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

John Cox

Tom,

Thank-you for the synopsis of Davies-Unruh, your explanation brought my off topic question back to the subject here via the Hopf fibration though I'm still wrapping my head around how that must work. Non-vanishing torsion is not the same as non-vanishing torque, if we look at it macro-mechanically. If we bolt up a lateral structural member to the side of a vertical column, there will be no shear stress on the bolts once the nuts are torqued to where the clamping pressure creates more friction between the mating surfaces than the rated load the lateral member will be subject to. The friction on the seat of the nut and bolt head will prevent the nut from backing off, the applied torque will be maintained.

That maintained torque is therefore non-vanishing. But it does not radiate from the center of the bolt, it is tangential and would be in parallel physically with the same tangential transform of stress from the bolt to structural members as would be of non-vanishing torsion which translates both locally to each component or globally to the structure. The sustained mechanical non-vanishing torque is where it goes local. It is also gravitationally linked through the globalization. If you strike a beam with a hammer you can hear the wave run down the length of it, and reverberate. Even though there is no shear stress on the bolt which is perpendicular to the bolting flanges of the structural members, the lateral beam is coupled to the vertical column by friction maintained by torsion through that bolt. And just like the singing of a sound beam, the global non-vanishing tangential torsion translates through localized torque down the vertical column in a manner that is parallel to Newton's equating the proportional length of a projectile to it's penetration of a media, independent of it's mass.

As to Davies-Unruh, I had been of the understanding that the infalling observer was accelerating beyond the vertical gravitational acceleration, which would make it reasonable to assume that black-body radiation would be experienced by the accelerating observer which would not be observable from a relative non-accelerated reference. jrc

Thomas Ray

John R, black body radiation -- a classical phenomenon -- differs from Hawking radiation and Unruh radiation. These are quantum mechanical effects of virtual particles.

John Cox

Tom,

I stand corrected on the element of relative acceleration per Davies-Unruh, but as to the boundary condition between black-body radiation and virtual particles, this is perhaps where I part company with probably everybody here. I don't want to get on a soapbox, but; Momentary violation of conservation of energy which begets virtual particles as quantum fluctuations, was another point on which Bohr bested Einstein due to A.E. trying to explain all as accelerations through space without recourse to actual fields, though he also stated his belief that there is no region of space bereft of any sort of field.

I long ago opted out of the notion of the photon being a 'massless particle' and Planck's Constant being an empirical scalar quantity. Now everybody can throw vegetables at me and say 'You can't do that! We've invested over a century of exponential increase of mathematical inventions in Planck! and Lorentz! You'll cheat us of the cross-product treating Planck as a vector! Boooo!'

Okay, I'll shut-up. This pays so good, anyway. jrc

Michel Fodje

Let me summarize the argument I've been making which shows that the CHSH is fatally flawed and with it, Bell's theorem:

It is well known that the terms in the CHSH expression S = E(a, b) - E(a, b') + E(a', b) + E(a' b'), as derived, include a mixture of both counter-factual and actual results. Yet when we claim that QM violates the expression, we are using the exact same probability distribution for both actual and counter-factual results, which is an error.

To see this, consider the expression E(A) + E(B) where one of them is counter-factual. For example, say A is the outcome of one toss of a coin, and B is the other result we didn't get but could have gotten. A similar error will be to assume that the probability distribution which produces E(A) is the same distribution which produces E(B).

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.

So if QM is correct, then it is predicting the actual expectation values, not the counter-factual ones. But our inequality E(a, b) - E(a, b') + E(a', b) + E(a' b')

Michel Fodje

... But our inequality E(a, b) - E(a, b') E(a', b) E(a' b') less than or equal to 2 was derived using counter-factual results.

Therefore apparent violations of the CHSH are due do erroneous substitution of actual results from different sets of particles into an expression derived using a mixture of actual and counter-factual results from a single set of particles.

Joy Christian

Thank you, Michel, for your insightful contribution.

Welcome to FQXi. You bring a breath of fresh air.

Let me also make one technical observation. One of the first people to make the observation you have made (to my knowledge) was Arthur Fine. He pointed out quite early on in the history of Bell's theorem that the assumption of joint probability distribution for the incompatible quantum mechanical observables is an unreasonable assumption. The Bell-diehards, however, have never accepted his arguments.

Richard Gill

I propose to erase all talk of inequalities, bounds, proof, and violations from discussions of experiment. An experiment cannot violate a bound. Obviously anyone who says something like that is off their head ... or means something different. Obviously an experiment does not prove anything ... definitively.

I made two graphics which explain the rationale of a CHSH experiment. The experiment is done in order to discriminate between two theories. The theories predict two different theoretical correlation surfaces rho(a, b). In an experiment, one can try to determine, up to some experimental error, one or more points of the surface. Should we try to reconstruct the whole surface experimentally or just a few points? Well, if resources are limited, the smart thing is to restrict attention to just a few points, judiciously chosen so as to maximize the discriminating power of the experiment Obviously, these points should correspond to several different settings of both parties Alice and Bob. It turns out that the optimal choice, from Joy Christian's point of view (ie in order to maximize the probability that the experiment will (statistically) prove that he's right, are the famous CHSH settings 0 and 90 degrees for Alice, 45 and 135 for Bob.

Just four points (those four points( is better than any larger number, better than any set of any other points! (This is connected to Tsirelson's theorem. Here's a 2005 article in IEEE-TIT: http://arxiv.org/abs/quant-ph/0307125 about the matter).

"It is all so simple. How could I have not known this before" (Pierre, in Tolstoy's "War and Peace"_Attachment #1: quantum.png Attachment #2: classical.png

Richard Gill

"Why do Alice and Bob need to press buttons market H and T? They should have no input to the random H/T state which represents spin 'up/down'."

OK, bad notation.

Alice has two buttons one marked "0 degrees" the other marked "90 degrees"

Bob has two buttons one marked "45 degrees" the other marked "135 degrees"

Does this make things more clear?

Stuff arrives from source at Alice and Bob's apparatus. Alice and Bob each press one of their buttons (at random, for instance). Each of their apparatus starts flashing a red light marked "up" or a green light marked "down".

Alice and Bob write down their setting and which light flashed.

Now repeate 10 000 times.

Richard Gill

Tom asked whether the simulation of a continuous function is a continuous function. Well Tom I have news for you, our computers are discrete things. They are Turing machines. There are only finitely many possible different inputs and only finitely many possible different outputs (in finite time, that is).

I suspect the same holds for the universe.

Fred Diether

Nope. Rotation is continuous for sure.

Judy Nabb

Peter,

Please remind me how local inequalities become relative. It all fits nicely then a day later it's gone! It's like a wave pattern, eureka moments interspersed with blank moments. I need to grasp the logic again.

I'm also confused by reluctance of some to accept detector influence on the system as I understand it's both been shown (the rotating filters) and fits nicely within QM. Can you explain the reasons? That also was worrying me while thinking about it on the plane.

My trip was great BTW thank you. It's always good to see how universities in other countries approach the task. Also useful in my other role as an editor. And sunshine too!

I see discussion has drifted. That's a shame with such a nice circumvention right before us, as I recall! How's you re-write going? I'm happy to give you more editorial views if you wish.

Judy

Thomas Ray

Richard,

Here's some news for you, too. Since 2003, we have known, and since 2006 we have been adequately convinced, that all singularities on the 3 manifold are extinguished in finite time. (Perelman, Hamilton, Thurston)

This means that with topological surgery, continuation of the Ricci flow on the half open interval [0,1) avoids the singularity and proves that the manifold is simply connected.

Since 2007 (actually about 2010 for me and for you not yet) we have known that the simply connected parallelized 3-sphere admits strong quantum correlations through " ... the discipline of parallelization in the manifold of all possible measurement results." (Christian, Disproof of Bell's Theorem p. 13)

The finite state machine presents no barrier to the continuous function.

Thomas Ray

"Please remind me how local inequalities become relative."

That inequalities are relative is trivial.

The solution to relative inequalities of two expressions cannot correlate the expressions -- there will always exist a "greater than" or "less than" relation between the results. If the quantities are correlated, only one can be local, the other nonlocal. This is not the same as strong quantum correlations with exact and manifestly local solutions.

In Bell's inequality and its variations, one is not comparing one side of the expression to the other, or comparing two "relative" inequalities as in Peter's proposal which compels nonlocality exactly as Bell says; one is predicting the outcome of a single observation of a single particle.

What Joy has done, is to identify the source of strong quantum correlations in the structure of the space; i.e., the correlation function of two dichotomic variables. If one understands general covariance, one can see how the framework extinguishes the boundary between quantum and classical domains, which reduces to Einstein's aphorism, "all physics is local." That is not relative inequality, it is relative becoming.

pjackson

Richard,

"There are only finitely many possible different inputs and only finitely many possible different outputs"

That was the precise point my IQbit essay made; but nature is only 'binary' recursively to the Planck limit. So binary mathematics can only ever be a good approximation to nature until we get massively bigger and 'quantum' computers!

It's normally quite good enough, but would it be wiser not get too carried away with it's resolving powers, or assume nature dumbs itself down just to suit us!

Best wishes

Peter

PS; I note I need to respond to Judy above on detector influence. Do you really suggest, despite Weihs et al etc, that the analyser has no effect at all on the particles interacting!?

pjackson

Judy,

The local and relational inequalities come from the same source. Tom has it part right but missed the important bit, so assumes my theory 'compels nonlocality', which is false. The circumvention is more fundamental; No 'prediction of outcome' is required at all.

The problem is largely that the derivation is too simple! To first re-grasp the LOCAL inequalities; recall there is no 'UP' in space. Both A and B have all degrees of freedom which chair in space they sit in and which way up and round it is. As in the 45 degree filter case, the setting choice, so field electron orientation, dictates the (Red/Green) finding itself AND it's intensity ('probability'). This remains true WHATEVER the EM field relation to the propagation axis. The states found are then both random and symmetric! The causes are spin flip and non mirror polar symmetry of OAM. Best to visualise that with a 'picture' so as not to loose it. I'll explain this carefully for Tom & Richard too.

Now coming to A,B RELATIVE correlation from there seems to need ~6 more years of intellectual evolution (2020 vision) to see the simplicity, but the Bayesian distribution suggests some, as you, able to do so now; Don't try to do it from the 'local' data. Picture Bob and Alice in their chairs with any (Bloch sphere ) orientation. The only relational datum is that the approaching particles (both with both 'spins' as all OAM) have the same propagation axis. Each will then be modulated, again subject to setting. Orientation ALSO has an effect, but symmetrically. Lets just do 3 particles; Alice uses 0,0,0 and finds 100% G,G,G. Bob uses 0, 60, 180, and finds R,G,R.

"But he can't!" all those tied to QM's unproven and unexplained assumptions of 'singlet state' and 'collapse' will cry! Yet I show that classically he can, as both major 'time resolved pair' experiments have confirmed (in the 99.999% of data dumped as assumed down to a systemic error). When the bin fulls of findings are eventually returned to the tosser (A & B were 10 light years apart!) so called 'weak measurement' statistical analysis cannot access that pair comparison data. Now just superimpose both local inequality plots onto the same graph and compare the relative A,B finding; i.e. if both chose 90 degrees they both find 50:50! Both 0 or 180 = full and anti... etc.

Like the rest of the DFM, it's all about using the correct 'datums'. The truth uses only unfamiliarity and our false assumptions to hide right before our eyes. I did say it was "unbelievably simple"!

I've asked Richard about the detector business, I identify it as just another false assumption most don't properly examine. Glad you had a good trip. Yes I'd love to draw on your editing skills, thanks. In mid re-write now with a new table and figs.

Best regards

Peter

pjackson

Judy,

oops, forgot to pivot the quadrant! Spheres have no 'axis' except of OAM, so they have an invariant curvature and cosine law across all 3 axes. The data 'dumped' in each bin could be interpreted in various ways as we wish. Because the wrong assumption is used (input) the output seems not to make sense.

Actually you may be best to forget the quadrant and think of each identical position, (say 30^o) as a new notional 'datum' for each of A and B of 0 degrees. As each 'other' setting is compared to that datum the apparent cosine curve is recreated as the cosine relation is valid on all possible planes through a sphere. It will then always re-emerge statistically if assuming 'singlet states'. A self fulfilling prophecy really.

Does that help?

Best wishes

Peter

PS, In another life I was pub champ at 'Asteroids' on a 'table' machine with a rollerball control, which if you kept going returned you back in from the other side of the screen, infinity built in!, and you had to fight to change the angular momentum of the ball all the time. That was just a 2D screen but a hint of Bloch spheres was there in the 3D to 2D transition.

John Cox

Pete,

"...rollerball control, which if you kept going (rolling the control ball in the same direction; mine) returned you in from the other side of the screen,"

You got it Pete, There's 4pi exactly. jrc

[deleted]

John, Pete,

Yes, I've got it too (again). Simply beautiful. I hope the new description is easier to retain. I've remember how the blue quadrant works too (re-reading the instructions helped) just set any edge to either of the angles and that becomes the datum 0 for the angle to the other (or +1?) I see what you mean about being as tautological as Bells.

John, I think Pete's suggesting we need the basic full 4pi r^2 for the surface area of a sphere, then admit angular momentum into spin to give it an axis and consider as two hemispheres. That seems right as the implications are rather exciting.

Has anybody ever yet found a 'monople'? Do you think they exist Pete? I assume you don't, magnetic or not.

Have you understood the proposition Tom? You seem to speak a different dialect but it looks like simple geometry. Does it look anything like Joy's to you? And if Richard is still reading this, any understanding yet? And what was your view on detector influence?

Judy

Thomas Ray

"Have you understood the proposition Tom?"

Yes.

"You seem to speak a different dialect but it looks like simple geometry."

That's the problem with it. It lacks the degree of freedom that comes with nonzero torsion of the given topological structure. One will never do better than the Bell-Aspect result on the Euclidean plane or 2-manifold, which is also simple geometry, i.e., dependent on multiply connected detector settings which cannot replicate a continuous measurement function in 8 dimension spacetime.

"Does it look anything like Joy's to you?"

No. John R is correct that 4pi rotation projects to a flat screen of correlated points at opposite edges (in fact, Joy has explained it in these terms before). These boundary edges on the computer's screen, however, are not self similar to the correlations found in a simply connected topological framework of the Hopf fibration.

Sooner or later one has to realize, speaking the 'dialect' of topology, that the space of measurement constrains correlations on the 3-manifold, that is, the surface of our 3 dimension space embedded in 4 dimension spacetime -- and not the 2-manifold. This is not an exotic mathematical space; it is the space in which we live. The parallelized 3-sphere proves the case.

Strong quantum correlations exist, and we measure them. Conventional quantum theory claims that they exist because they are measured. Joy's framework explains that this is an illusion; the correlations exist independent of the observer.

[deleted]

John, Judy,

That's correct. So called 'pure singlet states' are monopoles. They can't exist. To have a north pole requires a south pole. It's yin and yang. You can only ever see or 'measure' one at a time, but the other state doesn't 'collapse'. 'Quantum spin' does now not have to be the mystery Neils Bohr had to assume so long ago. Time to move on perhaps?

Judy's about right John. I use the comparable surface areas of multiple patches on a Bloch sphere. That's the real product of statistical analysis of so called 'weak measurement'. I have a nice diagram on the way. 'A picture's worth a thousand words'. My statement that there is no up in space is possibly more profound than most will realise. Any two vectors on a Bloch sphere then have an equivalent relationship. I may drop the 'pivoting blue segment' and go straight to 3D as it may prove simpler for Tom and Richard etc. to understand, and perhaps even Joy. If anybody else has read it and has a clue do speak up!

I'm now happier with my written description. I might even get to write an essay too!

I don't mind now being Pete, I've always been both but suddenly I now prefer it, I can't imagine why (lol). Funny thing 'human nature'.

Best wishes

Pete

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