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

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

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

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

Time isn't asymmetric, John. The perceived linear order of time is created by you (and every conscious observer) in your own mind. Your claim: " ... space is the non-linear state and time is the linear order" is impossible in a continuous spacetime. The problem with your claim, when it comes to how nature actually behaves, is that you can't distinguish it from a personal belief. Time conservation is in fact as firm a physical principle as conservation of angular momentum -- there's the vector-scalar relation that falsifies your claim.

Getting on topic here, that is exactly the trouble with the Bell-Aspect view of reality. Time drops out of the equations of standard quantum theory, so the linear order of things in space (and linear superposition of states) is "just so," given the choice of observer orientation. Your own "just so" story meshes perfectly. Only that isn't how the real world presents itself to us -- all physics is local, and natural events are nonlinear. So much for naive realism.

"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."

Well, that makes no sense, and contradicts itself as well. Inertia is not equivalent to action. In a continuous spacetime, past and future events are metaphysically real.

"Now which aspect of it should be mathematically modeled? Relations between measures?"

What does that mean? If it means the relation between time and angular momentum as described above, you're out of luck for your linear model.

"We could use the math of relativity to correlate intervals of distance and duration,"

And what does this mean?

" ... or we could use ideal gas laws to correlate scalars of volume, temperature and pressure."

Or this?

Best,

Tom

Tom,

Joy's "measure space" is S^3, which is not owned by Hestenes' spacetime algebra. It is owned by Quaternion Algebra. It is only coincidental that spacetime algebra has Quaternion Algebra as a sub. Quaternion Algebra is a 7-fold sub-algebra of Octonion Algebra. Joy could remove all references to spacetime algebra or replace it with Octonion with no loss. So your claim that "Your (my) octonionic construction is incapable of computing that function" has no foundation. I haven't and for that matter can't change Quaternion Algebra in any way that impacts the complete definition of S^3. Your claim S^3 is different from "my" R^4 is specious since my work is not simply R^4 without the algebra behind it, or R^8 for that matter. S^3 is embedded with the norm 1 restriction. This restriction may make for interesting features like closure for Quaternion products of included points, but is WAY too restrictive to be the foundation for a full description of the totality of our physical existence.

The question is not about characteristics of S^3, it is about your claim Joy's work finally made sense to you apparently because it tied into some reverence you held a priori for your definition of "continuous" in regards to the problem at hand, being Bell's Theorem. If you backed into this "revelation", discussion over. A big part of Joy's problem selling his concept is justification of using S^3 "measure space" in a theory that seems to purposely omit details of the actual "measurements" being physically taken, where both in the end seem to statistically accumulate discrete +1, -1 measurement data. If you have substance and not just empty statements, help our friend out by educating the skeptical.

As for your claim on my presentation "It is not an analytical framework", tell me what is wrong with my Ensemble Derivative and how it can't be the foundation for general covariance for meaningful differential equations descriptive of physical reality. Don't do so with more empty statements about Octonion Algebra not being spacetime algebra, or your definition of "coordinate free" instead of the real requirement for a definition that is a proper functional diffeomorphism. Good luck with that.

Rick

Tom,

"The perceived linear order of time is created by you (and every conscious observer) in your own mind."

It is created by the order in which information(conveyed by light) reaches my point of reference, as compared to the order it reaches other points of reference/observers.

The geometry of spacetime is based on the constant of the speed of light, but then the whole dynamic process of light radiating about is then left on the cutting room floor, in order to make the resulting geometry somehow foundational.

"Inertia is not equivalent to action."

No, but it is an aspect of it. Describe for me action without inertia. Even 'when acted on by another force,' amounts to the intersection of different inertial actions.

"In a continuous spacetime, past and future events are metaphysically real."

But your criteria was "how nature actually behaves," not how we happen to map it out. The past at least is metaphysically real in these books sitting on my desk, but in reality, it's another matter.

Regards,

John M

John,

After this, we should move this endless and mostly pointless dialogue elsewhere.

"(linear order) is created by the order in which information(conveyed by light) reaches my point of reference, as compared to the order it reaches other points of reference/observers."

And no doubt you find this statement non-mystical.

"The geometry of spacetime is based on the constant of the speed of light,"

No it isn't.

" ... but then the whole dynamic process of light radiating about is then left on the cutting room floor, in order to make the resulting geometry somehow foundational."

No. Light (electromagnetism) isn't part of spacetime geometry, because general relativity is a theory of gravity, not a theory of light.

"' Inertia is not equivalent to action.'

"No, but it is an aspect of it."

Not.

"Describe for me action without inertia."

Principle of least action.

"Even 'when acted on by another force,' amounts to the intersection of different inertial actions."

True, but irrelevant.

'In a continuous spacetime, past and future events are metaphysically real.'

"But your criteria was 'how nature actually behaves,' not how we happen to map it out. The past at least is metaphysically real in these books sitting on my desk, but in reality, it's another matter."

Metaphysically real elements are in reality, not outside of it.

Best,

Tom

Tom,

You are right. These are points we've beaten near to death already, no sense cluttering this thread,

"Metaphysically real elements are in reality, not outside of it."

As residue of prior events and prior thoughts.

Regards,

John M

Though I was trying to address Jonathan's point about foundational geometries being inherently evolutionary.

Tom,

"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."

And from your message to 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."

I haven't designed a computer, but, given equal efforts at best quality of construction, I would trust the digital computer over the analog computer to more faithfully replicate a continuous function. My reason for saying this is that I envision that the digital computer code does not deteriorate unless used. And, it is used intermittently. The uncoded analog signal experiences continuous deterioration.

The important question of this messages has to do with:

"... to simulate a continuous measurement function with randomly changing boundary conditions.

Therefore, a continuous measurement function ... requires random input to a continuous trajectory, in order to replicate the function."

I removed "simulated on a digital computer", was it required in some way for your statement to reflect accurately your meaning?

Also, my impression of "...a continuous measurement function with randomly changing boundary conditions...(simulation)...requires random input to a continuous trajectory, in order to replicate the function." is that it is not easily clear to me that this should be true.

A little more explanation might help.

James Putnam

Rick Lockyer & Tom,

Thank you Rick for joining in and sharing your opinion here.

Rick: "A big part of Joy's problem selling his concept is justification of using S^3 "measure space" in a theory that seems to purposely omit details of the actual "measurements" being physically taken, where both in the end seem to statistically accumulate discrete +1, -1 measurement data."

Tom replied: "Joy's measurement framework realizes quantum correlations on a *parallelized* 3-sphere. This requires linearly independent vector fields at each point. Which means that actual measurement functions *up to* diffeomorphism are non-degenerate (the function continues) and meet the general relativity requirement for coordinate-free geometry without invoking co-variance. We are talking actual, physical measurement results here, continuous from an initial condition.

I am off track here. Are these "physical measurement results" serving as inputs? If I just don't understand the whole meaning of this exchange, please disregard the question rather than draw this thread off track with me.

James Putnam

For the record..

I do not dispute the notion that the evolution of cosmological form can be, or is, continuous - despite the focus of Physics folks on the swift transitions that punctuate, and sometimes actuate, the course of changes. I was merely focusing on the fact that there could be no complex form, without the dependency on existing conditions (at a given time and place) from which to build. I was alluding to the fact that, in Octonion algebra, a solution is built in stages - where once a particular sense (left or right) and starting place is chosen, ensuing calculations MUST have a particular order and direction. And I was stating that a framework wherein this is required and allowed, or which admits such dynamism, is a prerequisite for orderly evolution of cosmological forms with the properties we observe.

I was NOT stating that evolution of form can proceed ONLY through orderly stages, but rather that what is possible at any moment is dependent on prior results which create existing conditions. To re-state it again; the Octonion algebra re-creates or embodies procedural evolution, in the sense that there is a causal dependency on the direction and order of completion of prior stages in the calculation - as well as the accumulating result - which is determined partly by the initial choice and partly by the internal structure of the Octonions themselves.

I hope this clarifies where I stand.

Regards,

Jonathan