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

" ... 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

Jonathan,

""Does physical reality evolve with time?""

Or is time simply an effect and measure of the process of evolution?

Is this process truly a vector of evolving configurations, or is it one state that evolves?

Is blocktime necessary, or is it real dynamism?

Regards,

John M

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

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

Rick,

"Personally I have no idea what you are talking about, and I believe I have a good appreciation for continuous functions."

The subject is, a measurement function continuous from the initial condition.

Your octonionic construction is incapable of computing that function. It is not an analytical framework. All along, the value of linear algebra in Joy's measurement framework has been restricted to defining a measure space (Hestenes' spacetime algebra), not describing the function. He most certainly has addressed the subject in those terms, as have I.

Best,

Tom

Rick,

To elaborate further, if you read this whole thread and my reply to Jonathan:

"I always get a little uncomfortable here when we get into the properties of the division algebras in which the measurement framework is explained. It isn't the discrete measure space that accounts for the result; it is the simply connected continuous function that allows correlation of points of the parallelized 3-sphere. I look at the division algebras as a scaffold from which to build the framework, and I fully expect that when the measurement *theory* is complete, the scaffold may be removed."

Only if you could prove that your octonionic construction is simply connected, would it be consonant with Joy Christian's measure space. I see no way to do that, since the R^4 of your construction is a different animal than the S^3 of Joy's.

Tom,

And one is nature's creation.

Regards,

John M

Tom,

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

Keeping in mind that that linear order is also the ticking of the individual clock and nature is lots of individual clocks all ticking their own rate in the same space. So space is the non-linear state and time is the linear order.

Regards,

John M

That sounds fine, John, for chatting purposes. The work comes by way of incorporating it into a theory that corresponds to how nature actually behaves.

Best,

Tom

Tom,

"The work comes by way of incorporating it into a theory that corresponds to how nature actually behaves."

In other words, one that doesn't include blocktime and explains why time is asymmetric.

Possibly one where time is an effect of action and due to the inertia of this action, proceeds through the changing patterns resulting from the dynamics of nature. One where past and future do not physically exist, but are projections of this process.

Now which aspect of it should be mathematically modeled? Relations between measures? We could use the math of relativity to correlate intervals of distance and duration, or we could use ideal gas laws to correlate scalars of volume, temperature and pressure.

Regards,

John M