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

Robert McEachern

Tom,

Is a coin, in your pocket, "heads" or "tails"?

Heads or Tails?

Whatever objective reality, measurement framework you think exists, USE IT NOW to state, once and for all, your ONE WORD ANSWER. Heads or Tails? Don't disturb it , or touch it and thereby disentangle it, just use your framework to provide the answer.

Since whatever objective reality, measurement framework you think exists, exists BEFORE as well AFTER you make your answer, it is, as they say "intuitively obvious to the casual observer" that that objective reality, measurement framework you think exists does not CAUSE the coin to become EITHER heads or tails. If it did, then the coin in your pocket would be either heads or tails, BEFORE you observe it - just like Bertlemann's socks are whatever they are, before being observed.

So which is? Heads or Tails?

The answer has nothing to do with the topology of space - that does not change when the answer is given, nor does the coin change, nor does the coin's relationship to the topology of space change. So what changed in the cosmos? One thing ONLY. The observer's decision-state: the observer's DECISION to make a DECISION.

"simply the conventional view of quantum mechanics"

Conventional interpretations of QM deny the very existence of coins - precisely because they do not even realize that they do so - a macroscopic, classical entity that is simultaneously in two states at once - not (heads OR tails), but "mysteriously" (more like superstitiously) both at once - (heads AND tails) And a coin remains an unrepentant, uncollapsed, two-sided superposition of (heads AND Tails), even after the observer has confidently, and DEFINITIVELY (defined to be so), DECLARED it to be otherwise - either heads OR tails.

Rob McEachern

Thomas Ray

Alan,

An article by Boris Tsirelson linked by Richard Gill earlier, explains entanglement.

Thomas Ray

"Heads or Tails?

Whatever objective reality, measurement framework you think exists, USE IT NOW to state, once and for all, your ONE WORD ANSWER. Heads or Tails?"

Unmeasured.

Alan Lowey

Okay, thanks. I'll give it some more thought..

Thomas Ray

" ... acknowledge the logical possibility that particles might be able to travel faster than light."

Do you acknowledge the logical possibility that the sun's movement might be caused by Apollo driving his fiery chariot across the heavens?

Alan, logical possibilities are determined by a framework of assumptions. Relativity, however, is not merely an assumption; it has measured correspondence to physical facts.

[deleted]

Obviously.

And with no hope of ever measuring it, using your framework.

Because your framework does not address the real, objective problem. Neither do any of the conventional interpretations of QM. The problem is a profound misunderstanding of how a single bit of information actually behaves., when an attempt is made to actually measure it.

But as you have astutely observed, just as long as you never even attempt to observe such a thing, you will never have any difficulty in explaining your observations. Hence:

"There are no correlated events that need to be explained.",

since there are no events at all, until you DECIDE to cause them to exist. It is the topology of your mind, not the topology of space, or the topology of the entities being observed, that is the DECIDING factor.

Rob McEachern

Thomas Ray

What about this more recent Philip Pearle paper?

It stands to reason that Richard Gill -- an acknowledged world class expert in martingale theory -- would be partial to a derivation of Schrodinger's equation from a theory (CSL) that injects a random function into the Hamiltonian. And Pearle's motivation is clear: The founders of quantum theory relied on a collapse state " ... to ensure that a preferred basis state, once chosen by nature, would remain chosen. They thereby relinquished the hope to describe reality." Pearle then goes on to revive the hope with the probabilistic model that effectively proves Richard's conjecture: "There does exist a radius distribution such that the cosine is reproduced exactly."

However, being probabilistic, it doesn't do anything to answer the seminal problem of a finite set of measurements made in a finite time interval. That's why I claim that my conjecture: "For every classical measurement, there exists at least one quantum state," is dual to Richard's conjecture; classical measurements hold in the infinitely small. Pearle acknowledges:

"The difficulty is that quantum theory just gives the probabilities of these events: it does not give the probability of transitions between these events."

Some years ago, when I wasted my time arguing with creationists who claimed the fossil record does not support Darwinian evolution for the lack of "transitional fossils" -- it became clear to me that no matter what transitional fossils are identified, one can demand transitions between the transitions.

When it comes to manifest events, then, I think that proof of the existence of "at least one" transitional event in any interval -- even if unmeasured or unmeasurable -- supports Einstein's claim of "up to diffeomorphism" in the specified continuous spacetime.

Tom

Thomas Ray

" ... with no hope of ever measuring it, using your framework."

Rob, the coin exists in a definite unmeasured state in my pocket, whether I choose to measure it or not, just as the moon exists whether I am looking at it or not.

Philosophers call it metaphysical realism.

Alan Lowey

Thomas,

The link you supplied is unnecessarily confusing. This link here is much better and written in plain English:

Quantum Entanglement - University of Cambridge

The problem was brought into focus by a famous paper in 1935 by Einstein, Podolsky and Rosen, who argued that the strange behaviour of entanglement meant that quantum mechanics was an incomplete theory, and that there must be what came to be known as 'hidden variables' not yet discovered. This produced a famous debate between Einstein and Niels Bohr, who argued that quantum mechanics was complete, and that Einstein's problems arose because he tried to interpret the theory too literally.

However in 1964, John Bell pointed out that for certain experiments classical hidden variable theories made different predictions from quantum mechanics. In fact he published a theorem which quantified just how much more strongly quantum particles were correlated than would be classically expected, even if hidden variables were taken into account. This made it possible to test whether quantum mechanics could be accounted for by hidden variables. A number of experiments were performed, and the result is almost universally accepted to be fully in favour of quantum mechanics. Therefore there can be no 'easy' explanation of the entangled correlations. The only kind of hidden variables not ruled out by the Bell tests would be 'non-local', meaning they would be able to act instantaneously across a distance.

...............

Am I right in thinking that the discovery of particles traveling at 10,000 times the speed of light would make quantum mechanics "complete"? Einstein's relativity would simply be sent to the recycling center and the concept of quantum superposition not needed.

Alan

Thomas Ray

This [link:www3.amherst.edu/~jrfriedman/NYTimes/071100sci-quantum-mechanics.html] New York Times article [/link]from 2000 explains in pretty clear terms how experimental evidence fits (or doesn't) to the question of locality and realism:

"An experiment measuring how one observation affects a later one should distinguish whether quantum mechanics or a macrorealistic theory rules the everyday world.

The difference between the two can be seen by thinking of a child swinging back and forth in the dark. The two quantum states -- clockwise versus counterclockwise current or the alive versus dead cat -- correspond to the child's being on the left- or right-hand side of the swing's arc.

Imagine shining a flashlight on the right-hand side of the swing and seeing nothing. In a macrorealistic theory, the child continues to swing back and forth, undisturbed.

In quantum mechanics, however, the mere act of looking, whether the child is seen or not, disturbs the possibilities because, as Dr. Leggett explains, the superposition has been destroyed.

In essence, in a quantum mechanical world, not seeing the child on the right-hand side resets the child's swing to the top of left side of the arc, altering the probabilities of where the child will be seen later.

And that, most physicists believe, is what the experiments will eventually show.

'I think most physicists, including myself, would be extremely surprised if quantum mechanics did fail for large objects,' Dr. Lukens said. But, he added, 'Every so often we are surprised.'"

Note that the quantum mechanical interpretation is conditioned on prior probability. A non-probabilistic classical framework is not burdened with that assumption.

Thomas Ray

Alan, you're confused because you still think that entanglement only refers to quantum entanglement.

John Cox

Alan,

Nice links, as were those from Tom and Fred. I need to learn more (much more) of topology before I address an idea about the why and where-for of rotation empirically, and hence OAM. But I quite understand your fascination with the rotating helix as a key to understanding and inquiry, much like John Merryman loves vortexes. The thing is both can be found in the framework of Joy Christian's work if you follow the very practical comments of Jonathon Dickau on March 5 & 6. Once I have a better handle on terminology and usage I'll get back to this as the origin of rotation, but for now....

The rotating helix being a model of EMR is also a preferred idea of Peter Jackson, and one I've toyed with over the years in amateurish fashion. The problem is not with the concept but that it is not complete. While it provides the typical sinusoidal curve which is the signature of any electromagnetic inductance event, it does not provide an endpoint which is necessary by Planck.

E=hv states that the quantity of energy in the Planck Constant will be present in each and any wave event, and the photoelectric effect means it must be distinct. The helix, rotating or not cannot distinguish where that particle moment is. It depends on an observer position looking at the helix and saying 'Now'. Which if you think a moment, kind of stretches the relativity principle beyond rational bounds.

Say we have a large ball. Paint it black and put it out in space. Now we poke an axle through it and start it rotating gently. We hotwire a highway marking paint truck, load it on a rocket and go paint a reflective stripe on the ball pole to pole, so that we go from one pole to the other as the ball makes one full revolution. Now as a paradox twin is returning home he has a space buoy which when caught in the headlight of his spaceship will look for all the world like a big helix corkscrewing through space. Of course his headlight only shines on a portion of it but enough to see that it is helical. It's not really a regular helix though, there is probably a proper geometric name for the stripe so let's call it a 'helipoid' until somebody that knows corrects me.

Now. Whether a helix or helipoid, we have a picture of OAM. If we want a model of EMR and the signature the sinusoidal curve we can use the helipoid. The speed of axial rotation is constant but at the surface progressing from pole to equator the true speed on the stripe will increase to maxima, then fade back to axial speed at the other pole. This would mean that a repetitive event occurs in any wave event such that the density of energy changes with an expansion of size that maintains an equivalent angular momentia at any given point along the helipoid, while producing a true physical particle moment at the endpoints of the wave event. It just looks for all the world like a rotating helix.

If we want a model of an evanescent wave in the field of an electron, or electronic field of an atom, we can use the helix. It too is the signature of angular momentum. At origin of such a wave event the helix would look for all the world like a perfect circle but would still be a regular helix because the rotation progresses across time, it just has not started to propagate across space. And this is where topologically S2 morphs in deformation into S3.

Given pi is irrational, a true sustained finite length of radius would require rotation because the length on circumference would continually seek completion to behave spatially as a perfect circle, or the circle must continual deform.

Sorry for the length of this. One of these days maybe I'll figure out how to post links without freezing up my POS cheap idiot box. The Geeks won't deal with me without a credit card, like I want some Ukrainian 'freedom fighter' to hack what little I have in the bank so they can default on 150bn they owe the Ruskies. Pewrsonally I think Kerry and McCain should have come home from Nam before they poked their noses in over there. Peace, jrc

Alan Lowey

John and Thomas,

I genuinely appreciate your attempts to make the situation clearer for me. I have a mental block when it comes to the term "classical" though. In this next link which I happened across, they explain it thus:

Cosmic Experiment Aims To Close Loophole In Quantum Theory (Mar 5 2014)

In the classical picture, two objects in different regions of space could not influence each other faster than the speed of light.

This is my problem. I've convinced myself that the 'classical' picture of reality is wrong. Just like a whole list of eminent scientists of the day. I was convinced of this since my schooldays and even though I studied physics and astronomy at degree level, I never succumbed to accepting the mainstream belief of Einstein's relativity, or anything else for that matter. I've formulated my own theory of where it all went wrong and it starts with Newton's theory of gravitation without a mechanism.

Our differing views is due to cognitive bias imo.

Alan

Alan Lowey

Congruence bias made the most impact when reading through the list.

John Cox

Alan,

I'm okay with individual cognitive bias. I've certainly got my own. jrc

Robert McEachern

Tom,

"the coin exists in a definite unmeasured state in my pocket, whether I choose to measure it or not"

If you "choose to measure it", then it would not be unmeasured.

But you were asked to choose to make that measurement, and then explain how your framework can confidently state that the coin is now in a definite state of being either heads or tails, while it, simultaneously, never ceases to be a superposition of both heads AND tails (it never becomes other than a two-sided coin) and while another observer, can just as confidently state that it is, simultaneously, in the exact opposite state, than the one that you have measured, by merely choosing a different axis of observation.

Those are the perfectly correlated, perfectly repeatable, perfectly verifiable, and perfectly falsifiable events, that your framework needs to explain, if it is to account for even such mundane objects as the coins in your pocket.

Rob McEachern

Jonathan Dickau

I'll begin this discussion again here...

Consider random coin flips onto a finite flat surface. What happens if we change the measurement space from a flat piece of paper to a Möbius strip? If we make the strip attractive or sticky, so that coins lie flat to its surface when thrown, there is a continuous range over which the coins might lie at a particular angle to a fixed observer - and therefore considerable ambiguity over what constitutes 'heads' or 'tails,' because a determination requires a choice of evaluation criteria by the observer, as to which way is up. If we further stipulate that a 'heads' showing on one side of the strip is a 'tails' as seen from the other - a fairly ordinary assumption - we can then talk about quantum correlations and proceed to an analogy with Joy's model.

We tend to think of space as a collection of outward facing orthogonal extents, and R3 is such a space whose unitary norm is a 2-sphere. That is; the Euclidean 3-space R3 is of the nature of a 2-sphere or S^2, in terms of its variational properties. So the conventional assumption of R3 as a background space is more precisely stated that local space approximates the interior of an infinitely large 2-sphere. However; it is erroneous to assume that the geometry of spaces continues to have this nature, as the number of dimensions increases. In fact; we need only move up to dimension 4 to have non-commutative terms appear in distance relations. Accordingly; air or space navigation (3D plus motion) uses quaternion algebra.

If you look at the Mathworld entry for 'Ball' it is clear that the maximal (hyper-) volume occurs for dimension ~5.25, and falls off thereafter. The fact that the 24-dimensional Leech lattice is the maximally compact close-packing structure clearly shows that the image of space as a flat collection of outward facing extents breaks down at some point. When geometry of higher dimensions is involved with Physics; one must always consider what the intrinsic properties of that dimensionality are. Some spaces offer a great variety of smooth or piecewise linear spheres, including exotic ones, while other dimensional spaces are rather tame. But Joy has discovered that if we assume the 4-dimensional and 8-dimensional sphere constitute the background space we inhabit, then there is a natural explanation for quantum correlations via topology - because these spheres are parallelizable and parallelization is like forcing all coins to lie flat on the same fabric.

Specifically; Joy posits that space is a parallelized 3-sphere residing in an embedding space with the topology of a 7-sphere, both of which have Möbius-like surfaces. So while this looks locally-flat, it is very different from R3.

All the Best,

Jonathan

Jonathan Dickau

To be very explicit...

I am stating that Joy's explanation for quantum correlations explicitly involves the properties of Möbius-like surfaces, applied to the background space our universe inhabits. If you understand that the topology of Möbius strip is a twist away from a flat space, and imagine what it would be like if you could twist a 3D space into the next higher dimension in the same way (creating torsion), then an understanding will emerge about what Joy has been saying.

All the Best,

Jonathan

Alan Lowey

Johnathan,

That explanation sounds just like the aether/topology equivalent of a twisting helical wave/particle solution.

Alan

Alan Lowey

Hey, I've found a youtube video which is an excellent summation of the whole caboodle:

Divinely Planted Quantum States

Alan

Alan Lowey

At last! Someone in authority saying that a simple solution is assuming that Einstein's relativity is wrong and that faster-than-light communication is possible. "The obvious conclusion" given at Time = 6 min.

Alan Lowey

LOL!

Fred Diether

Niles Johnson: Visualizations of the Hopf fibration

Alan Lowey

Too much math not enough common sense

[deleted]

Very nice, Jonathan.

You write, "When geometry of higher dimensions is involved with Physics; one must always consider what the intrinsic properties of that dimensionality are."

This is true not only for higher dimensions, or else Joy's detractors would have seen the error of Bell's choice of measure space long before he did. If one thinks that R^3 is a big enough configuration space for what we observe, it is only because they employ the infinite dimension Hilbert space on the interval (- oo, oo). Why, one would ask, is that not a big enough space for any physical measurement purpose, given that it is infinite?

Because it is actually not infinite. It is two-dimensional, like the complex plane which the Hilbert space generalizes.

The real R^3 is what it is -- it's what we experience as 3-dimension creatures with 4-dimension brain-minds. The physics of Bell's theorem does not reach the 3 dimension level, nor the 4. It is not analytical at all.

Conventionally, quantum theory assumes a normed time metric, t = 1, on the assumption that it is identical to the measure interval (- oo, oo). It is not.

As Hilbert space generalizes the Euclidean plane, topological space generalizes the Euclidean sphere. The simplest complex sphere, S^3 -- the Riemann sphere on which Einstein formulated the Lorentzian metric -- has only one simple pole at infinity, not two. It is this point at which R^3 is compactified and where the definition oo/0 = 1 departs from the linear arithmetic rule that division by zero is impossible, and which fixes the true initial condition of an arbitrarily chosen time metric. In real measure space, division by zero is still impossible; however, real measurement results reflect factorizability of higher dimensions in the limit of the division algebras (S^7), and this allowance accounts for the nonzero torsion of parallelized S^3 that results in realizing the "impossible" Bell prediction E(a,b) = - a.b

Joy's claim has always been crystal clear: nature's choice of topology is itself the hidden variable.

All best,

Tom

Thomas Ray

Argh. Lost my log-in. Last was mine.

Richard Gill

All this could be fine, perhaps, if Joy's math were correct. Unfortunately (IMHO) it isn't. It's a kind of science fantasy instead. As poetry, it is inspired. But changing definitions mid argument, confusing local and globally defined variables, mixing up "for all" and "there exists...".

Take the recent simulation experiments for instance. According to Joy, a "state" is a pair (e, theta) which has to satisfy some property for all a and b. He verifies this property for one particular a and one particular b. It is easy to check that no (e, theta) exists at all, satisfying the property for all a and b!

He was lucky that some half-baked derivation from his S3 "model" ended up looking much like detection loophole models studies decennia ago by Phil Pearle, Caroline Thompson and many others. Michel Fodje was able to latch on to this and produced a first computer simulation of something vaguely like Joy's model (some formulas came from Joy, others came out of thin air). However it didn't quite work but after a lot of hard work we were able to find the version of the unsharp spinning ball model which exactly reproduced the cosine, which Joy could thereafter "adopt" as his own ... in Pearle's (1970) classic paper.

Joy has nowhere given a *derivation* of r ~ 2/sqrt(V) -1, where V ~ Unif([1, 4]), from Joy's S^3 model. He has just adopted it. We know from Pearle's work that this particular choice is not even unique. So even if Joy could derive the probability distribution of r from first principles, there is no reason why it would coincide with Pearle's.

Joy's simulation model is a local hidden variables model which can be interpreted in two ways: (1) detection loophole, the outcome of measurement is ternary not binary. The statistics do not violate the generalized Bell inequalities for a 2 x 2 x 3 experiment (2 parties, 2 settings, 3 outcomes). (2) conspiracy loophole. The probability distribution of the hidden variables depends on the settings a, b. Easy to get whatever correlations you like.

Thomas Ray

" ... confusing local and globally defined variables, mixing up 'for all' and 'there exists...'

Someone is surely guilty of that, though it is not Joy.

Local-global distinctions disappear in the topology of nonvanishing torsion.

Thomas Ray

Richard, your tendentious argument conspicuously continues to disregard the configuration space in which physical results are realized. You write:

"Take the recent simulation experiments for instance. According to Joy, a 'state' is a pair (e, theta) which has to satisfy some property for all a and b. He verifies this property for one particular a and one particular b. It is easy to check that no (e, theta) exists at all, satisfying the property for all a and b!"

That's because your space is not big enough to see that properties satisfied for particular a are satisfied for all b ; and those satisfied for particular b are satisfied for all a .

S^3 is identical to S^2 X S^2. That isn't poetry; it's a fact of topology. Analytic continuation isn't poetry; it's a fact of analysis.

Joy Christian

Tom,

There is no need to defend my work against every uninformed polemic. My results and arguments speak for themselves. Serious scientists are studying my work using their own brains. They are not interested in polemics. They can think for themselves.

Joy

Richard Gill

Tom, as usual your arguments are totally uninformed of the actual content of the matter at hand. In other words, they are completely vacuous.

You write "That's because your space is not big enough to see that properties satisfied for particular a are satisfied for all b ; and those satisfied for particular b are satisfied for all a ".

Whose space??? I'm talking about Joy's space. I'm talking about the Math of Joy. He specified the spaces involved...

His own computer implementation of his own math exhibits the same feature. Checking something holds for a particular a does not guarantee that it hold for b as well.

It is all science fantasy, it is not mathematics and it is not physics.

Richard Gill

And as Joy said "Serious scientists are studying my work using their own brains. ... They can think for themselves."

Take an example from that, Tom. 1. Study Joy's work, and 2. use your own brains.

Fred Diether

Is Richard grumpy today? :-) We have studied Joy's work quite extensively; thank you. You freely admit that you don't understand some of Joy's math so why don't you get back to asking questions about what you don't understand? We will try to explain. Are you not asking questions anymore because you don't want to understand?

Fred

Thomas Ray

"1. Study Joy's work, and 2. use your own brains."

Richard, I should think it obvious that I am not using your brain to study Joy's work, or anything else.

That's part of the point, really -- the objective science is independent of our brain-minds. We do not live in a brain-mind created reality.

Thomas Ray

"Checking something holds for a particular a does not guarantee that it hold for b as well."

It doesn't? Quantum correlations don't exist?

Richard Gill

Fred wrote "Is Richard grumpy today?". I was more than usually annoyed at Tom's nonsense. I am sure it is well meaning, but it raises the level of noise here to such a level that a normal discussion between sensible people is drowned out completely.

By the way, to those studying Pearle (1970): there are a lot of misprints and a lot of funny notations. The normalzing constants sometimes get out of hand but fortunately one can always normalise to find the right answer. It is worth struggling through to the end. So many important innovations in one short paper. For instance, on the way he introduces the chained CHSH inequality for experiments with more than two settings, which later has been reinvented several times.

Thomas Ray

Richard, why do you think it is nonsensical or unreasonable to ask you to explain how you know the space you calculate in, is capable of producing the quantum correlations we observe?

Of course, I mean well.

Thomas Ray

" ... one can always normalise to find the right answer."

Then why do you disallow nature the same freedom? Experimental metaphysics would demand it, in order to determine if a quantum-classical boundary really exists. If nature doesn't normalize, there is no such boundary -- no wave function collapse, no isolated points of spacetime.

Jonathan Dickau

Thank you Richard..

But another participant in this forum was already kind enough to forward to me Pearle's paper, which I am beginning to work through. I am currently of the opinion that differences arising in the interpretations of Pearle and Christian are related to whether we ascribe uncertainty to missed observations and lack of knowledge or the indeterminacy of events themselves.

This is rather a slippery subject, and I am again reminded of Heisenberg - who used the term 'unsharfe' - which implies more that quantities are indistinct than that they are uncertainly observed. Perhaps a measured entity can have an actual orientation halfway between two axes of measurement, rather than a 50-50 probability. But in any case; I am eager to read more about what Phil Pearle has to say.

Regards,

Jonathan

Jonathan Dickau

And yes Tom,

I'd rather imagine a real child swinging, whom we can only see part of the time, rather than see it as a situation where by watching we can keep the child from appearing or make it insubstantial somehow. This is one case where the absence of evidence is not the evidence of absence we might imagine it to be.

All the Best,

Jonathan

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