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

Thomas Ray

"Bellarmine had shown himself a better scientist than Galileo by disallowing the possibility of a 'strict proof of the earth's motion,'"

Which is true, though not useful. By the same criterion, one cannot experimentally verify Kepler's first law (elliptic planetary orbits) because " ... because any finite-precision measurement of the orbit is consistent with an infinite number of mathematical curves. In practice, what we can deduce from Kepler's law is that measurement of the orbit will, to a good approximation, be consistent with the predicted ellipse." (Leslie Lamport, "Buridan's Principle," Found. Phys. April 2012.)

Joy has also independently given this example of Kepler's law and continuous functions.

This is my own interpretation of how classical uncertainty obtains, independent of scale.

Thomas Ray

"Joy has made this statement (cite available upon demand ... it was in Scott Aaronson's blog): "So far there has been absolutely no evidence for the validity of Bell's Theorem in any purely classical, macroscopic domain." I haven't been able to get him, Fred or Tom to elaborate on or defend that curious assertion."

No one has dodged that issue, Nick -- it's simply a true statement. Bell's experimental protocols are the same as EPR's, purely classical. Joy's argument is that the choice of domain makes a difference in the measured result.

The real question being dodged by Richard, you and all Bell loyalists is the one I have asked: "What is your measure space, and how do you know it?" That's a reasomnable and objective question.

Richard Gill

Of course the choice of domain makes a difference. Multiply Alice's outcomes by square root of 2 and suddenly, hi presto, it is easy to come up with local hidden variables models with CHSH = the Tsirelson bound 2 sqrt 2. Luigi Accardi tried 20 or more years ago to sell a suite of computer programs which allegedly proved Bell wrong by using this trick. More recently, Bryan Sanctuary has unwittingly used it: many people have noticed that it is easy to get correlations 1/2 cos^2( difference between setting angles) with local hidden variables. He rediscovered such a model and now calls on all the experimenalists to divide all their correlations by 2 in order to prove that his model is correct.

There are very good reasons why the whole Bell story centers around binary outcomes. How you choose to code them doesn't matter a damn. Just call them "+" and "-" and count the different observed patterns ++, +-, -+, --.

So the domain matters if you insist on defining correlation = product of outcomes, while it doesn't matter if you define correlation = (N(++)+N(--)) / (N(++)+N(+-)+N(-+)+N(--)). If you read Bell carefully you will find out which choice is the meaningful one.

This is the reason why Joy's original model with outcomes +/-1 embedded in the space of quaternions is totally misguided. Moreover, Joy still needed to redefine correlation, and he still needed a sleight of hand switching of a sign by confusion between locally and globally defined variables, in order to get the result he was after. This is the reason why Tom's repeated chit-chat about continuity and domain is just noise, which is enveloping the discussion in a smoke-screen of irrelevant and in appropriate verbiage.

The newer versions of his model, I call it "Christian 2.0" have a different approach but again are shipwrecked on a confusion between local and globally defined variables. In other words, notational ambiguity which allows one to surreptitiously switch meanings in the course of some tricky computation where no one without any mathematical discipline notices what is going on.

Richard Gill

Sorry, misprint:

while it [the domain] doesn't matter if you define correlation =

(N(++) + N(--) - N(+-) - N(--)) / (N(++) + N(+-) + N(-+) + N(--))

One could more succinctly write ( N(==) - N(!=) ) / N(==) + N(!=)

Since N(==) + N(!=) = n fixed = number of runs, we see that we are just talking about probabilities (relative frequencies) N(==)/n, and N(!=)/n

Of course this is all for experiments with binary outcome. There exist generalized Bell inequalities for the case of outcomes taking a larger number of different values.

Thomas Ray

"There are very good reasons why the whole Bell story centers around binary outcomes. How you choose to code them doesn't matter a damn. Just call them "+" and "-" and count the different observed patterns ++, +-, -+, --."

Right. How they are encoded in the space of measurement functions, however, makes the difference between a complete measure space of paralleized S^3 and the incomplete space R^3.

R^3 cannot encode the complete reversible function.

Just as Richard's bluster and snide put-downs cannot cover up his error.

Richard Gill

Tom said: "The real question being dodged by Richard, you and all Bell loyalists is the one I have asked: "What is your measure space, and how do you know it?" That's a reasomnable and objective question."

It is an unreasonable question. We are just looking at relative frequencies of discrete outcomes. It does not matter a damn that there is some kind of continuous physics underlying what we see. Finally we just count clicks in four photodectectors. Preferably with event ready detectors so that time is essentially discrete, and at each time step, there is one click in just one of Alice's two detectors, and one click in just one of Bob's two detectors.

A small amount of experimental noise (however fundamental you might think its origin would be) doesn't spoil things. If there is a large amount of missing events or multiple events then the experiment is not "fit for purpose", or at least, the data-analysis has to take account somehow or other of the deviation from an ideal set-up. There are many tools around for doing this properly. Only last year did we see the first "detection loophole free" experiments on polarization of photons. Earlier, the locality loophole was closed for polarization of photons, and the conspiracy loophhole too. We just await the experiment in which all three loopholes are closed simultaneously. I am told it is about five years ahead of us. The top groups are racing to be the one to get the prize.

Richard Gill

Sorry for the snide comments. Everyone can decide for themselves what is bluster.

Richard Gill

Tom said "Richard said 'There are very good reasons why the whole Bell story centers around binary outcomes. How you choose to code them doesn't matter a damn. Just call them "+" and "-" and count the different observed patterns ++, +-, -+, --.' Right. How they are encoded in the space of measurement functions, however, makes the difference between a complete measure space of paralleized S^3 and the incomplete space R^3."

A good example of meaningless bluster: "How they are encoded in the space of measurement functions, however, makes the difference between a complete measure space of paralleized S^3 and the incomplete space R^3"

Joy Christian

Complete and detailed local-realistic derivation of ALL quantum correlations can be found in several chapters of my book:

Joy Christian

as well as on my blog: http://libertesphilosophica.info/blog/.

Richard Gill

Peter, you gave them the free choice to pick a random card from a pack of cards and each get to see a number and a colour. You did not give *me the free choice to tell them in advance any particular sequences of numbers to use for the first run, second run, etc.

You free choice was not a free choice. You obliged Alice and Bob to determine the settings of their detectors in one particular way, as part of the outcome of one single "measurement without a setting".

Your model and your experiment are irrelevant. The fact that you think it has solved all the enigmatic problems of entanglement, shows that you do not appreciate what those problems are.

Thomas Ray

"A good example of meaningless bluster: 'How they are encoded in the space of measurement functions, however, makes the difference between a complete measure space of paralleized S^3 and the incomplete space R^3'"

If it were meaningless, Richard, you would be able to explain either:

a. That no complete measurement space physically exists., and be able to prove it; or

b. That your measure space is complete, with boundary between classical and quantum events, and be able to show exactly where that boundary is.

How you find this to be "bluster," I have no clue.

Nick Mann

Bellarmino was also the inquisitor who condemned Bruno to immolation at the stake. (This was at least a decade before the Galileo affair began.) Apparently he came to feel really bad about that but it was kind of too late. It may have helped preserve G. though.

His refusal to look through Galileo's telescope is of course what brands him in the minds of people today. Paul Feyerabend tried to excuse it by stating that the cardinal knew nothing about optics, was aware he knew nothing, had no particular reason to trust Galileo's explanation and didn't want to view something which might well be erroneous. Problem with that, however, is that the Jesuits already had an observatory in the Vatican and Bellarmino was the highest-ranking Jesuit in the Church and also had scientific training as well as access to all of the resources he'd have needed, as an extremely bright guy, to learn as much as Galileo knew. In other words it's just possible he was being disingenuous. Unlike any posters here.

Thomas Ray

"We are just looking at relative frequencies of discrete outcomes."

You are not, however, looking at how relative outcomes effect a continuous function.

Thomas Ray

" ... Joy still needed to redefine correlation, and he still needed a sleight of hand switching of a sign by confusion between locally and globally defined variables, in order to get the result he was after."

Actually, it is you Bell loyalists who rig the measure space to get your desired results. There's no sleight of hand in Joy's result -- both hands are pairwise correlated, always as a local result of a globally continuous function.

Thomas Ray

"His refusal to look through Galileo's telescope is of course what brands him in the minds of people today."

Nick, I don't have any esteem for religious leaders past or present; I am more of a mind (metaphorically) that the world will be safe "when the last king is strangled with the entrails of the last priest," as Diderot put it.

You are way off the mark on how science is done, however, to imply that induction -- making conclusions from empirical evidence -- is the primary means of investigation. Einstein didn't have to go on the eclipse expedition to know that his theory is correct.

Thomas Ray

"So the domain matters if you insist on defining correlation = product of outcomes, while it doesn't matter if you define correlation = (N(++)+N(--)) / (N(++)+N(+-)+N(-+)+N(--)). If you read Bell carefully you will find out which choice is the meaningful one."

Joy does not define correlation differently from Bell. You can keep sidestepping the issue of topology, though you will run out room to step before the topology runs out of continuous paths to complete the measure (correlated points of the Hopf fibration) as calculated from the initial condition.

Nick Mann

Tom,

"No one has dodged that issue, Nick -- it's simply a true statement. Bell's experimental protocols are the same as EPR's, purely classical. Joy's argument is that the choice of domain makes a difference in the measured result."

Then why has he not said that? Although I can't make sense of it anyway. Bell formulated the (classical) local realism underlying EPR's argument so it could be tested against the (non-classical) predictions of QM in the quantum domain. Maybe you believe this is an invalid test: applying a classical regime in the quantum domain. Well, classical tools are the tools we got. I don't believe the Bell experiments mandatorily mean the entire quantum world is nonlocal (a classical concept) anyway.

Now, the classical domain. Are you disputing the validity of Harrison-like experiments applying Bell to classical objects? Fine ... but why? 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.

Thomas Ray

"Then why has he not said that?"

Nick, what do you think Joy's framework is all about?

Thomas Ray

"I don't believe the Bell experiments mandatorily mean the entire quantum world is nonlocal (a classical concept) anyway."

Try interpreting Bell-Aspect results without nonlocality.

"Now, the classical domain. Are you disputing the validity of Harrison-like experiments applying Bell to classical objects? Fine ... but why?"

Am not familiar with that protocol.

"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."

Huh? You have seen it, if you've ever read a proof of Bell's theorem.

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