection which allows a measurement on one to instantly affect the behavior of the other, or some other picture of what's going on "behind the scenes".

The assumption that the relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition seems to me to be the most reasonable assumption. Isn't this what qm's application of the law of conservation of angular momentum in Aspect 1982 is based on?

But "relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition" is still very vague, it doesn't tell me what this "due to" consists of--for example, whether you are imagining that "due to their being emitted in opposite directions" they were assigned the same properties at birth and just carried these unchanging properties with them to the location of the measurements (which of course would mean the properties were local hidden variables, so that's ruled out by Bell), or if "due to their being emitted in opposite directions" they were given an FTL connection that causes any measurement on one to instantly affect the other, or some other picture of exactly how their common emission explains later correlations.

I don't understand what you mean by "aren't applicable".

As in irrelevant. See above.

Doesn't help me either--and here you snipped out the questions about classical EM which were meant to specifically probe my confusion about what you mean by terms like "aren't applicable" and "irrelevant", which is why I repeat them again in this post, please actually address these questions this time. Again, I'm confused about whether you think that the nature of the experiment and what sort of correlations are being measured (ignoring the detailed statistics of the results) invalidates Bell's local realist assumptions, or whether you agree that with slightly different results Bell's assumptions might indeed by applicable.

BIs are violated because they're based on a formulation of joint detection (entanglement) preparations which requires the inclusion of a variable which is irrelevant wrt those contexts.

It doesn't "require" the inclusion of the hidden variable. If I say that in general z can be a function of w,x,y and write this as z=f(w,x,y), this doesn't rule out the possibility that y is irrelevant and the correct function is z=w^2 + 2x, since you could always rewrite this as z=w^2 + 2x + 0y. Bell's proof is general, it totally rules out the possibility that the QM measurement statistics could be explained by any local realist theory, including one where the only local variables that influenced the measurement results were non-hidden ones.

It's possible to understand these experiments in local realist terms without requiring that the mathematical model include any local hidden variables.

No, it's definitely not possible to understand the experiments in local realist terms, if you think it is you're fundamentally misunderstanding Bell's proof. If you assume there are no hidden variables and simply redefine λ to refer to the state of all non-hidden local variables in the immediate region of the each measurement (including variables whose state may represent properties of the electron that it was assigned at birth and that it just "carried with it", unchanging, to the region of the measurement, so that the states of these variables could be correlated for the two particles in the region of each measurement) then the proof would still work fine and would show that you can't explain the violation of BI in a local realist theory where the measurement results are determined by local non-hidden variables in the region of the measurement.

Edit: Isn't what qm does is define the relevant relationships and then relate those relationships accordingly?

I don't know what you mean by "relate those relationships" as separate from "define the relevant relationships". QM just gives mathematical functions which tell you the probability of some measurement result(s) given knowledge of some other measurement result(s).

 

[Gordon Watson]

... <SNIP> ...

QM just gives mathematical functions which tell you the probability of some measurement result(s) given knowledge of some other measurement result(s).

Dear JesseM and vanesch, I agree with Jesse's point above.

Earlier in this thread, vanesch cited Sakurai and http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality

I'd be pleased to see the QM probabilities for the eight (8) probabilities (P1-P8) in the cited text.

Can you provide them, please?

Thank you, JenniT

 

[JesseM]

Dear JesseM and vanesch, I agree with Jesse's point above.

Earlier in this thread, vanesch cited Sakurai and http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality

I'd be pleased to see the QM probabilities for the eight (8) probabilities (P1-P8) in the cited text.

Can you provide them, please?

Thank you, JenniT

Those probabilities are for the various hidden-variable states, not for measurable outcomes (you can't measure more than one angle a, b, or c for a given particle). Since QM doesn't say anything about hidden-variable states which may or may not exist, only about measurable outcomes, QM does not assign probabilities to P1-P8. But what Bell shows is that we can imagine any possible combination of probabilities for P1-P8 in a hidden-variable theory (with the probabilities being in the range 0 ≤ Pn ≤ 1 and adding up to 1, of course), and the theory will always predict that the inequality P(a+, b+) ≤ P(a+, c+) + P(c+, b+) will be respected, but QM predicts this inequality is violated.

 

[Gordon Watson]

Those probabilities are for the various hidden-variable states, not for measurable outcomes (you can't measure more than one angle a, b, or c for a given particle). Since QM doesn't say anything about hidden-variable states which may or may not exist, only about measurable outcomes, QM does not assign probabilities to P1-P8. But what Bell shows is that we can imagine any possible combination of probabilities for P1-P8 in a hidden-variable theory (with the probabilities being in the range 0 ≤ Pn ≤ 1 and adding up to 1, of course), and the theory will always predict that the inequality P(a+, b+) ≤ P(a+, c+) + P(c+, b+) will be respected, but QM predicts this inequality is violated.

Thanks Jesse,

So: Would it be OK if I post, for discussion, a local realistic hidden-variable theory under this heading: What's wrong with this local realistic counter-example to Bell's theorem?

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments.

D: Have them recognizing topology associated with the spherical symmetry of the singlet state.

E: Have them breaching Bell's inequality.

F: Have them based on nothing more than high-school maths and logic.

PS: I'm an engineer, I'm here to learn, and I could be mistaken -- which is not the same as being crackpot.

Thanks again,

JenniT

 

[JesseM]

Thanks Jesse,

So: Would it be OK if I post, for discussion, a local realistic hidden-variable theory under this heading: What's wrong with this local realistic counter-example to Bell's theorem?

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments.

D: Have them recognizing topology associated with the spherical symmetry of the singlet state.

E: Have them breaching Bell's inequality.

F: Have them based on nothing more than high-school maths and logic.

PS: I'm an engineer, I'm here to learn, and I could be mistaken -- which is not the same as being crackpot.

Thanks again,

JenniT

I think as long as you are willing to listen to arguments as to why your argument might be flawed, it should be OK to post. Keep in mind though, the idea is that on each trial the experimenters choose randomly which of the 3 angles a, b, c to use, in a way that's uncorrelated with which of the 8 hidden states occur on that trial, and that it must be true that whenever they pick the same angle, they get the same result (which is guaranteed as long as you assume the possible hidden states of the particle pair must be one of the 8 listed in the wikipedia article, rather than other possibilities where not all the hidden states are opposite for Alice and Bob, like if Alice's state was +++ while Bob's was +--) And do you understand that if Alice chooses angle a and Bob chooses angle b, it must be true that P(a+, b+) is equal to P3 + P4 since those are the only probabilities corresponding to hidden states which have + in the a-column of Alice's particle and + in the b-column of Bob's particle? Likewise if Alice chooses a and Bob chooses c, then P(a+, c+) = P2 + P4, and if Alice chooses c and Bob chooses b, then P(c+, b+) = P3 + P7. If all the probabilities have non-negative values, it should be obvious that you can't come up with any values for the probabilities that don't satisfy P3 + P4 ≤ (P2 + P4) + (P3 + P7), since this can be rearranged as (P3 + P4) ≤ (P3 + P4) + P2 + P7 and neither P2 nor P7 can be negative.

edit: another option would be to just say what part of this argument isn't making sense to you...presumably you are not claiming you can find non-negative values for P2, P3, P4, P7 which fail to satisfy (P3 + P4) ≤ (P3 + P4) + P2 + P7 so there must be some earlier point in this argument, like maybe the step that says P(a+, b+) = P3 + P4 and P(a+, c+) = P2 + P4 and P(c+, b+) = P3 + P7, that's different from what you had when you were analyzing the problem.

 

[vanesch]

Thanks Jesse,

So: Would it be OK if I post, for discussion, a local realistic hidden-variable theory under this heading: What's wrong with this local realistic counter-example to Bell's theorem?

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments.

D: Have them recognizing topology associated with the spherical symmetry of the singlet state.

E: Have them breaching Bell's inequality.

F: Have them based on nothing more than high-school maths and logic.

PS: I'm an engineer, I'm here to learn, and I could be mistaken -- which is not the same as being crackpot.

Thanks again,

JenniT

We're walking on a thin line here, I'm not entirely sure that all my co-mentors will agree.

But for sake of pedagogy, be my guest. It is clear to me (and to Jesse I think) that you have a misunderstanding of what is claimed, what is going on and what all this is about, so as it is always pedagogically interesting to see a wrong argument developed in order to pinpoint the misunderstanding, go ahead.

However, I have to warn you: you are attempting to find numbers which have to satisfy mutually incompatible inequalities.

You are trying the equivalent of something like the following: find 2 numbers x and y such that x > 0, y > 0 and x + y < x - 1 and x + y < y - 1 or something.

So "good luck"

 

[harrylin]

In the last paragraph, after equation 30.[/QUOTE

There he writes that "one can exchange signals" as the proper-time τ elapsed for each of the particles is unequal to zero...
To me that sounds as if it can have to do with the entangled particles exchanging signals at speeds less than light.

(About "none of which contradicts [..] the assumption that nature is locally causal": - see also my PS below!)

That's the view of many, and maybe it was Bell's intention, but that isn't what BI violations, definitively and unarguably, indicate -- which is that the LR formulation on which the formally and experimentally violated BI is based is incompatible with standard qm and the experimental preparation. No more, no less. This is what I meant by the minimalist interpretation and unarguable applicability of Bell's theorem. [..] BI violations don't contradict the assumption that nature is exclusively local.

"LR" stands for local realism I suppose... Thus you hold that the class of LR theories that the Bell Inequality disproves is incompatible with the experimental preparation??

As I mentioned in a previous post, BIs are based on the requirement that entanglement be modeled by (local hidden) variables which are irrelevant (even in an exclusively locally causal world) wrt entanglement (which depends exclusively on global properties and measurement parameters), and that if lhv's are required in the model of entanglement, then the predictions of such a model will necessarily be skewed.

Then according to you, Bell's theorem (BI => "no local deterministic hidden-variable theory can reproduce all the experimental predictions of quantum mechanics") is basically wrong or misunderstood?
For it does not make sense to require a theory to model an effect by means of irrelevant variables - that is a false requirement!

PS: I now see that my questions here above about "none of which contradicts the assumption that nature is locally causal" have already largely been answered - apparently both with "yes".

 

[JesseM]

ThomasT, I can't edit the post any more, but when I wrote this:

But "relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition" is still very vague, it doesn't tell me what this "due to" consists of--for example, whether you are imagining that "due to their being emitted in opposite directions" they were assigned the same properties at birth and just carried these unchanging properties with them to the location of the measurements (which of course would mean the properties were local hidden variables, so that's ruled out by Bell), or if "due to their being emitted in opposite directions" they were given an FTL connection that causes any measurement on one to instantly affect the other, or some other picture of exactly how their common emission explains later correlations.

...I should have said "which of course would mean the properties were local variables, so that's ruled out by Bell", as the properties that each particle carries with them may not necessarily be hidden ones, and as I explained Bell's proof rules out all local realist explanations regardless of whether they involve hidden or non-hidden variables.

 

[harrylin]

[..]In any case, based on Avodyne's comment in post #30 it sounds like Joy Christian's model just ignores the real-world observation that the experimenter always sees one of two discrete results (pointer going to +1 or -1), and instead posits a sort of hypothetical universe where the results are elements of Clifford algebra.[..]

That is not the case, see my comment in post #34.

 

[JesseM]

That is not the case, see my comment in post #34.

OK, if the communication was by email, do you still have the emails? I'd be interested to see his exact words...

 

[vanesch]

Thank you vanesch.

Can you also fix each page header?

It would give PF a better look if its page-headers were error-free.

I could, but it is too much work. I'd have to edit each individual post.

 

[Gordon Watson]

I could, but it is too much work. I'd have to edit each individual post.

OK; thanks; no worries. I thought that the page header, that occurs once every 16 pages or so, was automatically derived from the OP's opening header.

 

[Gordon Watson]

We're walking on a thin line here, I'm not entirely sure that all my co-mentors will agree.

But for sake of pedagogy, be my guest. It is clear to me (and to Jesse I think) that you have a misunderstanding of what is claimed, what is going on and what all this is about, so as it is always pedagogically interesting to see a wrong argument developed in order to pinpoint the misunderstanding, go ahead.

However, I have to warn you: you are attempting to find numbers which have to satisfy mutually incompatible inequalities.

You are trying the equivalent of something like the following: find 2 numbers x and y such that x > 0, y > 0 and x + y < x - 1 and x + y < y - 1 or something.

[Emphasis added by JenniT.]

So "good luck"

1. OK; let me sleep on it. I'm time-poor at the moment -- and I would want to be readily available for such a thread.

2. In the interim, could you elaborate, please, on the "equivalent" that you think I am addressing?

JesseM provided helpful additional remarks, reinforcing issues to be addressed.

So I would certainly want to ensure, and explain why, I am not falling into the apparent conundrum that you have in mind.

Thank you,

JenniT

 

[ThomasT]

There he writes that "one can exchange signals" as the proper-time τ elapsed for each of the particles is unequal to zero...
To me that sounds as if it can have to do with the entangled particles exchanging signals at speeds less than light.

Yes, but this has to do with what "amounts to a null-like condition on the spin bi-vector", and that "despite that the addition of two momenta in ordinary spacetime remains timelike and the difference of the momenta is spacelike, consistent with the spacelike separation of the two particles 1, 2 moving along the z-axis in opposite directions, the addition laws of the poly-momentum in C-space is null-like". So, "since the interval in C-space (X₁ − X₂)² is null one can exchange signals from the locations 1, 2 in C-space".

An LR description of the sort that Einstein and Bell (and most everybody else I would guess) would consider an LR description wouldn't have the entangled particles exchanging signals in order to account for the correlation between θ and the rate of coincidental detection. Rather, it would identify some sort of common cause as being the determiner of the entanglement between the particles.

Maybe Christian's C-space formulation can be translated into a bona fide LR account, but I don't know how that might be done. Maybe you can give it a try.

"LR" stands for local realism I suppose...

Yes LR stands for Local Realism or Local Realistic.

Thus you hold that the class of LR theories that the Bell Inequality disproves is incompatible with the experimental preparation??

Yes. At least that much follows from the fact of experimental violations of BIs.

My current way of thinking about it is that all bona fide LR or LHV theories of entanglement are ruled out.

As I mentioned in a previous post, BIs are based on the requirement that entanglement be modeled by (local hidden) variables which are irrelevant (even in an exclusively locally causal world) wrt entanglement (which depends exclusively on global properties and measurement parameters), and that if lhv's are required in the model of entanglement, then the predictions of such a model will necessarily be skewed.

Then according to you, Bell's theorem (BI => "no local deterministic hidden-variable theory can reproduce all the experimental predictions of quantum mechanics") is basically wrong or misunderstood?

I think that it's been thoroughly demonstrated, that "no local deterministic hidden-variable theory can reproduce all the experimental predictions of quantum mechanics" wrt entanglement preparations. But many (most?) people take violations of BIs to be indicating that either nature is nonlocal or that local hidden variables don't exist. I just currently think that there's a more parsimonious explanation for why BIs are violated.

Anyway, this isn't the thread to get into that, and I apologize for temporarily derailing it. It appears that the thread is back on topic talking about Christian's stuff.

Ok, just one more ...

... it does not make sense to require a theory to model an effect by means of irrelevant variables - that is a false requirement!

The lhv's aren't irrelevant physically wrt the individual data streams, but they're irrelevant or superfluous wrt an accurate statistical accounting of the correlation between θ and rate of coincidental detection. My current line of thinking about it might be wrong, but I just have this nagging feeling that the effective reason why BIs are violated, and the correct interpretation of Bell's work, has to do with something much more mundane than that nature is nonlocal or that lhv's don't exist.

 

[ThomasT]

ThomasT, I can't edit the post any more, but when I wrote this:

But "relationship between their motional properties is due to their being emitted in opposite directions from the same atom during the same transition" is still very vague, it doesn't tell me what this "due to" consists of--for example, whether you are imagining that "due to their being emitted in opposite directions" they were assigned the same properties at birth and just carried these unchanging properties with them to the location of the measurements (which of course would mean the properties were local hidden variables, so that's ruled out by Bell), or if "due to their being emitted in opposite directions" they were given an FTL connection that causes any measurement on one to instantly affect the other, or some other picture of exactly how their common emission explains later correlations.

...I should have said "which of course would mean the properties were local variables, so that's ruled out by Bell", as the properties that each particle carries with them may not necessarily be hidden ones, and as I explained Bell's proof rules out all local realist explanations regardless of whether they involve hidden or non-hidden variables.

Ok, thanks for your comments, JesseM. Not wanting to derail this thread any more, I'm going to go over our discussion in this thread and will probably start a new thread on it, but this will take longer than I originally thought it would.

 

[Gordon Watson]

I think as long as you are willing to listen to arguments as to why your argument might be flawed, it should be OK to post. Keep in mind though, the idea is that on each trial the experimenters choose randomly which of the 3 angles a, b, c to use, in a way that's uncorrelated with which of the 8 hidden states occur on that trial, and that it must be true that whenever they pick the same angle, they get the same result (which is guaranteed as long as you assume the possible hidden states of the particle pair must be one of the 8 listed in the wikipedia article, rather than other possibilities where not all the hidden states are opposite for Alice and Bob, like if Alice's state was +++ while Bob's was +--) And do you understand that if Alice chooses angle a and Bob chooses angle b, it must be true that P(a+, b+) is equal to P3 + P4 since those are the only probabilities corresponding to hidden states which have + in the a-column of Alice's particle and + in the b-column of Bob's particle? Likewise if Alice chooses a and Bob chooses c, then P(a+, c+) = P2 + P4, and if Alice chooses c and Bob chooses b, then P(c+, b+) = P3 + P7. If all the probabilities have non-negative values, it should be obvious that you can't come up with any values for the probabilities that don't satisfy P3 + P4 ≤ (P2 + P4) + (P3 + P7), since this can be rearranged as

(A) (P3 + P4) ≤ (P3 + P4) + P2 + P7 and neither P2 nor P7 can be negative. [Emphasis and identifier added by JenniT.]

edit: another option would be to just say what part of this argument isn't making sense to you...presumably you are not claiming you can find non-negative values for P2, P3, P4, P7 which fail to satisfy (P3 + P4) ≤ (P3 + P4) + P2 + P7 so there must be some earlier point in this argument, like maybe the step that says P(a+, b+) = P3 + P4 and P(a+, c+) = P2 + P4 and P(c+, b+) = P3 + P7, that's different from what you had when you were analyzing the problem.

Thanks Jesse, your attention to explanatory detail is to be applauded. It is much appreciated. (A) is the very point that I planned to address -- a very clear impossibility.

My idea is to show that (A), an impossibility, is not mandated by all local realistic hidden-variable theories.

I personally do not require LHV's to do the impossible, going beyond QM. I seek LHV's which are explanatory -- requiring neither recourse nor inference to FTL or NL (non-locality).

PS: In my view, the remarkable spherical symmetry of the singlet state seems not much addressed in this connection. But I'll sleep on it, and triple-check the idea, until I have more time for involvement.

Thanks again, JT.

 

[JesseM]

Thanks Jesse, your attention to explanatory detail is to be applauded. It is much appreciated. (A) is the very point that I planned to address -- a very clear impossibility.

My idea is to show that (A), an impossibility, is not mandated by all local realistic hidden-variable theories.

OK, but do you agree that in a LHV theory, in order to explain how the two experimenters always get the opposite results when they pick the same angle (and they are picking angles at random), it must be true that each time the source sends out a particle pair, it must create them with LHV that predetermine what their results will be for any possible angle, in such a way that they each are guaranteed to have opposite predetermined results for every angle?

If that's the case, then whatever the hidden variables may be, if we are only interested in the predetermined results for three possible angles a, b, and c, every combination of hidden variables should fall into one of the following 8 categories:

1. Particle 1: a+ b+ c+ / Particle 2: a- b- c-
2. Particle 1: a+ b+ c- / Particle 2: a- b- c+
3. Particle 1: a+ b- c+ / Particle 2: a- b+ c-
4. Particle 1: a+ b- c- / Particle 2: a- b+ c+
5. Particle 1: a- b+ c+ / Particle 2: a+ b- c-
6. Particle 1: a- b+ c- / Particle 2: a+ b- c+
7. Particle 1: a- b- c+ / Particle 2: a+ b+ c-
8. Particle 1: a- b- c- / Particle 2: a+ b+ c+

...where, for example, if the hidden variables fall into category #4 that means they predetermine that particle 1 will give + if angle a is chosen, - if angle b is chosen, and - if angle c is chosen, while particle 2 is predetermined to give the opposite result for each angle. Of course the hidden variables can be much more complicated than this, so just knowing that they fall into category #4 doesn't tell you the full value of all hidden variables (for example it doesn't tell you what the predetermined result would be for some different angle d), but even if there are an infinite number of distinct possible hidden-variable states, each one must fall into one of the eight categories above depending on its predetermined results for angles a, b, and c.

If you don't see why this would necessarily be true in a LHV theory, please explain the specific point you would dispute--for example, do you disagree that the hidden variables must give a predetermined result for each possible angle in order to explain how the experimenters always get opposite results whenever they pick the same angle?

 

[Gordon Watson]

OK, but do you agree that in a LHV theory, in order to explain how the two experimenters always get the opposite results when they pick the same angle (and they are picking angles at random), it must be true that each time the source sends out a particle pair, it must create them with LHV that predetermine what their results will be for any possible angle, in such a way that they each are guaranteed to have opposite predetermined results for every angle?

If that's the case, then whatever the hidden variables may be, if we are only interested in the predetermined results for three possible angles a, b, and c, every combination of hidden variables should fall into one of the following 8 categories:

1. Particle 1: a+ b+ c+ / Particle 2: a- b- c-
2. Particle 1: a+ b+ c- / Particle 2: a- b- c+
3. Particle 1: a+ b- c+ / Particle 2: a- b+ c-
4. Particle 1: a+ b- c- / Particle 2: a- b+ c+
5. Particle 1: a- b+ c+ / Particle 2: a+ b- c-
6. Particle 1: a- b+ c- / Particle 2: a+ b- c+
7. Particle 1: a- b- c+ / Particle 2: a+ b+ c-
8. Particle 1: a- b- c- / Particle 2: a+ b+ c+

...where, for example, if the hidden variables fall into category #4 that means they predetermine that particle 1 will give + if angle a is chosen, - if angle b is chosen, and - if angle c is chosen, while particle 2 is predetermined to give the opposite result for each angle. Of course the hidden variables can be much more complicated than this, so just knowing that they fall into category #4 doesn't tell you the full value of all hidden variables (for example it doesn't tell you what the predetermined result would be for some different angle d), but even if there are an infinite number of distinct possible hidden-variable states, each one must fall into one of the eight categories above depending on its predetermined results for angles a, b, and c.

If you don't see why this would necessarily be true in a LHV theory, please explain the specific point you would dispute--for example, do you disagree that the hidden variables must give a predetermined result for each possible angle in order to explain how the experimenters always get opposite results whenever they pick the same angle?

I'm about to lose power for 6+ hours; will get back to you.

 

[Gordon Watson]

I'm about to lose power for 6+ hours; will get back to you.

Jesse, sorry for delay. My general answer to your concerns is YES; for I'm familiar with many of the Bell fundamentals. But there's a subtlety, associated with my understanding Bohr's attitude to EPR -- which I'm at present attributing to "topology" -- which questions the impossibility equation.

So the earlier points raised remain valid. Most of my case is based on simple maths -- so errors can be easily spotted and agreed, such errors perhaps having important lessons about BT, as vanesch points out.

The OP will:

A: Deliver P1-P8.

B: Have them summing to unity.

C: Have them fully compatible with QM-style experiments; delivering accepted QM results.

D: Have them recognizing a topology [for want of a better word] associated with the spherical symmetry of the singlet state and measuring-device settings.

E: Have them challenging the basis of Bell's inequality.

F: Have them based on nothing more than high-school maths and logic; so no fancy maneuvers are involved -- and the discussion should be understood by most everyone.

PS: It would be good to have vanesch's concern [above; re, x, y, etc.] spelt out -- to minimize the chance of blunder.

JenniT

 

[yoda jedi]

For several years Joy Christiaan has been publishing about the disproof of Bell in a typical EPR setup, his latest (?) publication being http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.4259v3.pdf" .

In a nutshell his argument is that Bell uses an invalid topology for the EPR elements of reality (1D instead of 3D). When using Clifford algebra the author says he can reproduce the Bell inequalities.

Does he have a valid argument here?

This http://www.physics.utoronto.ca/~aephraim/2206/Sprague-ChristianDisproofBell.pdf" further summarizes his arguments

ps. I haven't seen his articles being published somewhere else then Arxiv, but Carlos Castro references him claiming about the same http://www.m-hikari.com/astp/astp2007/astp9-12-2007/castroASTP9-12-2007.pdf" .

http://www.bbk.ac.uk/tpru/BasilHiley/Algebraic Quantum Mechanic 5.pdf
The orthogonal Clifford algebra and the generalised Clifford algebra, Cⁿ,
(discrete Weyl algebra) is re-examined and it is shown that the quantum
mechanical wave function (element of left ideal), density operator (element
of a two sided ideal) and mean values (algebraic trace) can be constructed
from entirely within the algebra. No appeal to Hilbert space is necessary.
We show how the GNS construction can be obtained from within both
algebras. The limit of Cⁿ as ⁿ->oo is shown to be the extended Heisenberg algebra.
Finally the relationship to the usual Hilbert space approach is discussed.


The Clifford Algebra Approach to Quantum Mechanics B: The Dirac Particle and its relation to the Bohm Approach

http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4033v1.pdf

In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the Bohm approach is incorrect. We obtain the fully relativistic version by using an approach based on Clifford algebras outlined in two earlier papers by Hiley and by Hiley and Callaghan. The relativistic model is different from the one originally proposed by Bohm and Hiley and by Doran and Lasenby. We obtain exact expressions for the Bohm energy-momentum density, a relativistic quantum Hamilton-Jacobi for the conservation of energy which includes an expression for the quantum potential and a relativistic time development equation for the spin vectors of the particle. We then show that these reduce to the corresponding non-relativistic expressions for the Pauli particle which have already been derived by Bohm, Schiller and Tiomno and in more general form by Hiley and Callaghan. In contrast to the original presentations, there is no need to appeal to classical mechanics at any stage of the development of the formalism. All the results for the Dirac, Pauli and Schroedinger cases are shown to emerge respectively from the hierarchy of Clifford algebras C(13),C(30), C(01) taken over the reals as Hestenes has already argued. Thus quantum mechanics is emerging from one mathematical structure with no need to appeal to an external Hilbert space with wave functions.

The Clifford Algebra approach to Quantum Mechanics A: The Schroedinger and Pauli Particles

http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4031v1.pdf

In this paper we show how all the quantum properties of Schroedinger and Pauli particles can be described entirely from within a Clifford algebra taken over the reals. There is no need to appeal to any `wave function'. To describe a quantum system, we define the Clifford density element [CDE] as a product of an element of a minimal left ideal and its Clifford conjugate. The properties of the system are then completely specified in terms of bilinear invariants of the first and second kind calculated using the CDE. Thus the quantum properties of a system can be completely described from within the algebra without the need to appeal to any Hilbert space representation.
Furthermore we show that the essential bilinear invariants of the second kind are simply the Bohm energy and the Bohm momentum, entities that make their appearance in the Bohm interpretation. We also show how these parameters emerge from standard quantum field theory in the low energy, single particle approximation. There is no need to appeal to classical mechanics at any stage. This clearly shows that the Bohm approach is entirely within the standard quantum formalism. The method has enabled us to lay the foundations of an approach that can be extended to provide a complete relativistic version of Bohm model. In this paper we confine our attention to the details of the non-relativistic case and will present its relativistic extension in a subsequent paper.