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

"You (unnecessarily) assign lambda as the orientation choice for the algebraic basis used, then sum over lambda_k with the requirement on Nature of a 50-50 statistical choice of +1 and -1."

Come on, Rick. The variables are nonlinear input to a continuous function. The experimenter is forbidden to assign initial condition. That's the whole problem with Bell's choice of measure space.

"The math works out to the same conclusion for either orientation choice."

The math does not work, however, for a function continuous from the initial condition. One would get only a flat line for A, flat line for B.

Tom

Aw shucks,

Rick makes some good points, and deserves some acknowledgment for what he gets right. It is absolutely accurate to state that some of the constructions used by Joy are cast in the Quaternion case, because it captures the most salient features, and that this works because S3 and S7 share certain essential properties - topologically speaking. It is clear that the case stated with S7 is more general, but might be harder to sell because people are scared off by Octonion algebra.

Beyond this; I think that the dynamism I talk about in the comment below is an essential feature of the Octonion algebra that makes it indispensable, for explaining the Physics involved, rather than just a convenient representational schema. On the other hand; I think that realizable geometry is absolutely necessary to Nature, for creating persistent structures. The Octonions describe the actions and motions possible on S7, and without the curious properties of that algebra, some portions of Joy's argument (especially as involves GHZ states) fall apart.

I think the geometry and topology involved does constitute a deeper truth, but this does not make the powerful algebra of the octonions any less essential to understanding those remarkable properties.

Regards,

Jonathan

I should probably add..

It is obvious to me that without some of the dynamic properties of the Octonions, it is likely not possible for nature to evolve topological spaces at all, but their existence (following the reasoning of Kainen) assures that this geometry must evolve or emerge. Again; the hierarchy of spaces smooth > topological > measurable, which Connes talks about (also in NCG 2000) involves the application of rules with progressively stricter conditions, as Fred was talking about with algebras above.

Spelling this out; the Associative rule in Algebra is pertaining to the subject of Surfaces or Topological distinctions - because it deals with interiority/exteriority, in determining what is or must be inside of what. The applications of parentheses can be equated with the creation of a topological boundary or distinction, in that each may be seen to be a container or separator from those elements that lie outside the boundary.

In my view; this process of acquiring topology flows naturally, once S7 or the Octonions come to be, or are well-defined as a system. I don't see how one could get topology from a blank slate without the strongly directed evolution of a number type like the octonions.

All the Best,

Jonathan

" ... in my view algebra provides merely a convenient representation of the deeper truth, which, for me, is topology---in particular, the topologies of S^3 and S^7 (I do not care much about S^1)."

Right on! Whatever misunderstanding that I or anyone has about this measurement framework, let it not be that the model isn't analytical.

Joy,

Referenced document eqs (16) and (17) seem to be multiplying as I stated. Perhaps my cursory look missed something.

Rick

" ... where the relative orientation lambda is now assumed to be a random variable, with 50/50 chance of being +1 or - 1 at the moment of creation of the singlet pair of spinning particles."

Seems clear to me that A and B are dichotomous variables. Classical probability.

Jonathan,

Thank you. That was a serious direct answer. The ensuing conversations were enjoyable to read.

James Putnam

P.S. The enjoyment of reading new on-subject messages about Joy's accomplishment has returned for now.

Tom,

Me: "You (unnecessarily) assign lambda as the orientation choice for the algebraic basis used, then sum over lambda_k with the requirement on Nature of a 50-50 statistical choice of +1 and -1."

You: "Come on, Rick. The variables are nonlinear input to a continuous function. The experimenter is forbidden to assign initial condition. That's the whole problem with Bell's choice of measure space."

You quoting Joy later in same thread: " ... where the relative orientation lambda is now assumed to be a random variable, with 50/50 chance of being +1 or - 1 at the moment of creation of the singlet pair of spinning particles."

Come on me??

I have yet to see Joy weigh in on your connecting his work to your personal view of continuous functions as implied here. Maybe this is because he does not have any better idea than I do about just what you are implying. Personally I have no idea what you are talking about, and I believe I have a good appreciation for continuous functions.

Perhaps you could elaborate.

Rick

If I may offer,

I know that a crucial point Joy makes in his book is the anomalous choice of a binary measurement space by Bell, implying a codomain equivalent to S0, where the unit 0-sphere contains only the points -1 and +1, a disconnected space. A key observation, to understand Joy's work, is that a disconnected measurement space is unduly restrictive, or unrealistic.

Indeed; J.B. Pors et al., in their paper on Shannon dimensionality, show experimentally (using a circular phase plate) that a broader range is available than can be represented by a binary choice. They clearly demonstrate that the actual codomain of quantum correlations is at least as 'big' as S1, or subdivisions thereof, but do not set an upper bound on its actual range.

Joy's assertion that the actual codomain is S3 provides both a continuous range and a simply connected topology. This choice can explain a broad variety of phenomena which have been attributed to non-local entanglement. But the big piece is that the measurement space is continuous, not disconnected.

Regards,

Jonathan

Thanks Florin, for the great picture/quote.

And no John I don't think Blocktime captures the essence of time's mode of transit. The dynamism I speak of is both deterministic and open-ended, so I am really mostly in agreement that it is the evolution of form and structure which creates the flow we see as the progress of time, rather than seeing time as something linear or space-like.

I had an interesting discussion with Huw Price about this question at FFP10, championing my view of Entropy as depicting the spreading of energy or substance into a medium - rather than the common view that entropy represents disorder. His talk focused partly on the utility of the Blocktime view for relativists, and I pointed out some drawbacks (or undesirable implications) in our conversation.

On the other hand, maybe if it was an 8-dimensional block... In that case, though; since the Octonions rule, time's evolution would still be a process of becoming and not a straight line.

All the Best,

Jonathan

Hi Jonathan,

How do you make the connection from the paper that "They clearly demonstrate that the actual codomain of quantum correlations is at least as 'big' as S1,..."? Your last paragraph is mostly right on the money except the codomain is S7. EPR-Bohm only requires S3 which is part of S7.

Best,

Fred

To those familiar with Joy's work, both those in support and those in agreement. I am a novice who is unfamiliar with the computer programs used to do the simulations credited with proving or disproving Bell's theorem, but I have a few innocent, well meaning, even if naive questions to ask:

Do the Lines and Planes contain the same number of pixels?

Are the Planes made up of Lines?

If yes, where did the Plane get its 2-dimension from if the Line has only 1-dimension?

If no, what then is the Plane made of?

Does a short line ___ have the same number of pixels as a long one _________?

Is it right for Digital (discrete) assumptions to be used for simulation and be unacknowledged in giving a conclusive answer to a Continuous debate?

I raise these questions not to derogate from anyone's work. Indeed, I am made to understand by Jonathan that Joy's work is meant to bring back reality to the Quantum domain. A worthwhile task. But we must not sweep anything under the carpet if the truth and the whole truth must be unveiled by this laudable task.

Akinbo

Jonathan,

Given the constant for relativity is determined by the speed of light and the lightcone for any event is only completed by its occurrence, it would seem that while it can be said of the future that something will happen, given this limit, it would seem there is a theoretical and practical limit on actually knowing what will happen. Which complicates basic determinism.

Also, since it is not just a process of becoming, but unbecoming as well, as events fade into the past, with constant dynamic change, the past also gets to be quite obscure.

In a sense it gets back to the cyclical concept of time, as the future/present is being 'woven' from strands pulled from the past.

Florin,

We are on agreement with that.

Regards,

John M

Jonathan,

" ... sequential evolution - through procedural stages - is a must ..."

Actually -- no.

The assumption of linear order is also a blind spot for Bell believers. Nonlinear evolution is evident not only in Joy Christian's framework of quantum correlations, it is evident in the Gould-Eldredge model of punctuated equilibria and in Per Bak's avalanche model. The former is empirical; the latter is mathematical. In every way, the universe reveals itself as a spacious Present in dynamic equilibrium at every scale.

It's appropriate that Master Oogway is a turtle. Those who accept the existential nihilism of a linearly ordered universe believe that every time they poke their head out of the shell, they measure the course of history -- while they miss the wonder of a continuously evolving real world all around them.

All best,

Tom

Tom,

Or protect themselves from an unpredictable non-linear dynamic that can only be navigated linearly. Thus the necessity of linear order in an environment that is frequently hostile to it. We all have our shells, having frequently bumped against yours.

Regards,

John M

"Is it right for Digital (discrete) assumptions to be used for simulation and be unacknowledged in giving a conclusive answer to a Continuous debate?"

Akinbo, a digital computer cannot do other than compute digitally. Every computer simulation of a continuous function substitutes difference equations for the differential equations that describe a continuum.

An analog computer can faithfully replicate a continuous trajectory, given boundary conditions -- that is not adequate, however, to simulate a continuous measurement function with randomly changing boundary conditions.

Therefore, a continuous measurement function simulated on a digital computer requires random input to a continuous trajectory, in order to replicate the function.

Best,

Tom

"Thus the necessity of linear order in an environment that is frequently hostile to it."

So long as one understands that the linear order is one's own creation, not nature's.

Best,

Tom