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

Thomas Ray

Hi Peter,

If you google point-line duality, you'll find it.

https://www.google.com/#q=images+for+point+line+duality

Thomas Ray

Peter, the free choice you give Richard (or anyone) is only "free" if he is allowed to choose at any time in the process and not just at the source. In other words, after you have compiled your data and by some process I don't comprehend have managed to find that Bell's inequality is not violated (although I don't think you will get that result because I see no true hidden variables in your protocol), and then Richard chooses his detector settings and you run that input, you will inevitably find that the inequality is violated -- why? -- no matter where in the spectrum of continuous colors he makes his choice, the angle of betweeness is fixed by detector dependence and is not continuous with the spectrum.

Yes, if you buy into the "quantum Randi challenge" this may be another way to validate the rotation through 2pi radians that Bell-Aspect predicts; it does not, however, constitute experimental evidence that hidden variables either do or do not exist. It simply verifies its own assumption.

I think my example of squaring the circle with compass and straightedge is apt: it is impossible because it would require a physically impossible infinite number of steps. Of course, we now know that it is not an insoluble problem to calculate the limit for approximate square equivalents to a given circle; what Richard disdains as merely utilitarian. However:

One can square the circle in non-Euclidean space. Obviously, this obviates Euclidean angles for the 1-to-1 correspondence of square to circle that results. What it also does, though, is to obviate dependence on an arbitrarily bound choice function; what I mean by that, is that the extra degree of freedom required to make the choice function identical to the correlation function (Joy's C_a,b) is built into the measure space as the limit of S^n parallelization. That is the true hidden variable.

Much of my own research is devoted to proving that the structure of S^3 topology obviates the axiom of choice for all real continuous functions. In other words, proving that the measure space is complete.

Best,

Tom

Thomas Ray

John R,

Not meaning to wander too far afield, re your comment, "Years ago I made a little magnetic octahedron that held itself together, it was fragile and weakest at the antipodal points but it would sit on the table til it was jolted."

You might be interested in the attached on hypergeometric projection which I extracted from a long paper of mine. You'd have to read my ICCS2006 paper to understand how I derived the numbers -- however, this short sketch heuristically conjectures that spheres of disjoint union 2 2 are inherently unstable (see octahedron figure)because of dynamic time dependence (cf. quantum decoherence).

We can discuss offline if you'd like: thomasray1209@comcast.netAttachment #1: 2_Pages_from_timebarrier80108.pdf

Akinbo Ojo

Thanks Tom and Peter for throwing some light.

Tom just on impulse without deeper thought... You mention the application of the calculus to physical systems and as you pointed out calculus in the way it was invented by Leibniz and Newton made use of the "limit". What does "limit" mean? This is suspicious as it suggests that despite all best efforts to make space and time continuous and infinitely divisible ad infinitum (without limit) mathematically, there has to be a "limit" physically and mathematically before calculus can be made to work to describe dynamics. The question is what will this infinitesimal value be, if there must be a limit? dx in dx/dt can certainly not work with a value zero.

Akinbo

Nick Mann

If Joy Christian's hypothesis represents physical truth, then "entanglement" as conventionally modeled is an invalid concept necessarily without real-world application. As he has noted, there can certainly be no genuine entanglement-based "quantum computation." For the purpose of this question I'm not defining "quantum computation" in an ideal sense in which significant useful scaling up might be accomplished. Keeping it simple. Now, Wiki says:

"As of 2014 quantum computing is still in its infancy but experiments have been carried out in which quantum computational operations were executed on a very small number of qubits.[6]"

http://en.wikipedia.org/wiki/Quantum_computer

If true, has this been accomplished sans entanglement? Or is the statement a bald-faced lie on the part of individuals who know better? Or are these people merely ignorant? Possibly delusional?

Nick Mann

This severe simplification from Tom a while back:

"Once again, researchers are relying on the probabilistic, linear nature of quantum theory (superposition, non-locality) to arbitrarily rule out classical processes. In fact, complex systems science is scale invariant, and principles such as the law of requisite variety, small world networks, nonlinear feedback functions, have the potential to explain microscale effects without the conventional quantum assumptions."

I imagine Richard knows these guys:

"We put forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness, as advocated by Phillips and supported by recent dynamical cluster approximation results on the Hubbard model, sets the necessary microscopic conditions. The crucial insight is due to Weng, who demonstrated that, in the presence of Mottness, the fundamental workings of quantum statistics change, and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing it further using numerical methods. The pseudo-gap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi-Dirac statistics. Proof of principle follows from Ceperley's constrained path integral formalism, in which states can be explicitly constructed showing a merger of Fermi-Dirac sign structure and scale invariance of the quantum dynamics." (J. Zaanen and B. J. Overbosch, "Mottness collapse and statistical quantum criticality", Phil. Trans. R. Soc. A 2011 369, 1599-1625 doi: 10.1098/rsta.2010.0188)

pjackson

Nick,

If all particles carries both spins, contrary to the QM assumption, would it be the case that the anomalous cuprate electron states could be explained classically via the micro magnetic field (commonly 'swirl' type) states.

It seems that the quantum statistics assumptions would certainly change as required, and there will be continuous transitions between the two states. The 'scale invariance' (gauge recursion) is at the heart of the 'discrete field' dynamics. I'm certainly no expert on Mottness, but the effects look right. Views?

Have you read any of my last 3 essays here? Or Bill McHarris's?

Best wishes

Peter

Thomas Ray

Ah, wikipedia swings and misses again.

Nick, you ought to educate yourself in the controversy over quantum computing, including D-wave which relies on classical concepts, and is tacitly endorsed by such high rollers as Google and NASA. You might also consider computer scientist Gil Kalai's arguments . And you might consider that the limited success of Shor's algorithm does not necessarily imply that quantum entanglement either exists or is scalable.

Most of all, you should see that there's absolutely no connection between the mechanics of quantum computing and my "severe simplification." That's a desperate reach, dude.

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.

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

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

Yes you do. You tacitly assume that the experimental outcome will be not be independent of the probabilities calculated in your mathematical model.

Richard Gill

Tom said "You tacitly assume that the experimental outcome will be not be independent of the probabilities calculated in your mathematical model."

You're saying that I tacitly assume that if I know the right physical model and do the calculations properly, then the probabilities I calculate would be close to the relative frequencies which I would observe in experiment.

I don't assume that tacitly, I assume it explicitly. As do all experimental physicists. You are saying that experiment is superfluous because by assuming some results you will see those results, hence every experiment always generates what the experimenter wants to see.

Well it sure would save a lot of money if we cancel all funding of experimental physics. Seems to me we can abolish all physics, altogether.

(I am more in favour of abolishing all funding of economics, management "science", and psychology).

Thomas Ray

"You're saying that I tacitly assume that if I know the right physical model and do the calculations properly, then the probabilities I calculate would be close to the relative frequencies which I would observe in experiment."

Richard, your knowing of the 'right physical model' depends on your expectations of what you have already observed of the physical model. Verifying your expectations a posteriori is not the same as predicting results from a mathematicallly complete model; i.e., a logically closed judgment.

"I don't assume that tacitly, I assume it explicitly. As do all experimental physicists. You are saying that experiment is superfluous because by assuming some results you will see those results, hence every experiment always generates what the experimenter wants to see."

Not every experiment. Michelson-Morley failed. Prediction of the orbital precession of Mercury succeeded. The problem with the quantum mechanical model is that it doesn't make predictions. It retrodicts expectations.

"Well it sure would save a lot of money if we cancel all funding of experimental physics."

At least, experiments that are not really experiments -- like the "QRC" or such contrivances.

"Seems to me we can abolish all physics, altogether."

Why not? -- you've already abandoned scientific method.

"(I am more in favour of abolishing all funding of economics, management "science", and psychology)."

Well, those aren't hard sciences, either.

John Cox

Tom,

Thanks for the pages, I moved to this thread because the other has gotten long in the tooth. That's not surprising when what I've been learning is that comments are coming from different kinds of maths with conflicting definitions, or rather definitions that are contrary to how the math at hand is presented.

The hell with Wikipedia, I went a got a Cliffsnotes pre-calculus and found a couple sites about 3D animation which are more helpful is demystifying the framework. After that, 'a'lice and 'b'ob can waltz around all they want. Back to the books for this kid. jrc

pjackson

Tom,

Thanks, but it's not 'point/line' but any 'dynamic' duality I was after. I'm familiar with the former (your first link), it's the second that's dead. But if it's the same topic it's no help. I'm trying to find any prior examples of what I've derived, which is smooth 3D duality of motion.

I'll answer you other post below, but it does look like you're missing the key point the experiment is based on. QM when formulated assumed there could be such a thing as 'pure' quantum states, (spin up, spin down) purely on the basis that we only ever found one or the other.

Quantum 'spin' is no better defined than 'matter' itself, but it's recognised as (quantum) angular momentum (AM), because it's measured as an exchange of AM and everything self contained, so rotational or orbital, has AM.

It's also a fundamental truth of AM (that QM seems to have missed) that it always has two conditions subject to observer aspect (so which way you look at it/measure it);; both clockwise and anti clockwise spin.

Have you worked out which way Earth spins yet? It is of course BOTH directions at once. Just because you look from above the north pole and find 'clockwise' does NOT mean that the southern hemisphere spin state 'collapses!' Now that's true of ALL spin 1/2 particles, including the electrons of the detector EM field.

Those electrons 'flip' at 90 degrees detector dial angle. So the AM transfer is then found to be in the opposite direction!! A man of your intellect should not have to think about the implications of that fact for too long before the penny drops.

...like a 100 tons of rock through the muddy foundations of QM.

I propose that is a genuine 'physical' theory, with a rather significant variable 'hidden' right before our eyes.

Have you found the implication? - thus the prediction of the aberrations in Aspect and Weihs 'time resolved pair' experiments, which proved to be born out - in the 99.999% of data discarded for lack of a theory to fit it!

Best wishes

Peter

John Cox

Peter,

"I'm trying to find any prior examples of what I've derived, which is smooth 3D duality of motion.'

Try www.spaceandmotion.com it's a wave structure of matter site with linkable citations but I think the webpage is inactive at present. I've run across a few math and physics sites that deal with the ying and yang of relative motion.

As to the rationale of the line and plane having equal number of points, to make it dynamic ; drop the absolute, you can always cut the difference in half and still miss it. It's utilitarian; to graph anything you start from 0 but have two axes, hence 0=o,o so your line can extend along both axis(s), that means simply that an ordered set of points just like o,o exists that are silly because the set is less than zero. But that projects ordered pairs at any point along the line so that you can have a graph that encloses an area between the axes that actually has points in it. That's the same rationale as the imaginary number ( i ), a negative value on the number line is just -x, but sqrt -1 is also -1, so if you have a sqrt -1 you can also have a -1^2 which is an ordered set of points at the identical designated place along a line metric. As a matter of nuts and bolts utility it means that, yes a line is a set of ordered pairs (o,o ---> o sub n, o sub n) as might be projected across a plane of ordered points ( as distinct from ordered pairs of points) that are themselves projected as lone points from the ordered pair of points along each axis. The diagonal line that would project would still be an ordered pair set so that it can project a plane of lone points as the square of the hypotenuse. So yes, to evaluate vectors, the line at any designated value will have the same number of points as the plane.

0,0,0,0

We ain't takin' it to the Fair, as they say. It's close enough for gov'munt work. jrc

Akinbo Ojo

Tom, what is dx in Calculus? Is it the infinitesimal distance between one point and the next?

Akinbo

Akinbo Ojo

Where does Joy Christian belong?

"Anybody who's not bothered by Bell's theorem has to have rocks in his head."

To this moderate point of view I would only add the observation that contemporary physicists come in two

varieties.

Type 1 physicists are bothered by EPR and Bell's theorem.

Type 2 (the majority) are not, but one has to distinguish two subvarieties.

Type 2a physicists explain why they are not bothered. Their explanations tend either to miss the point entirely (like Born's to Einstein) or to contain physical assertions that can be shown to be false.

Type 2b are not bothered and refuse to explain why. Their position is unassailable. (There is a variant of type 2b who say that Bohr straightened out the whole business, but refuse to explain how.)

See p.4, Is the moon there when nobody looks?

To the extent that Joy sides with Einstein against Bell he has my vote even if we disagree on some of the fundamentals.

Akinbo

Joy Christian

Thank you, Akinbo, for your vote.

The issue from the introductory pages of my book you are concerned about is a trivial issue. It is about the difference between a compact and a non-compact topological space. Sometimes a non-compact space can be compactified by adding a single point at infinity. This dramatically changes the properties of the space, with tangible, measurable, physical consequences.

In any event your concerns about "points" and "lines" are unrelated to the issues that preoccupied both Einstein and Bell.

A sign of a good scientist is to be able focus on the important issues without getting distracted by the whole shebang of the science, the arts, the life, and the universe. That is why John Bell was such a great scientist. He crystalized one very important issue, that of the tension between locality and reality in Einstein's argument against Bohr. The rest is history.

Unfortunately Bell also made a terrible mistake in the process. He missed a very important property of the physical space we live in---namely, the spinorial property. This is the issue you should be focusing on---not the trivial introductory parts of my book. You can find out more about it on my blog.

Akinbo Ojo

Joy, my reason for wanting clarification on what you called the trivial introductory parts is that not doing so can turn round to haunt the conclusions inferred at the end. If it is not too much to ask, how is 'the spinorial property of space' to be described in simple language to a non-professional mathematician? It is when I know this that I can concur that "points" and "lines" are unrelated to the issues that preoccupied both Einstein and Bell. Thanks.

Akinbo

Joy Christian

Akinbo, this video may help, provided you ignore all the quantum mechanical propaganda it tries to perpetuate. What the video describes is just the well known spinorial property of the physical space.

Akinbo Ojo

Joy,

Just watched the video. Thanks. It seems to bring up the age-long debate between the relational and substantival views of space but now on the quantum instead of the classical scale. Is it the observer or space itself that determines whether an object is rotating (spinning)? Like David Mermin would ask, 'does an object spin when nobody looks?'. According to the relational and Machian view it is the fixed stars that determine and give you the properties that a rotating object experiences. According to Newton it is the space itself that confers those properties on you, as he sought to demonstrate in his famous Bucket and Globe experiments.

I am inclined towards the substantival view and would answer Yes, an object can be assumed to spin even when nobody looks because it is space that matters and agrees that you spin. If I am correct, then in the EPR arguments, space is looking and is a participant, probably the 'hidden variable'. I can only say more after reading more...

Akinbo

Thomas Ray

"If I am correct, then in the EPR arguments, space is looking and is a participant, probably the 'hidden variable'."

Excellent, Akinbo. Unfortunately, though, not in the EPR argument, or we wouldn't be having this debate today.

However -- and I don't know how to address this without using technical language -- where Einstein could only show that his theory applies 'up to diffeomorphism,' i.e., the limit of physical (Lebesgue) measurement criteria, I personally think Joy's framework promises to be the foundation of a theory admitting active diffeomorphism, where the structure of space actually determines a measurement outcome.

Thomas Ray

Here is a more plain language version of what I'm talking about. It's one entry in Kevin Brown's book length collection Reflections on Relativity which I think is excellent reading for those who wish to know Einstein's theories in the their full depth and beauty.

pjackson

Tom,

"..by some process I don't comprehend have managed to find that Bell's inequality is not violated.."

We actually find the Bells Inequalities ARE violated, but I think that's what you meant. I've better explained the 'hidden variable' below I hope; it's the reversability of detector field orientation ('spin flip') at 90^o, which means that, due to non-mirror symmetry, angular momentum transfer will be the 'other' way subject to setting angle (the 'other' photomultiplier will click').

This false assumption identified by the 'discrete field' model is as fundamental as any could be. There is no requirement for Bob to find 'up' if Alice finds 'down'. HE TOO CAN FIND 'UP'!

You then correctly and perceptively identify that; "the angle of betweeness is fixed by detector dependence and is not continuous with the spectrum." which is the exact effect of the above discovery, and in no way 'disqualifies' it as the rational solution.

The experiment is classical and reproduces the QM predictions with no valid 'rule violations'. I also think many also misunderstand the real point of Occams razor; which is that the SIMPLEST solution is not only the right one but is also often far simpler than anybody has previously conceived.

The toroidal spin/orbit relation, where the 'charge' is spinning in its (helical) orbital path also explains the 720 degree 'return' characteristic of a spin 1/2 particle. That does 2 things; opens the way to fermionic QG, and, I suspect may provides some form of topological connection to something like Joy's 'parellelised 3 sphere'. But exactly how is beyond me.

There is one good way to falsify the DFM hypothesis; to find anything spinning or orbiting with any type of angular momentum that does not implicitly have BOTH spin directions subject to orientation. Do throw any you can think of at it.

Best wishes

Peter

[deleted]

"...what is dx in Calculus? Is it the infinitesimal distance between one point and the next?"

It doesn't mean anything by itself, Akinbo. As you said earlier, what we mean to write is dx/dt, the derivative of x with respect to t. There is nonstandard analysis (Abraham Robinson) that deals mathematically with real infinitesimal objects; however, if we speak of physical applications which obey real (Lebesgue) measurement criteria, we come up against the primary reason that Einstein intended general relativity to be only an intermediate step to a complete theory of gravity.

As it is, general relativity is mathematically complete -- i.e., it is a set of closed logical judgments on a specified domain that predicts measurable phenomena that we have verified to be true. In other words, the independent mathematical model corresponds 1 - 1 with the physical measurement.

If the domain is of infinite range, we run into the problem of cosmology -- what is the derivative of x when t = 0? That's why physicists say the theory "blows up" near the singularity of creation. We can only "wind the clock back" to a short time interval after the theoretical big bang event, on the assumption of a point of infinitely dense mass-energy at the beginning of time (whatever that means).

Quantum cosmology has the advantage of probability calculations based on the assumption of fluctuations in energy values in 2 dimensions. A deterministic (classical) theory, however, begs pairwise correlation of particle events over an infinite range of the continuous 4 dimensional spacetime domain, which gets to your questions:

We already know that in 4 dimensions, if one asks "where did creation begin?" -- the answer is "at every arbitrarily chosen point of spacetime." Quantum theory allows -- on the assumptions of quantum entanglement and nonlocality -- that correlations measured in 3 dimensions describe all phenomena locally and the events not measured are assumed nonlocal. What does "nonlocal" mean? -- it implies that all phenomena are observer-created, and that every local measurement in 3 dimensions changes the configuration in 4 dimensions. ("God plays dice.") However:

The assumption of 2 primordial correlated points that prevents physics from blowing up at the singularity implies that all quantum correlations are primordial. So the question of how much distance exists between one point and another is moot -- the events are correlated at every distance of the 4 dimension domain, because the domain is continuous (and if Joy Christian is right, also simply connected), without the assumptions of entanglement and nonlocality.

Ordinary calculus, whether in ODEs or PDEs, is burdened with having to arbitrarily specify boundary conditions (dx/dt). It is obvious that we need a different mathematical method to have a classical theory of quantum correlations in which all measurements are real and local, independent of boundary conditions, probability measures and arbitrarily chosen coordinate systems.

Joy Christian's topology-based research supplies the framework that makes such a theory possible -- we can wind it back all the way to the singularity, where the non-zero torsion built into the topological model rescues us from the cosmological problem, and where we can see that the singularity exists (and is avoided) for every measurement function continuous from the initial condition.

Best,

Tom

Thomas Ray

Argh. Last was mine.

Akinbo Ojo

Thanks Tom. Quite a lot to digest. No further questions at the moment but I will revisit again. Have you read the Is the moon there when nobody looks paper I linked?

All the best

Akinbo

Thomas Ray

Peter, there's no profit in verifying that Bell's inequality is violated. That's what quantum mechanical theory predicts. What we're looking for is that the inequality is violated without entanglement or nonlocality. That requires a degree of freedom that your model lacks.

"There is one good way to falsify the DFM hypothesis; to find anything spinning or orbiting with any type of angular momentum that does not implicitly have BOTH spin directions subject to orientation."

Spin and orbit direction are orientable by definition, with choice of initial condition. Your hypothesis is not falsifiable, because -- as in the "spinning dancer" illusion, and in Bell-Aspect experiments -- we can only extract information on one orientation for each observation.

The orientability of Joy Christian's framework is a topological artifact caused by compactification of R^3 on S^3 by a point at infinity. In other words, natural orientability is itself a topological property not realized in plane (either Euclidean or complex) domains and the numerical implementation of measurements in those domains. In my reading of objections to Joy's framework, this is the very hardest thing for detractors to grasp though it follows from elementary topology.

Even the extended complex plane C^ (Riemann sphere) with its point at infinity that compactifies the plane is insufficient unless there is a means of analytic continuation on the manifold S^2 X S^2 that doesn't send every result to infinity. Because S^2 X S^2 is identical to S^3, it is factorizable over the manifold at the limit of S^7 parallelizability -- which means that Joy's measure domain is continuous, flat, and of infinite range on parallelized S^3. All correlated results go to 1 or - 1 without boundary, without arbitrary coordinates, without any more than classical (coin toss) probability:

The only results possible on the equator of S^3 are 1, - 1, and the imaginary number i. In a complete (4pi) rotation, i disappears, though topological torsion does not. Both orientations remain anti-correlated, so that extra degree of freedom is built into the topological structure.

I wish I could make this simpler and shorter. I can't.

Best,

Tom

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