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

Joy, this is just beautiful! My quick impression is that it may actually be experimentally replicable with electron input. It already reads like an experimental computation model.

Still nothing from the cone of silence where the critics are huddled?

(Great work by Michel Fodje!)

And I think that because the statistical function of Fodje's simulation verifies the topological structure of Roth's simulation, we can conclude, significantly:

The simulation of a continuous function is a continuous function.

Does it get more physically real and local than that?

I picked up a portion of a comment you made to a correspondent in sci.physics.foundations that I think is relevant:

"It is also important to realize that an orientation of a manifold (like that of a 3-sphere) is both a local and a global property at the same time. It is local in the sense that a basis is chosen at each point of the 3-sphere. But since this choice must be made consistently throughout the 3-sphere, its orientation is also a global (or a topological) property."

This local-global relation is an absolute breakthrough accomplishment, for future research directions -- including quantum computing without entanglement.

Yes, beautiful and impressive work for mathematicians. While not wanting to be a kill joy, it is only mathematicians who will insist that all lines and all planes, no matter their size contain the same number of points as my post on Nov. 5, 2013 @ 11:06 GMT refers.

Physicists, are now belatedly catching up with the idea that this is unlikely to be so. Einstein was already unto this long before as mentioned in a link. In a likely Quantum gravity theory there is likely to be a Planck limit at 10-35m. That being so, this line _____ and this _____________________ cannot contain the same number of points as Tom claims, since a Planck length cannot contain more than one point as it is indivisible.

I therefore stand to be corrected, that both Bell's theorem and its Disproof being founded on the assumption that there is no limit to distance at the Planck length will not be of much use to physicists standing at the gate between Quantum and Classical physics waiting and ready to "Tear down this wall"!

Akinbo

There is no wall, Akinbo.

"In a likely Quantum gravity theory there is likely to be a Planck limit at 10-35m."

What makes you think that?

Thanks for showing up, Florin.

All spaces of a continuous measurement function are make-believe, because a computer is a 3-dimensional instrument. What you, Vongehr, Gill and others have never understood, is that computing in a 4-dimensional continuum introduces a degree of freedom that differentiates the choice function of the experimenter, or programmer, from random input that simulates the choice function of naturally occurring classical randomness.

The computer doesn't care what space it is computing in. Until you realize that the Python implementation of a Java program implies that the simulation of a continuous function is a continuous function, you are going to be stuck in an outdated belief that 3-dimension computability = reality. Welcome to the 21st century, where Flatland is only a memory.

Best,

Tom

I know, Joy, but I don't think he making the claim to intentionally mislead. After all, the programmers who wrote these simulations are his own colleagues. He has to argue with them, not us theorists.

I am convinced that he thinks -- along with other believers -- that reality cannot be expressed in any but probabilistic terms (Vongehr has raised this belief to a level of religious fervor) and any *objective* evidence to the contrary must be a trick of some kind.

Sooner or later, one accepts that classical randomness is self-correcting, that nature fulfills all evolutionary possibilities completely and continuously -- or one condemns oneself to a prison of existential nihilism.

If it were true that the subjective mind creates external reality by changing the probability of physical manifestation in a moment, that reality is observer-created, it would be impossible that free will exists as other than illusion. All the probabilities would self-annihilate in a single bounded lump of perfect three dimension information -- like a six-sided die with no markings, no pips.

All along, probabilists have assumed that the pips we draw on the two dimension surface of a three dimension reality represent the total sum of information in a moment. They have forgotten that we don't live in three dimensions, and that the moment is much larger than even the superposition of states that they imagine. Or can imagine.

All best,

Tom

Here's a good example of what I'm talking about, picked up at sci.physics.foundations from John Reed:

"I have looked at the code for this new simulation. If we lived in a two dimensional world, it would mean something, but I don't see any connection to the previous simulations or the experiments dealing with Bell's theorem. There is no reference to Clifford algebra, bivectors or a parallelized three sphere. It's all now just picking random numbers and taking the cosine of their difference. What is the meaning of that? The experiments are done in three dimensions."

Continuous binary random input (the ThrowDie function in Chantal's program) is not a case of picking random numbers; it is a case of input to the continuous function that uses classical randomness to simulate 4-dimension continuity.

I have heard Joy explain over and over and over to countless individuals that the same classical randomness that applies to Newtonian physics produces strong quantum correlations without assuming entanglement, superposition and nonlocality. The measurement framework is entirely *classical.* Therefore, manifestly local.

CA and the bivectors thereof, apply to the spacetime algebra (Hestenes) which is simply another mathematical translation of classical (Minkowski) spacetime. The parallelized 3 sphere is the physical measure space of the simulation. The elements are all represented.

Tom

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