The Pearle model as a conspiracy loophole model

[gill1109]

Now that we have perfect simulation models, it's maybe time to step
back and ask ourselves what we have achieved. I think there is a little
problem with these simulations.

Note: I refer here to what I call the "clocked" variants
(Michel uses the word "clocked" with the opposite meaning).
For me, clocked means discrete time. For n runs from 1 to N: source
creates emission n, Alice and Bob choose settings n, measurement stations
generate outcomes n. Other words are: pulsed emission, synchronised
experiment, event-ready detectors.

The problem is in the heart of the simulation. In order to generate
outcomes for A and B we obviously need values of the settings
a and b, and we need a realization of the hidden state lambda.

In these Pearle / Thompson like models, lambda is effectively generated by
the rejection method: an initial randomization can generate both states lambda
and non-states - points lambda outside of what Joy defines to be the domain of
A(a, .) and B(b, .). So we just keep picking a lambda from the big set of states
and non-states, till we are lucky enough to get a state.

In both simulation models, the criterion for rejection depends on a and
b. In other words, the domain of the hidden state and hence also its
probability distribution, depends on a and b.

Maybe this only appears to be so? Maybe if you have checked that
some criterion involving a and b is satified, then it is also satisfied for
all possible a' and all possible b', hence it not actually "measurement
setting dependent"? Well, that is what Christian claims, but I have
problems with his use of "for all" and "there exists". And for me
it is clear that Bell's theorem shows that this selection *must* be
measurement-setting dependent. You can only violate Bell's inequality
by violating one of locality, realism, or no-conspiracy. In this case the
simulation is evidently local realist. So it violates "no-conspiracy",
aka "freedom".

In my opinion, the cause of all this sorrow is the attempt to simulate
Christian's S^3 based mathematics within the confines of local realism
on classical computers. That enterprise is doomed to failure ... by Bell's
theorem. Earlier, Christian always admitted this. He always said: you can't
disprove a true mathematical theorem. You have to *circumvent* one.

I believe that Christian's model cannot be reproduced in flatland. It would
need a kind of Möbius strip in space-time which alters the measurement
outcomes (the measurement outcomes which Alice and Bob
saw and collected in their respective labs) as they bring them back in their
space-ships, from their labs on distant planets on distant galaxies,
back to the main lab on Planet Earth.

[Joy Christian]

Conspiracy is in the eye of the beholder!

Here is the most accurate simulation of my 3-sphere model for the EPR-Bohm correlation: http://rpubs.com/jjc/13965

As you can see from scrolling down, wth sample size 10^7 the resulting plots are spectacular---especially the last one.

The initial function, as defined in eq. (7) of this document, is now



And the set of complete states, defined by eq. (11), with the above initial function, speaks for itself.

What may appear as a conspiracy from the flat-land, or R^3 perspective, is a sublime beauty of Nature from the sphere-land, or S^3 perspective.

[FrediFizzx]

Richard,

It doesn't really matter. Even though perhaps the simulations aren't 100 percent perfect, they still beat Bell and illustrate that he did in fact make a mistake as far as applying his model to the physics of EPR-Bohm scenarios. But Joy's model as best illustrated by geometric algebra goes beyond that and explains the origins of quantum correlations. A profound discovery.

What we should get back to is for you to ask more questions about what you don't have a full understanding of with Joy's math. Which you freely admit that there is some that you don't understand.

[Ben6993]

Richard wrote:

I believe that Christian's model cannot be reproduced in flatland. It would
need a kind of Möbius strip in space-time which alters the measurement
outcomes (the measurement outcomes which Alice and Bob
saw and collected in their respective labs) as they bring them back in their
space-ships, from their labs on distant planets on distant galaxies,
back to the main lab on Planet Earth.

Should not detectors settings, and all the simulation output charts, reflect a Moibus strip nature by ranging from 0 to 4π rather than from 0 to 2π?
Susskind's online autumn 2012 lecture 2 on Supersymmetry & Grand Unification describes an electron returning to its original state after a rotation of 4π. He says that if a prepared beam of electrons is split into two beams and one beam is grabbed by a magnetic field and that field is rotated by 2π, then when the two beams are recombined the interference pattern is different from what would have occurred had there been no magnetic field rotation. So the full range of magnetic field rotation, experienced by an electron, is 0 to 4π in the laboratory.

[Joy Christian]

Richard wrote:

I believe that Christian's model cannot be reproduced in flatland. It would
need a kind of Möbius strip in space-time which alters the measurement
outcomes (the measurement outcomes which Alice and Bob
saw and collected in their respective labs) as they bring them back in their
space-ships, from their labs on distant planets on distant galaxies,
back to the main lab on Planet Earth.

Should not detectors settings, and all the simulation output charts, reflect a Moibus strip nature by ranging from 0 to 4π rather than from 0 to 2π?
Susskind's online autumn 2012 lecture 2 on Supersymmetry & Grand Unification describes an electron returning to its original state after a rotation of 4π. He says that if a prepared beam of electrons is split into two beams and one beam is grabbed by a magnetic field and that field is rotated by 2π, then when the two beams are recombined the interference pattern is different from what would have occurred had there been no magnetic field rotation. So the full range of magnetic field rotation, experienced by an electron, is 0 to 4π in the laboratory.

The point you make, Ben, is indeed at the heart of what is going on. This is described in considerable detail in this paper: http://arxiv.org/abs/1211.0784. There is
no need for Alice and Bob to go to distant planets on distant galaxies and bring their measurement outcomes back to earth. The geometry of S^3 can be described by intrinsic torsion in Riemannian geometry, a very local concept. The torsion, , is a tensor field, defined at every point of the manifold S^3, which is one of the possible solutions of Einstein's field equations of general relativity, which in turn is a local field theory par excellence. So there is nothing "conspiratorial" about S^3.

[Ben6993]

Hi Joy,

Thank you for the reference to your paper. I note that it refers to a paper [6] by Y. Aharonov and L. Susskind, Phys. Rev. 158, 1237 (1967). This must be the work that Susskind referred to in his
lecture. He said that he had done the experiment himself in 1967 so that fits. That is evidence of a microscopic 4π cycle of rotation for the electron whereas your paper is aiming for a demonstration of a 4π macroscopic effect.

Reading your paper will be a good chore for me as it looks very difficult. (But not as difficult as your S7 quantum correlations paper which is too hard to go on my todo list.) Figure 4 looks familiar! Will the derivation of Figure 4 provide a different perspective on the sawtooth v -cosine curve? I note you write (approximately) that the two curves are equivalent geodesics under different topologies.

I would like to have a commonsense way of knowing that if a 2π rotation represents only half a cycle for an electron, then that is incompatible with R3. I note that you and Fred claim that that effect implies S3 holds, but does anybody claim it can hold in R3? This may be relevant to my view that the simulations cannot provide a winner between flatlanders and 3spherers.

My own view uses the analogy of two coins placed next to one another on a table. One heads up, the other tails up. The heads coin is rotated once around the tails coin without slipping at the contact point. The tails coin is motionless throughout. I think that the initial contact point for the heads coin describes a cardiod curve. And the head design rotates by 4π. The tails coin to me represents another dimension available to the electron and interfering with its motion. And it is a dimension available at every point in space. So that fits in better with S3, I presume. But not R3?

I am not sure that the 4π rotation will work macroscopically. In a macroscopic rotation, by analogy the tails coin might rotate too, whereas the 4π effect required a stationary tails coin in the cardiod analogy. But that is only an analogy and I haven't read your paper yet, and the macroscopic experiment has not been done yet.

[Joy Christian]

Richard Gill's misinterpretation of my model in his post above can be easily corrected by going through the derivation presented in this one-page document.

For the sake of argument, let us not worry about the small correction to the function we had been concerned about during the past few weeks.
The question then is: Does eq. (10) in the above derivation hold for all vectors or not? If it does, then I am right. If it does not, then Richard Gill is right.

So let us think about this step by step. Note that I begin with the definition of S^3, which is the model for the physical space I have been working with. Next, in eqs. (3) and (4) I have defined two quaternions, as functions of the same vector . Then the derivation of eq.(10) is quite straightforward, for the choice of the function I have made just above the box of eq. (10). As I mentioned, this choice is immaterial for the present concerns. So, does, then, eq. (10) hold for all vectors or not? But of course it does. To see this, let us consider a vector in eqs. (3) and (4) instead of the vector , and follow through the steps all the way up to eq. (10). So now we have derived eq. (10) again, but with vector instead of vector . This means that eq. (10) is valid for at least two vectors, say and . But what stops us from considering a yet another vector, say , and re-deriving eq. (10) in terms of this vector ? Well, you got the picture. We can derive eq. (10) for all vectors belonging to the tangent space , as indicated in the definition (11) of the set of complete states. Thus Richard Gill's concerns in his post are entirely unfounded.

[Joy Christian]

Dear Joy,

Regarding this complete.pdf document, would you please accept a minor change and say that ?

Can you write down a single pair such that for every ?

Just a single pair, please. I just need the three coordinates of and the value of .

I'm sorry to ask you this pedagogic example, but this will help me a lot to understand your model.

Thank you very much.

Zen.

Hi Zen,

I cannot accommodate your first request. The simply-connected topology of S^3 does not allow me to exclude points from S^3 at will.

For example, if we remove just one point from S^3, then it reduces to R^3. Conversely, S^3 is a one-point compactification of R^3. .

Now, with , for a single pair consider . It is clear that for every .

I hope this is helpful.

[Joy Christian]

Thank you very much, Joy.

Can you give one example of a pair with ?

Sure. Consider the pair with a nonzero and . Then will hold for all , provided you let the vectors and respect the product . Choose, for example, and check this out.

[Joy Christian]

Joy: thank you for your prompt answer.

Is it true that ?

I know what is bothering you. Your concerns are justified. We can certainly ask whether an individual vector such as is in or not. It surely is, because, after all, locally each is simply . It must be remembered, however, that, globally, is parallelized. What this means, among other things, is that each tangent space on can be coordinated only by an anholonomic basis satisfying a geometric product like . This in turn means that all vectors like , , and are subject to geometrical constraints like . It is therefore misleading to follow your line of questioning and wonder whether a specific vector is in a given or not. The correct way to understand the full geometry of is by following the derivation I have sketched in this post: viewtopic.php?f=6&t=28#p726. It is clear from this post and the one-page document it refers to that the inequality appearing in the set is a geometrical constraint arising from the parallelization of . In other words, what the EPR-Bohm correlation, and the quantum correlation in general, are telling us is that we live in a parallelized , not in a flat . This is not a particularly revolutionary or new hypothesis, apart from the fact that is far more counterintuitive than .

[Joy Christian]

Hi Joy,

Thank you for the reference to your paper. I note that it refers to a paper [6] by Y. Aharonov and L. Susskind, Phys. Rev. 158, 1237 (1967). This must be the work that Susskind referred to in his lecture. He said that he had done the experiment himself in 1967 so that fits. That is evidence of a microscopic 4π cycle of rotation for the electron whereas your paper is aiming for a demonstration of a 4π macroscopic effect.

Sorry for the delay in my reply, Ben.

Yes, that is the work Susskind refers to. The initial experiment has been repeated by now, independently, by several groups.

Reading your paper will be a good chore for me as it looks very difficult. (But not as difficult as your S7 quantum correlations paper which is too hard to go on my todo list.) Figure 4 looks familiar! Will the derivation of Figure 4 provide a different perspective on the sawtooth v -cosine curve? I note you write (approximately) that the two curves are equivalent geodesics under different topologies.

That is correct. The sawtooth geodesic corresponds, roughly, to the topology of the group SO(3), whereas the cosine geodesic corresponds to the simply-connected topology of the "spin" group SU(2). So, indeed, contrary to the non-locality/non-reality interpretation of the cosine curve popularized by Bell, I am saying that the difference is entirely due to the difference between the topologies of the groups SO(3) and SU(2), with the latter being homeomorphic to the parallelized 3-sphere.

I would like to have a commonsense way of knowing that if a 2π rotation represents only half a cycle for an electron, then that is incompatible with R3. I note that you and Fred claim that that effect implies S3 holds, but does anybody claim it can hold in R3? This may be relevant to my view that the simulations cannot provide a winner between flatlanders and 3spherers.

You can find demonstrations of Dirac's belt trick on the internet. That may help you understand the phenomenon in an intuitive way. But ultimately there is no escape from mathematics. So there is a good reason why my paper is so mathematical. The 4pi periodicity of rotation inevitably leads one to SU(2), which, as I mentioned, is topologically equivalent to S^3.

My own view uses the analogy of two coins placed next to one another on a table. One heads up, the other tails up. The heads coin is rotated once around the tails coin without slipping at the contact point. The tails coin is motionless throughout. I think that the initial contact point for the heads coin describes a cardiod curve. And the head design rotates by 4π. The tails coin to me represents another dimension available to the electron and interfering with its motion. And it is a dimension available at every point in space. So that fits in better with S3, I presume. But not R3?

Yes, that is a good way to think about it. You may find the discussion in the reference [3] of my paper useful in this regard [R. W. Hartung, Am. J. Phys. 47, 900 (1979)]. You may be able to see why the 4pi periodicity does not fit well with R^3 [or more correctly, with the rotation group SO(3) of R^3].

I am not sure that the 4π rotation will work macroscopically. In a macroscopic rotation, by analogy the tails coin might rotate too, whereas the 4π effect required a stationary tails coin in the cardiod analogy. But that is only an analogy and I haven't read your paper yet, and the macroscopic experiment has not been done yet.

You are not the only one who is sceptical about my proposed experiment. That is one reason why I am having so much difficultly raising financial support for it.

[gill1109]

I too am sceptical about the proposed experiment, always have been; that is exactly why I am prepared to bet heavily on its failure. If Joy wins, he will get the Nobel prize. If I win, maybe "we" will all get the igNobel prize together.

[Joy Christian]

I too am sceptical about the proposed experiment, always have been; that is exactly why I am prepared to bet heavily on its failure. If Joy wins, he will get the Nobel prize. If I win, maybe "we" will all get the igNobel prize together.

Last summer Lucien Hardy told me that he would be "astounded" if my proposed experiment confirmed my expectation and produced the cosine correlation.

[Heinera]

I too am sceptical about the proposed experiment, always have been; that is exactly why I am prepared to bet heavily on its failure. If Joy wins, he will get the Nobel prize. If I win, maybe "we" will all get the igNobel prize together.

Hehe But one does not necessarily exlude the other. Remember Nobel laureate Andre Geim and the levitating frog?
I actually found the levitation experiment very fascinating, so I guess he got the igNobel only because there was a frog involved.

[Ben6993]

You can find demonstrations of Dirac's belt trick on the internet

Hi Joy: yes, I saw that a year or more ago following a reference by you or Fred on one or other thread. I also saw the 'waiter rotating a tray on one hand' with a similar effect. They are good to help visualisation for the microscopic (although I prefer the rotating coin analogy), but all of these have a macroscopic anchor point (e.g. the waiter's shoulder socket). So they only work macroscopically if you can have a macroscopic anchor point. If all the anchor points are microscopic, the question is, as far as I can see, whether all the microscopic anchor points in a macroscopic body can work together to sum to a single macroscopic anchor point. I am not sure about that, but it would be good to do the experiment.

If the effect was not found macroscopically in the experiment, I do not understand why I could not still believe in the microscopic effect. Cannot space be S3 for electrons and R3 for metal ingots?

Thank you for the references.

[Joy Christian]

If the effect was not found macroscopically in the experiment, I do not understand why I could not still believe in the microscopic effect. Cannot space be S3 for electrons and R3 for metal ingots?

You can certainly believe in the microscopic effect even if it isn't found in the macroscopic domain as I expect it to be found in my proposed experiment. Space can certainly respect S^3 symmetries at the microscopic level and R^3 symmetries at the macroscopic level. That is indeed what is usually believed by most physicists. It is usually believed that 4pi periodicity is respected only by microscopic systems like electrons. But that belief divides up the world into two disjoint worlds and leads to all sorts of interpretational problems of quantum theory. Following Einstein, I want to describe our single world using a single theory, without artificial boundary between the microscopic and the macroscopic. My inspiration comes from both Einstein as well as Bell---e.g., see the quote from Bell on the homepage of my blog.

[gill1109]

Following Einstein, I want to describe our single world using a single theory, without artificial boundary between the microscopic and the macroscopic. My inspiration comes from both Einstein as well as Bell---e.g., see the quote from Bell on the homepage of my blog.

So do I! And I believe it is already there. Belavkin's "event enhanced quantum mechanics", which is equivalent to the Girardi-Rimini-Weber and Pearle Continuous Spontaneous Localization models (since 2010 available in an elegant relatistically invariant version) does the job. The interpretational problems of QM are abolished. Time to get to work and do physics within, at last, an adequate framework.

[Joy Christian]

Following Einstein, I want to describe our single world using a single theory, without artificial boundary between the microscopic and the macroscopic. My inspiration comes from both Einstein as well as Bell---e.g., see the quote from Bell on the homepage of my blog.

So do I! And I believe it is already there. Belavkin's "event enhanced quantum mechanics", which is equivalent to the Girardi-Rimini-Weber and Pearle Continuous Spontaneous Localization models (since 2010 available in an elegant relatistically invariant version) does the job. The interpretational problems of QM are abolished. Time to get to work and do physics within, at last, an adequate framework.

I have no time for Belavkin's "event enhanced quantum mechanics", or for ad hoc models like Girardi-Rimini-Weber and Pearle Continuous Spontaneous Localization models. The interpretational problems of QM are abolished within my local-realistic framework by recognizing Bell's colossal error, as described in detail in my book:



Within my framework ALL quantum correlations are explained purely local-realistically. Time to get to work and do physics within, at last, the correct framework.

[gill1109]

I have no time for Belavkin's "event enhanced quantum mechanics", or for ad hoc models like Girardi-Rimini-Weber and Pearle Continuous Spontaneous Localization models.

The GRW / Pearle / CSL models are no longer ad hoc when viewed from the perspective of eventum mechanics. They can be derived from eventum mechanics. It is just a question of deciding what is the Hilbert space, what is the Schrödinger equation, what are the beables. Just like ordinary QM, event enhanced QM supplies a framework within which one can do physics.

The guy who has made these models relativistically invariant is D. J. Bedingham (Blackett Laboratory, Imperial College_.