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

John Cox

Tom,

You know me too well, yeah, I do have to see the geometric form of the math or it's like a bur stuck in my hair. Oddly though, this time I was sizing things up from the algebraic space.

"And that implies that there are no co-ordinates at all in local reality,..."

Which I think is the logic in Joy Christians approach, that is, supplying those points in a framework that bridges that excluded middle. QM actually lives in 2D but commutes to R^4, but that brings in SR, and SR is not simply connected to GR. So utilizing the elements of topology spans all those dimensionalities to allow 4D to relate to a reference co-ordinate in in any of the elemental dimension sets. It really addresses a very modest scope, that of providing 'a vehicle for assessing one quantum co-ordinate and one classical co-ordinate on the same terms.' and it should also be said 'in the same terms' mathwise. And while that is of modest scope, it delineates a first principal; that of the powers of prediction of physical phenomenon in reality being observable, there ought to be some real relationship between the classical and quantum. Keeping it to that modest scope is as it seems, is a Herculean task. But there again, that does seem to be the hallmark of truly original discoveries.

I am eagerly awaiting the book, I can see aspects of the topological elements, and getting a bit better comprehension of how the math sets the space. Geometrically it doesn't seem to need S^7 just looking at it, but simply the form of math limiting the division algebras to S^7 also encapsulates a mathematical boundary so that a concise measure space is had. Purely and simply utilitarian. So is any devised experiment.

And while it is argued that QM is not complete, neither is the Relativities. That's what we come for, to find what those missing links might be. Cheers, its too nice a day to waste. jrc

Thomas Ray

"Keeping it to that modest scope is as it seems, is a Herculean task. But there again, that does seem to be the hallmark of truly original discoveries."

Nice insight, John R. I share that sentiment -- work that is not overly ambitious requires no handwaving interpretations.

"And while it is argued that QM is not complete, neither is the Relativities."

General relativity isn't complete, and Einstein didn't intend it to be. Both special and general relativity are mathematically complete, however, meaning that the mathematics of both theories make closed logical judgements and predictions independent of physical phenomena.

Enjoy the glorious Spring weather. We're expecting thunderstorms.

[deleted]

I know that Joy, as did the late Fred Astaire, has seven moves for every other poor mortal's six, but I'm truly baffled now. I can't follow his footwork at all!

In the thread header above he appears to be quoting with approval this statement by Fred (following Richard's "I predict that Joy's experiment is going to falsify Joy's theory"):

"Only macroscopically if E(a, b) != -a.b for the macroscopic experiment. The quantum experiments themselves support Joy's theory microscopically."

Is he preparing a fall-back position in case Richard's right? He's already identified himself with AE's declaration -- "Da konnt' mir halt der liebe Gott leid tun. Die Theorie stimmt doch." Eddington didn't say, "Okay, then I won't brother." But that was then and this is now.

Nick Mann

Whatever.

John Cox

Pardon my ignorance,

does 'Only macroscopically if E(a,b)!= -a.b for the macroscopic experiment.'

mean; only if (exclusive, or non-commutative) what E is, as all of a; is then also to (:); what E is as all of b -> is equivalent to the dot product of -a.b (?) And is 'for the macroscopic experiment' meant as a target of the outputs, or as a detector setting for what correlates to what?

fire away! jrc

Joy Christian

John R,

Fred Diether is simply pointing out to Richard Gill that even if the proposed macroscopic experiment is somehow inconclusive, that unlikely eventuality by itself cannot undermine the already proven microscopic success of my local-realistic model: http://rpubs.com/jjc/13965.

In any case, Fred's comment is not the main point of my post. The crucial point is the unequivocal statement by Richard Gill---a diehard Bell-believer---that "So far, the experiments do not discriminate between quantum theory, Joy's theory, and local hidden variables theories."

In other words, so far the Bell mania is nothing but an unscientific belief system.

John Cox

Dr. Christian,

Thank-you for your gracious reply, maybe I'm starting to scratch the surface. Incidentally, having grown up in a small publishing company family, I've been quite impressed with your own, and other's with contractual affiliations with FQXi, self discipline and discretion exercised in limiting your active participation in what is intended as an open forum of debate. And these days, a FQXi 'mini-grant' is appropriately called, I can imagine the number of instances when you might be tearing your hair out wanting to tell numerous respondents, 'No! that's not what it's about!' The Foundation itself seems well ordered, and the moderators do a very credible job given their mandate to guide discussions to topics of fundamental issues, while fulfilling the essential role of 'gate-keeper' lest the line between advice and consent be blurred, as I think is also well kept by those like yourself with publishing obligations. And I have not found any other site so well rounded and functionally open as here at FQXi. Kudos to all. jrc

Thomas Ray

"I know that Joy, as did the late Fred Astaire, has seven moves for every other poor mortal's six, but I'm truly baffled now. I can't follow his footwork at all!"

Nick, when one understands covariance and the lack of boundary between classical statistical mechanics and quantum mechanics, one understands there is no boundary between quantum and classical domains. That is, as Einstein explained long ago in [link:www.relativitycalculator.com/pdfs/einstein_geometry_and_experience_1921.pdf] Geometry and Experience,[/link]" ... if two ideal clocks are going at the same rate at any time and at any place (being then in immediate proximity to each other), they will always go at the same rate, no matter where and when they are again compared with each other at one place. If this law were not valid for natural clocks, the proper frequencies for the separate atoms of the same chemical element would not be in such exact agreement as experience demonstrates. The existence of sharp spectral lines is a convincing experimental proof of the above-mentioned principle of practical geometry. This, in the last analysis, is the reason that enables us to speak meaningfully of a Riemannian metric of the four-dimensional space-time continuum."

Quantum mechanics translates the "clocks" into "entanglement." That is, "immediate proximity" means that they occupy a state of superposition until an experimenter undertakes to read one of them. One finds this observed time correlated only with itself (collapse of the wave function); i.e., the local time of special relativity -- with which quantum mechanics is compatible -- can correspond only to nonlocal time. Quantum mechanics is not compatible with general relativity.

There is no entanglement and superposition in a covariant theory of particle relations. "Immediate proximity" means that all particles were once in the same place -- not in linear superposition -- and correlated for all time locally because instead of collapsing due to an observation that causes the (illusion of) collapse, the wave function is continuous.

The initial condition of a pair of particles in Joy's measurement framework, determines evolution of the metric relation, without entanglement. Because these "clocks" are continuously correlated on the experimenter's chosen axis, as are all other pairs of particles sharing a metric relation on their respective axes, only the added degree of freedom (the topological structure) to measure these states -- accounts for the non-rigid character of spacetime that returns a pair of particles to their original state in a complete cycle of state evolution; a true map of the function to itself represented in the continuous sine wave, rather than an assumed discontinuous "collapse" of the wave to itself.

So your metaphor is apt -- Joy's model does incorporate a step, a degree of freedom, that the 'topologically naive' have missed.

pjackson

Richard,

"the fact that what you say makes no sense to me and vice versa has something to do with some trivial but stubborn misunderstanding or misconceptions."

If you'll focus on specific questions I think we can overcome that.

The matter you accused Judy of 'talking nonsense' about related to the mechanics of weak measurement experiments. Judy is aware how they work and what the output is, but you seemed to work off a false assumption (common it seems) that they somehow 'check on' the spin state prior to 'measurement'. Which they don't.

Weak measurement (WM) has far less data available the (Aspect/Weihs) time resolved measurement, which compared real actual pairs. So can only dump masses of data in certain bins. Now assuming you're right, and you're intelligent, you should see that this cannot be treated in the same way as time resolved data or quantify the same quality (without making unsupported assumptions). What is actually being 'measured' and compared is a 'difference', not any actual spin state.

Then I also see you haven't answered, so possibly not even thought about, the qustion of detector influence. We well know from the 'switch' at 90 degree, as well as other physics, that polarisers/analysers (pre-photomultiplier detectors) DO modulate particle state. You seemed to deny any effect! Can you please review that assumption too as it seems clearly wrong (though again perhaps no uncommon!). If you disagree, please justify your assumption.

Reviewing those 2 and getting them right will then open the door leading to better understanding.

Best wishes

Peter

Richard Gill

Peter said:

(1) "you seemed to work off a false assumption (common it seems) that they somehow 'check on' the spin state prior to 'measurement'. Which they don't."

I don't work off that assumption.

(2) "What is actually being 'measured' and compared is a 'difference', not any actual spin state."

What the experimenter is intending to measure is irrelevant.

(3) "You seemed to deny any effect! Can you please review that assumption too as it seems clearly wrong (though again perhaps no uncommon!). If you disagree, please justify your assumption."

I don't deny any effect.

============================================

I'm interested in loophole free Bell-CHSH type experiments.

These are defined in terms of an experimental protocol. Not in terms of any particular physics.

Here it is:

Alice and Bob are in different classrooms and in each classroom there is a magic black box, called "measuring device A" and "measuring device B" respectively. These two boxes are connected to another magic black box in another classroom, called "source", through some kind of cables, tunnels, or whatever. Anyway: all three black boxes had means to share any information they like. What's inside those boxes and who made them for what purpose is irrelevant. Alice and Bob's boxes each have two buttons, and two lights. The buttons can be pressed, the lights may or may not flash.

Now observe carefully:

Step 1. The connections are severed.

Step 2. Alice presses a button marked "0" or a button marked "90"; Bob presses a button marked "45" or a button marked "135". After Alice and Bob have each pressed a button, a red or a green light flashes on their box. They record their input and their output.

Step 3. The connections between the three magic black boxes are restored.

Steps 1 to 3 are repeated, say, 10 000 times. In between each repetition the two magic black boxes are briefly connected to another magic black box called "source" and then disconnected again.

It then turns out that

Prob(lights flash same colour | 0, 45)

= Prob(lights flash same colour | 90, 45)

= Prob(lights flash same colour | 90, 135)

= 0.15

Prob(lights flash same colour | 0, 135)

= 0.85

Please implement this using your spinning disks or cards or whatever. You can put anything you like in the blackbox and use whatever communication channels you like between the three.

If you think you can do it, please write a suite of computer programs which simulate your experiment, and win the Nobel prize.

Richard Gill

Yes, this is worth repeating:

So far, the experiments do not discriminate between quantum theory, Joy's theory, and local hidden variables theories

Regarding Joy's theory, things might change in a year or two, once we have performed his experiment using colourful exploding balls.

Regarding quantum theory, things might change in five years, if at last someone succeeds in performing an experiment which is both succesful and loophole free.

For a long time the loophole discussion was out of fashion in the physics literature. People scoffed at you if you wanted to raise the subject. However, now that the top experimental groups are racing to be first to do an experiment which does not have one of the well-known major flaws, it has suddenly become fashionable again. Obviously, if you want to get funding to do an experiment, and if you want people to cheer when you do it, you don't go around spreading the word that it is a waste of time.

Obviously if you think that the last experiment which was done was not going to be improved for 50 years, you don't go around telling everyone who important it is to improve the experiment.

The sociology of experimental physics is pretty damned transparent.

pjackson

Richard,

I can and have done so. But not with the assumptions used by QM, inherited by John Bell. You'll know it only takes one flaw in computer input to make outputs meaningless. I show a different starting assumption is possible and fits nature more coherently. It produces the result classically. I'm not a programmer so will explain intuitively.

QM assumes 'spin' as some mystical internal quality where; "superposed states collapse to singlet states." That mostly came from 'bizarre' 720^o spin 1/2. i.e. nobody understands what's supposed to be going on in any physical sense.

I show 720^o spin is classical (spin within spin) and involves real angular momentum. It then implicitly has BOTH a north and south pole, so BOTH spin directions.

But only one of course can be measured at once; so it's observer dependent (or propagation direction dependent assuming the axial propagation vector of optical science.)

As 'detection' needs a transfer of angular momentum to the analyser field electrons, the 'flip' of the electron field direction (each side of 90^o setting) then flips the field electron orientation, so reverses the finding. (the 'other' photomultiplier trips). Only verified optical science is invoked.

I can now put a glass panel on the black boxes to show how the results are produced. We have a ball spinning on an axis which pivots freely except for one degree of freedom which changing with the setting and can flip. A second smaller ball arrives whose spin axis is fixed horizontally (but either direction).

Firstly (as verified experimentally) before any 'correlation' we find a local amplitude difference on meeting subject to orientation (but on TWO planes). The detector angle can ('spin flip') reverse one axis each side of 90^o. The 'intensity' found then follows a squared cosine relationship. That is Malus' law. At 90^o (the equator) we can't tell which way (CW/CCW) it's spinning so get 50:50. At the poles it's absolutely certain (all the same or all opposite). 45^o is equivalent to 135^o, it's just the reverse '2D' cosine of the angle from the axis.

That give the 'Local' inequalities, which is a 'real' scaler. For the 'relative' relation just imagine a single transparent sphere and strike the angles from the axis, using any one as a datum for the other. (consider it as a relative surface area function if you wish. The relative 'intensity' (amplitude squared) plot gives the cosine curve (use as many places of decimals as you have time for).

Uncertainty is stepped down but remains. (There are many recursive higher order effects).

All is entirely classical. Bells logic is conserved but his theorem circumvented. I have an offer for you Richard, I'll write off the the 5000 euro's to get you to write the programme following that discrete field model ('DFM') protocol. You're nearer Sweden than me so perhaps you could also pick up our prize.

So the new (old) DFM law is; 'there are no monopoles in angular momentum'.

Best wishes

Peter

Richard Gill

Peter, J.S. Bell does not use any assumptions about QM. Nor do I.

Where is there any assumption about quantum mechanics in the following experimental protocol?

Alice and Bob are in different classrooms and in each classroom there is a black box, called "measuring device A" and "measuring device B" respectively. These two boxes are connected to another black box in another classroom, called "source", through some kind of cables, tunnels, or whatever, so that all three black boxes have means to share any information they like. Alice and Bob's boxes each have two buttons, and two lights. The buttons can be pressed, the lights may or may not flash. The communication channels can be switched on and off.

You are going to provide these boxes and engineer the communication channels between them. I don't mind what you put in them (spinning disks, shuffled packs of cards...) or how you manage the communication. Now comes the experimental protocol.

Initially the communication channels are open.

Now repeat, 10 000 times:

Step 1. The connections are severed.

Step 2. Alice presses the button marked "0" or the button marked "90"; Bob presses the button marked "45" or the button marked "135". After Alice and Bob have each pressed a button, a red or a green light flashes on their box. They record their input and their output.

Step 3. The connections between the three magic black boxes are restored.

Your job to engineer those three boxes and the channels between them so that:

Prob(lights flash same colour | 0, 45)

= Prob(lights flash same colour | 90, 45)

= Prob(lights flash same colour | 90, 135)

= 0.15

Prob(lights flash same colour | 0, 135)

= 0.85

To make life easier for you, I just ask you to write three computer programs with simulate the three magic boxes, to be run on three separate computers sending one another messages by internet (to simulate the communication channels). Fine by me if you just write one computer program but it must be clear that it could be broken into separate pieces as required.

I happen to know for sure that you can't do it. I'm not going to even start to try to explain why. If you want my attention (or the world's attention) you'll have to program it yourself of get someone else to program it for you. If you succeed you'll get the Nobel prize for the first loophole-free experimental violation of Bell's inequality, and moreover you will have totally revolutionarized the whole field of quantum physics, since you'll have shown that quantum entanglement is completely classical.

Richard Gill

Amusingly, in the experiment referred to in the wikipedia article, the "very small number of qubits" referred to turns out to be equal to the indeed very small number, 1

So that particular experiment did not even involve "entanglement" between several qubits.

I use the word entanglement here in its conventional theoretical meaning, within conventional quantum mechanics. In other words, it is a theoretical concept which only has meaning within a certain theory. The experimentally observable consequences of entanglement between a small number of physical systems which are in close physical proximity can easily be explained by classical physics.

Nick Mann

Tom,

It's astonishing that your header tag for "Time, Change & Self Organization" is a quote from Carl Jung ("... whatever is born or done at this particular moment of time has the quality of this moment of time"). However, possibly less astonishing is your neglecting to mention that he goes on to add "Here we have the basic formula for the use of the I Ching."

Although, to be sure, divination isn't mystical. Nor was Jung's declared general belief in synchronous acausal meaningful coincidences which inspired The Police among others. So you're off the hook.

Richard Gill

Maybe already 10 years ago, experimenters managed to factor the number 15 using half a dozen qubits

The answer was: 5 x 3

Their has not been much progress since then

Thomas Ray

Nick, did you read my last FQXi essay?

Florin Moldoveanu

Michel, you state:

"If say the probability distribution of Heads and Tails is (0.625,0.375), E(A) = 0.625*(1) + 0.375*(-1) = 0.25. But every time we get H, the other result we didn't get must be a T. Therefore the counter-factual distribution must be opposite to the actual one. E(B) must be 0.625*(-1)+0.375(1) = -0.25. Not 0.25."

Sorry, but I don't understand what you are trying to say here. What is E(A) and E(B)? Thanks.

Florin Moldoveanu

Richard, you state:

"Tom, I do not think that "quantum theory is a true scientific theory". It is logically fundamentally flawed because it both assumes and denies there is a boundary between quantum and classical domains."

Is this correct? Are you making the equivalence between Bohr's position (part of the Copenhagen interpretation) and quantum mechanics? The nonsense with measurement device being classical while measuring a quantum system was rigorously proven to be inconsistent. Nature is pure quantum and classicality is only a convenient FAPP illusion. Still, the measurement problem is open but the mathematical solution is within reach. Until then we should adopt late Asher Peres' approach:

"Even if quantum theory is universal, it is not closed. [...] While quantum theory can in principle describe anything, a quantum description cannot include everything. In every physical situation something must remain unanalyzed. This is not a flaw of quantum theory, but a logical necessity in a theory which is self-referential and describes its own means of verification."

Richard Gill

Peres is barking up a wrong tree.

I refer to the measurement problem, and I assume only a minimal, operational, "interpretation" of QM. The little bit of QM which every sane physicist agrees with, at least, operationally. (Hardcore MWI people are not sane physicists. Sane physicists may say they believe in MWI but it doesn't mean anything, except membership of a club where people shake one another's left hand instead of right hand).

(Some people think Bayesianly about probability, some think frequentistically, but again this is just membership of different clubs. FAPP there's no difference)

There already exist several solutions to the problem with QM, for instance Belavkin's eventum mechanics.

Thomas Ray

If Richard and Florin think that the space of all practical purposes is identical to the space of all possible measurement results, let them prove it.

Florin Moldoveanu

Belavkin is a step in the right direction (and so is decoherence), but is it the complete solution? I am seeking a dynamical explanation. A Fock space-like solution looks promising (because of creation and anihilation operators), but can it be derived without an appeal to Lorentz invariance and field theory baggage from pure geometrical considerations? Don't know yet.

Thomas Ray

" ... Lorentz invariance and field theory baggage ..."

That is, the real baggage packed by models that empirically correspond to local physical events, as opposed to the mystical baggage of quantum entanglement and nonlocality.

Richard Gill

The Belavkin approach *is* dynamical!! That's the whole point. Measurement collapse and unitary evolution are both real and each are one side (but a different side) of the same dynamic.

I think it is brilliant. It is so simple .. that's why no one thought of it before. Oftentimes the real truth is so simple and staring you in the face, that you don't see it. Because you are looking for something very elaborate. You can only see what you somehow expect to see...

Thomas Ray

Richard, do you stand by your abstract?

"We discuss V.P. Belavkin's approach to the measurement problem encapsulated in his theory of eventum mechanics (as presented in his 2007 survey). In particular, we show its relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman (1995, and more recent papers).

"Landsman writes 'those believing that the classical world exists intrinsically and absolutely [such persons later termed by him B-realists] are advised against reading this [his, 1995] paper'. He adopts a milder position, calling it that of an A-realist: we live in a classical world but to give it special status is like insisting that the Earth is the centre of the universe. The B-realists are accused of living under some kind of hallucination. Landsman presents arguments pointing in a particular direction to a resolution of the measurement problem which at least would satisfy the A-realists. We point out in this paper that the theory earlier developed by Belavkin (surveyed in his 2007 paper) seems to complete Landsman's program or at least exhibits a 'realisation' satisfying his desiderata. At the same time it seems that this completion of the program ends up giving both A- and B-realists equal licence to accuse the others of living under hallucinations."

Richard Gill

Tom, yes I stand by what I wrote in http://arxiv.org/abs/0905.2723

Richard Gill

Landsman (who is an A realist):

B-realist: The classical world exists intrinsically and absolutely

A-realist: we live in a classical world but to give it special status is like insisting that the Earth is the centre of the universe

Belavkin's model can be used to support either position. It embeds many possible, and in a mathematical sense co-existing, classical worlds in one quantum universe. An observer is a classical entity. An observer inhabits just one of the many classical worlds. Anyone reading this in an observer in the same classical world as I inhabit. So I do have licence to claim a special position for "my" classical world since it is the only one of any practical relevance to me. The others, for me, are metaphysical entities. Mathematical abstractions.

It seems to me that there is nothing wrong with taking a kind of weak anthropomorphic position in physics. It is fine that at the moment of the big bang many possible different laws of physics might have come into existence in different, isolated, mini-universes, and amusing to discuss how long they might have existed and how interesting or boring they might have been, but looking up at the stary sky at night I find our own particular mini-universe to have a rather more intensely compelling interest and reality than all the others., which from my point of view, truly are only imaginary.

Thomas Ray

"B-realist: The classical world exists intrinsically and absolutely

A-realist: we live in a classical world but to give it special status is like insisting that the Earth is the centre of the universe

Belavkin's model can be used to support either position."

Then it also supports Joy's framework. For if the Earth is not the center of the universe (indeed, the center of the 4 dimension universe is any arbitrarily chosen point), the classical world exists intrinsically (spacetime is actively diffeomorphic) and Joy's framework subsumes both positions A & B because it is coordinate free and non-probabilistic.

"It embeds many possible, and in a mathematical sense co-existing, classical worlds in one quantum universe. An observer is a classical entity. An observer inhabits just one of the many classical worlds."

Which why I support the many worlds hypothesis as trivially true. And Joy's quantum correlations as one of infinitely many correlated points of the Hopf fibration.

"Anyone reading this in an observer in the same classical world as I inhabit. So I do have licence to claim a special position for 'my' classical world since it is the only one of any practical relevance to me. The others, for me, are metaphysical entities. Mathematical abstractions."

Or -- metaphysically real.

"It seems to me that there is nothing wrong with taking a kind of weak anthropomorphic position in physics. It is fine that at the moment of the big bang many possible different laws of physics might have come into existence in different, isolated, mini-universes, and amusing to discuss how long they might have existed and how interesting or boring they might have been, but looking up at the stary sky at night I find our own particular mini-universe to have a rather more intensely compelling interest and reality than all the others., which from my point of view, truly are only imaginary."

So the only thing that makes your world real, is your belief that every other world is imaginary?

That belief, in fact, is exactly what motivates all belief in Bell's theorem and nonlocality.

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