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

One philosophical result of John Bell's choice of measurement space is a school called "super-determinism," which maintains that deterministic theories imply the absence of free will. Bell addressed the issue in a BBC interview with Paul Davies in 1985:*

"There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the 'decision' by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already 'knows' what that measurement, and its outcome, will be."

I think that believers in Bell's result (i.e., quantum configuration space cannot be mapped to physical space without a nonlocal model) tend to falsely associate Joy's measurement framework with superdetermism and the absence of free will. This is true only if one identifies "free will" with the choice of an experimenter to decide what measurement criteria to use.

Joy's measurement framework does not constitute a superdeterministic theory -- indeed, the experimenter's choice is irrelevant, because the experimenter is only another element of nature's choice. That Bell characterizes nature as "inanimate" betrays an ontological bias toward particle reality (and probability), while Joy's epistemic framework allows no bias of nature toward a predetermined outcome. The experimenter has just as much free will as the external reality.

*Picked up from a Wikipedia article which continues:

"Superdeterminism has also been criticized because of perceived implications regarding the validity of science itself. For example, Anton Zeilinger has commented:

'[W]e always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment, since then nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of nature.'"

Joy's framework explicitly verifies that nature does *not* determine the questions, nor the outcome. It is perfectly consistent with John Wheeler's participatory universe ("The situation cannot declare itself until you've asked your question. But the asking of one question precludes the asking of another."). The initial condition of the continuous measurement function is indifferent to which element of nature, the experimenter or the classicly random outcome, decides the question.

Tom

You say it well Tom..

Just upstairs, you state "The initial condition of the continuous measurement function is indifferent to which element of nature, the experimenter or the classicly random outcome, decides the question." This sums an important insight up nicely, as both nature and the experimenter may determine some outcomes, but an observer can't know whether what's observed reflects nature's choice or the orientation of the observer and/or observing apparatus.

I think part of it is that for most people there is a disconnect between a continuous range and discrete outcomes, but that is a built-in part of nature's way of representing things. And speaking of what's built-in, I like Fred's comment further up that nature created the number types in the reverse order we humans found them in, because the Reals are a limited special case, where the Octonions are the most general type, and the existence of the Reals - via the sums of squares - proves that the Complex, Quaternion, and Octonion numbers must be part of what defines reality, as well.

So in a way; the Octonions had to exist, for the Reals to come to be.

Just my two cents,

Jonathan

Tom,

There is no translation. Chantal's code is the drawing of a cosine curve sprinkled with some random noise, while Michael's code obtains the correlations from experimental outcomes.

So one is a decoy, the other one is the real deal.

On a scale from 1 to 10 I would score Chantal and Michael as follows:

Code quality Code value

Chantal 10 2

Michael 7 8

" ... by simply using a linear progressive bias the correlation curves can approach the QM curve."

Florin, one can take any of the machine languages separately in which Joy's measurement framework has been simulated, and bias it toward a linear result. This is a limitation of all machine languages (difference vs. differential) to simulate a continuous function.

The truly surprising and meaningful result of transporting the algorithm to four different programming languages is evidence that *the simulation of a continuous function is a continuous function.* That is, every time we use classically random input regardless of the program language, we get a smooth continuum of correlated points. This makes the simulated measurement framework a true nonlinear simulation of continuously random input -- in other words, random input to a 3 dimension simulation generates a 4 dimension reality, which is the one in which we live.

Florin, programming skill -- and even the debatable efficiencies of programming languages -- is entirely irrelevant.

The *science* of the simulation outcome is independent of computer results. Until you (and Vongehr and Gill) understand the meaning of a measurement function continuous from an initial condition, you are getting nowhere toward understanding why quantum correlations are a natural result of continuous classically random nonlinear input to the measurement function.

Florin,

Let me try and explain it this way:

Your consistent misspelling of Michel's name ("Michael") illustrates how languages differ in linearly ordered terms without affecting the meaning. The French spelling Michel means the same thing as the English transliteration of the Hebrew name Michael. Same goes for the Spanish Miguel and the Russian Mikhail.

The scientific meaning of a continuous measurement function simulation is indifferent to how the terms are linearly ordered. What we want to find out, is what happens when totally disordered elements of reality are subjected to a classically random function (coin-toss probability) -- is the result more disorder (noise), or newly ordered relations (information, such as names found in a look-up table)?

What we see is that the probability -- given a function continuous from the initial condition -- that the function generates ordered relations, is exactly the same as the probability for quantum correlations under the assumption of linear superposition (with implications for nonlocality and probability theory).

It makes the difference between a probabilistic measure schema on a disconnected space, and a deterministic classically random and continuous measure space. Christian's measure space assumes only initial condition and a measurement function continuous from the initial condition. That assumption cannot be made on the real line of ordered relations -- it requires the nonlinearity that we witness in almost all natural phenomena. The inescapable conclusion is the lack of boundary between quantum and classical domains.

Indeed!

The basic idea that there are persistent structures in Math, invariant regardless of how we approach or approximate them, seems alien to many. However, if one digs into the Math deeply enough; this seems to happen again and again - to a point where it seems undeniable that there is some pre-existing order to Math, that must appear no matter how it is probed.

That is the wonder of things like Frobenius' conjectures and the Hurwitz theorem, or the Poincare conjecture proof. The results definitively show that certain things believed to be separate or separable are intrinsically linked by the very nature of higher-order numbers and geometry.

It is unavoidable! Specific higher-order numbers and spaces MUST exist; and if higher-order spaces exist in any form, they MUST observe some specific geometric properties. This is hard for many people to wrap their heads around, however.

Regards,

Jonathan

Also to mention..

The nature of continuous number fields is different in kind from discrete numbers. If we observe the behavior of squaring over the positive Reals, endlessly iterated, only a value of 1 is stable - and any increment more or less, no matter how small, begins a steady march to either 0 or infinity. Zero, one, and infinity (the point that's typically forgotten), sounds familiar.

This result for multiplication also implies the inverse for division - infinite divisibility - which is part of the significance of the normed division algebras. In my view; their existence is the whole basis for reversibility, and symmetries, and finite groups, and a whole lot of other things considered essential to Physics.

More later,

Jonathan

Jonathan,

"It is unavoidable! Specific higher-order numbers and spaces MUST exist; and if higher-order spaces exist in any form, they MUST observe some specific geometric properties. This is hard for many people to wrap their heads around, however."

This may be mathematician talk, but, just in case: Are you saying that there exists actual physical volumes, your 'spaces', in addition to but external to our observed universe? Is it a higher dimensional reality that: "This is hard for many people to wrap their heads around?

James Putnam

This is amazing to me.

Except for some technical programming questions in sci.physics.foundations (which have been addressed and disposed of) I see only internet silence on this simulation that critics IIRC universally said is a prerequisite to having Joy's measurement framework taken seriously.

As they say in American baseball -- what are you waiting for, egg in your beer?

Tom

Joy, I agree. One has to have a personal agenda aside from the good of science to behave this way. Some made their agenda obvious from the beginning. I can't find any excuse for the others.

Leon Lederman and Dick Teresi asked, "If the universe is the answer, what is the question?"*

Non-Realists such as Anton Zeilinger imply that there are no questions at a foundational level. "Zeilinger says that some of the alternative non realist possibilities are truly weird. For example, it may make no sense to imagine what would happen if we had made a different measurement from the one we chose to make. 'We do this all the time in daily life,' says Zeilinger -- for example, imagining what would have happened if you had tried to cross the road when a truck was coming. If the world around us behaved in the same way as a quantum system, then it would be meaningless even to imagine that alternative situation, because there would be no way of defining what you mean by the road, the truck, or even you."

Zeilinger assumes -- as do all Bell's theorem adherents -- that the definition of objects precedes the measurement of correlations between objects. It should be no surprise, therefore, that the assumption of quantum entanglement generates a measurement result based merely on the definition of itself. The proof of the theorem is a nonconstructive tautology.

What Bell loyalists neglect is that there *is* no way of objectively " ... defining what you mean by the road, the truck, or even you." And there doesn't need to be. The realism of continuous functions does not depend on discrete definitions -- in every experiment purporting to show quantum entanglement and violation of Bell/CHSH inequalities, the experimenter and the apparatus are independently defined as real and local.

In *no* physical naturally occurring continuous phenomenon is this the case. The orbital path of a planet in reverse obeys the same physical laws as in forward, so it does "make sense to imagine that alternative situation." Zeilinger tacitly assumes that an observer wandering into a quantum system has a definition of itself that affects the definition of other particles in the system -- thereby the classical observer creates the quantum reality.

Were that true, the classical and the quantum space would have a definite boundary. Exploring the boundary would require the classical observer to be a quantum object, so the act of measurement would actually change the definition of the observer. This doesn't happen, of course, so one has to assume nonlocality along with entanglement. Because nonlocality violates relativity, one has to assume linear superposition to make nonlocality work.

Things in relation, however, don't depend on entanglement, nonlocality or superposition *at any scale.* Things in relation are scale invariant and coordinate free.

It should have been the simplest thing -- and would have been, were topology as advanced in 1964 as it is today -- to understand that Bell's choice of measure space (the real line) where neighboring relations are linear, is the wrong fit for nature, whose measurement functions are demonstrably complete, continuous and nonlinear.

Joy's simply connected measurement framework fits the observation of strong quantum correlations without assuming a rigged space that applies only to quantum measurement. It's the space in which we live, the space in which we experiment, a space which we are not compelled to imagine exists only in a mystical quantum entangled world.

The question is: Can the simulation of a continuous function be a continuous function? It is, and so the universe is the answer. The metaphysical realism of what exists in relation cannot be other than manifestly local.

Tom

* *The God Particle*

It's been over a month now since the start of this thread, and still the only defender of standard quantum (i.e., probabilistic) theory to come forward is Florin Moldoveanu. His arguments are refuted -- are they the best that can be made?

Referring again to the Pironio, et al, paper linked earlier:

" ... there is no such thing as true randomness in the classical world: any classical system admits in principle a deterministic description and thus appears random to us as a consequence of a lack of knowledge about its fundamental description.

"Quantum theory is, on the other hand, fundamentally random; yet, in any real experiment the intrinsic randomness of quantum systems is necessarily mixed-up with an apparent randomness that results from noise or lack of control of the experiment. It is therefore unclear how to certify or quantify unequivocally the observed random behaviour even of a quantum process."

The authors assume that nonlinear positive feedback (noise) in a quantum system can be mitigated by linear negative feedback on the assumption that quantum theory is "fundamentally random." Because of this assumption, the experimental controls on Bell-Aspect type results are statistically reconciled with the theoretical result (Bell-CHSH inequalities) by the imposition of negative feedback from the *experimenter.* In other words, by disallowing nonlinear positive feedback in the experimental protocol, the experiments validating Bell's theorem beg their own conclusion.

Joy's result shows unambiguously that natural nonlinear random input results in the smooth function of quantum correlations, with no boundary between quantum and classical domains.

Refute that.

Tom