Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

Thomas Ray

"You did not give *me* the free choice to tell them in advance any particular sequences of numbers ..."

Thanks for finally pointing out the flaw in this argument, directly.

By the same token, you did not give nature (i.e., the structure of the measure space) a choice to encode information in advance, covariant to the measurement function, which is what the Mobius-like topological torsion does.

Robert McEachern

Nick said:

"Are (a wild guess here) you maintaining that the set algebra derivation of Bell is invalid and Bell tests on classical objects are meaningless because there's a tautology of some sort involved? I'd really like to see that argument. "

I just gave you the argument. What don't you understand about it?

The only argument for accepting that "subtle" premise, that provides the only significance to the theorem, seems to be:

I did not prove it. I did not test it. I did not bother to think of any alternatives. Therefore, it must be true. QED.

Rob mcEachern

Nick Mann

"Try interpreting Bell-Aspect results without nonlocality."

I'm following Chris Timpson here (it's epistemological metaphysics):

"The simulation fallacy is also evident in the common claim that Bell's theorem shows us that quantum mechanics is nonlocal, or the claim that the experimental violation of Bell inequalities means that the world must be nonlocal. Of course, what is in fact shown by these well-known results is that no local hidden variable model can simulate the predictions of quantum mechanics, nor provide a model for the experimentally observed correlations. But these facts about the simulation don't lead directly to facts about the simulated: the fact that any adequate hidden variable model must be nonlocal does not show that quantum mechanics is nonlocal (this, of course, is an interpretation dependent property), nor show the world to be nonlocal."

Or as old Alfred Korzybski used to say: The map is not the territory. (If he hadn't been such a shameless huckster he'd be more highly regarded today than is the case.)

"Am not familiar with that protocol."

Am not surprised. Is yer loss.

Richard Gill

Spot on, Nick. "what is in fact shown by these well-known results is that no local hidden variable model can simulate the predictions of quantum mechanics, nor provide a model for the experimentally observed correlations. But these facts about the simulation don't lead directly to facts about the simulated: the fact that any adequate hidden variable model must be nonlocal does not show that quantum mechanics is nonlocal (this, of course, is an interpretation dependent property), nor show the world to be nonlocal."

In order to say if the world is local or nonlocal we have to decide what the word "local" actually means. I think it only has meaning within a mathematical model. In other words, it is mathematical models of reality which can be characterized as "local" or "non-local".

Next, how do we do that characterisation? We have to decide what objects in the model are supposed to be "real" in the sense of being physically located in space-time. For instance, whether or not you think that QM is a local theory depends on whether or not you think the wave function is "real" in that sense.

Mathematically, Bell's theorem tells us that the predictions of QM cannot be reproduced by models which have the three properties of locality, realism, and freedom (no-conspiracy). These three properties have got technical definitions and they only have meaning relative to mathematical models of reality. They are properties of such models.

We talk in words. We think we talk about reality but the best that we can say is that we talk about models of reality. Ways to think about reality. We want ways to think about reality which are good as basis for predictions of reality. So whether or not not QM predictions can be reproduced by local realist theories without recourse to conspiracy, is a mathematical question. Whether or not nature exhibits those predictions in another matter. So far no one has performed a loophole free experiment. It may happen in the next five years.

Richard Gill

At the heart of Bell's arguments is a mathematical theorem. Bell was a physicist, not a mathematician, so he was not in the job of proving theorems. Mathematical theorems are tautologies. Here is a mathematical theorem:

Given an $N\times 4$ spreadsheet of numbers $\pm1$ with

columns $A$, $A'$, $B$ and $B'$, suppose that, completely at random, just

one of $A$ and $A'$ is observed and just one of $B$ and $B'$ are observed

in every row. Then, for any $\eta \ge 0$,

$$\Pr(\langle AB \rangle_\text{obs}\langle AB'

\rangle_\text{obs}\langle A'B \rangle_\text{obs}-\langle A'B'

\rangle_\text{obs}~\le~ 2 \eta) \ge 1- 8 e^{- N ( \frac \eta {16})^2 }.$$

Here, $\langle AB \rangle_\text{obs}$ is defined as the average of the product A times B over those rows of the spreadsheet in which A and B are observed, etc.

You can find theorem and proof in my paper at http://arxiv.org/abs/1207.5103

You will also find applications of the theorem to the analysis of LHV computer simulation models in the same paper (section 9).

You can find an illustration of the theorem by some computer simulation experiments at

http://rpubs.com/gill1109/Fred3

I call this my "spreadsheet theorem". You can also call it the spreadsheet tautology, if you like.

Richard Gill

Everything is illuminated by your last remark, Tom. You already said that you agreed with Bell's theorem. It does not bother you because you adhere to super-determinism, or conspiracy, or no-free-choice.

pjackson

Richard,

You misread the protocol. The 'number' is the angle. Please choose a random sequence of settings for A and B (from; 0,30,60,90,120,150,180 for simplicity)and I'll run the experiment. I can do the commentary right here so you can reproduce it.

Give me a list of say 20. If you wish you play Bob and I'll play Alice. I'll offer this random selection for Alice, but shuffle the order or pick your own if you wish.

0,150,180,90,60,30,120,90,180,60,180,0,30,120,150,60,180,120,30,60.

What the experiment models is 'singlet' particle states but testing the present 'optical science' paradigm of spin as opposed to that assumed 90 years ago for QM, and reproducing the results of all QM experiments to date (and also those of optical science). The 'spectral colours' represent a 'hidden' but also directly RELATED 2nd order distribution WITHIN each part of the binary Red/Green distribution. i.e; "singlet state" is an 'incomplete description' of nature, so must inevitably fail to faithfully model it.

Let's say for instance we consider our planet, and the relative speed of rotation measured from the (barycentric frame) near the equator and near the poles. Two planets spin 'directions' will certainly be binary, but if say 'tilt angle' changes, then so may the discrete VALUES of 'spin', (so end up similar at the poles).

This does NOT falsify of even TRY to falsify Bell's algorithm, but it uses a different fundamental assumption which may identify what 'entanglement' really 'IS'. The model may be said to finally clarify exactly 'what' we are measuring.

Best wishes.

Peter

If anybody else fancies offering lists of settings please by all means do.

Thomas Ray

Super determinism: maybe

Conspiracy: definitely not

No free choice: that's your view, not mine. For if the choice function exists, when you invest it all in detector settings, you assume no free space, because the settings become the boundary conditions for all events including those not observed. In a complete theory of measurement functions, there are no boundary conditions.

Thomas Ray

Nick, if you had been reading, you would know that this pertains to the open question I have repeatedly posed:

Is the simulation of a continuous function a continuous function?

I conjecture, not. It has nothing to do with a simplistic distinction between the map and the territory, however -- for if the territory is continuous, the map is a faithful guide to its structure, as topology informs us.

"'Am not familiar with that protocol.'"

"Am not surprised. Is yer loss."

Someday you must share with us what it's like to be all knowing.

Thomas Ray

As usual, Richard is cherry-picking the facts he only wishes were coherent with his world view and weaves them into a tendentious argument.

What he neglects is that a mathematical theorem is a tautology because it is a true mathematical statement. It gets to be called true, for the reason of its logical consistency with a particular set of axioms.

My many bosses may sympathize with his wish that the world we live in is a flat spreadsheet with neat boxes changing values according to the rules of linear arithmetic.

Demonstrably, however, our world does not obey a set of axioms that would make this conclusion true.

That Richard identifies his mathematics with physical reality contradicts his claim of independence of the model from the physics. But that's the problem with tendentious thinking -- always a contradiction.

Thomas Ray

" ... it is mathematical models of reality which can be characterized as 'local' or 'non-local'."

Really?

Once again, Richard argues contradictory points with a trick called talking out both sides of one's mouth.

If there were a real boundary between local and global values, there would be no way to derive real valued continuous functions from real valued variables. That is, because all real valued functions of a real valued variable are continuous, all real functions are local.

And, uh -- Richard -- that's a mathematical tautology.

If your conjecture is true, Bell's theorem is an entirely nonlocal model having nothing to do with the physics of the real world.

You've just validated Joy's argument. Congratulations.

Thomas Ray

To reinforce my point about the independence of mathematics from physical experience, I am copying my post from Zeeya Merali's article on Anthony Aguirre here:

I find Aguirre's closing statement profound:

"The mode of theoretical physics has tended toward elevating certain descriptions as more 'true' and 'fundamental', and the other descriptions as 'in principle derivable' from these. I think it is worth contemplating a different approach: that just as the Experienced Reality description is far more useful than the 'Unitary Block' in some applications (and far less in others), that we take Experienced Reality as an equally true description that is complementary to, but not derivative of, the Unitary Block. Perhaps the nature of time is telling us something about the nature of truth."

Unitarity depends on experience, and always has. In Einstein's words, "The most incomprehensible thing about the world is that it is comprehensible." It is only comprehensible in experience, and we don't experience the infinite transition between one event and another, because the brain-mind processes information discretely. That fact compels me to answer at least one of Aguirre's excellent questions (no. 1) this way:

The speed of light constant as relates to experience, is independent of its empirical value. Rigid transformations in spacetime depend on a constant nonzero metric. That the metric is always length 1 locally, is why we normalize the speed of light in quantum mechanical calculations and call events not measured, "nonlocal." Time drops out of the equation. In Einstein's world, though, all physics is local, and the global value of c is also length 1; there are no actual, physical, rigid transformations in continuous spacetime. Therefore with no boundary between local and global events, whatever value the speed of light is measured to be, does not affect our unitary experience.

Tom

John Cox

Tom,

Topology is used for computer graphics because the compact algebra is so much faster than other maths and does not need to generate N^2 points of reference to animate a continuous change of shape. That pretty much consigns N^2 to the category of unmeasured states. Are we then to assume that in that unmeasured state in general that both Alice and Bob are in their primes? They are getting pretty old. And the only measurable probable state that matters in finding funding is practical application. jrc

Thomas Ray

I'm not looking for funding, John R. I consider myself fortunate in being compelled to do something I would do whether I am paid for it or not, and to delight in it for its own sake.

I think that was part of Grisha Perelman's unspoken message.

Nick Mann

Richard,

"So far no one has performed a loophole free experiment. It may happen in the next five years."

You say something similar in "Statistics, Causality and Bell's Theorem". I won't ask which group you think has the best chance to bring it in first.

Tom,

Harrison's 1981 paper in AmJPhys:

http://www.phy.bme.hu/~palotas/Harrison-Bell-Inequalities.pdf

Harrison discusses macroscopic Bell experimentation (and, mutatis mutandis, it works with any set of separable physical objects no matter how variegated):

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html

A paper that discusses several Bell derivations including the set theory one (page 13 plus):

http://arxiv.org/abs/quant-ph/0512050

Richard Gill

Dear Tom

I don't have much insight into who is most likely to do it first. Last year, both the Zeilinger group (Vienna) and the Boulder (Colarado) - Geneva consortium claimed to be the first to do the first detection loophole free experiment on polarization of photons. The other loopholes having been closed, in photon polarization experiments, earlier. So I would certainly put my money right now on the polarization of the photon, as being the physical system with which the first definitive experimental proof of non-classical consequences of entanglement will be supplied.

Gregor Weihs (Innsbruch) and Marek Zukowski (Gdansk) have a lot of insider knowledge and might be able to tell you more. They can both name several groups, alongside those the just mentioned, which are clearly also "in the race". But I'm not going to quote from private correspondence with them here.

Richard

John Cox

Tom,

I think you are fortunate in that, friend. Most people's compulsions are not so benign. jrc

Thomas Ray

Dear Richard,

If one thinks a detection loophole is the issue, I've no doubt that one can close it, and here's why:

Once Bell's inequality is shown to be violated, any variety of experiments to prove it are all of a class of Bell-Aspect demonstrations. There is no class of experiments that show Bell's inequality to hold.

There can't be, because the arithmetic theorem is true, and despite all the mystery attached to it by believers, it's really quite simple. One has to remember why we use inequalities to formulate statements we mean to generalize to n numbers. As put so nicely in Gowers' Princeton Companion ...' "Let x and y be two nonnegative real numbers. Then ( \/x - \/y)^2 = x y - 2 \/xy is a nonnegative real number, from which it follows that 1/2 (x y) >= \/xy. That is, the arithmetic mean of x and y is at least as big as the geometric mean.""

As I said, length 1 globally corresponds to every length 1 measure locally. Therefore:

If physically demonstrated that the probability that Bell's inequality is not violated is zero -- the probability that the demonstration is false is unity. Why am I confident?

Because all real functions of a real vaued variable are continuous.

All best,

Tom

Thomas Ray

I take i t back, Nick. I had read the U Toronto article some time ago (I remembered the "heights distribution" example)).

It is a nice survey of results. It does not answer the problems posed here.

Thomas Ray

That's kind of you, John R. The work of Godfrey Hardy is a good example, however, that one never knows whether something pursued for purely esthetic reasons will turn out to be 'useful.' I like to think that someday everything useful will be motivated by what is esthetically pleasing. :-)

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