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

As I see it..

All of the descriptions of super-determinism I've found are an extension of some conventional assumptions about the nature of spacetime, such as the blocktime view. I think that rather than being a matter of scale, over which super-determinism might apply, it is a question of topologies - such as how a simply connected surface or space is fundamentally different from a manifold that is not simply connected.

That is; the crux of Joy's work is the assumption that - regardless of appearances - we do NOT live in a 3-d semi-Euclidean space, with Riemannian curvature. Instead; we live a a simply-connected space, that appears to be Euclidean because of parallelization. But this assumption is seldom entertained, and does not correspond to the workings of any background space in which super-deterministic theories are framed (so far as I know).

So I would continue to assert that if the dimensionality of the source and target environment are different - reality CAN be super-deterministic in the realm of the source, but embrace free will in the target space. Specifically; even if nature makes strong and/or inflexible choices in 8-d space, this does not prevent there from being free will in a 4-d subspace - which is indistinguishable from absolute free will within that space. However; that range will be severely constrained, when compared to absolute freedom of choice in 8d. It may in fact be true that super-determinism in octonionic space is needed to assure freedom in quaternionic space - where we reside.

Regards,

Jonathan

One could restate the above as follows..

When discussing action from spaces that are non-commutative and non-associative; the possibility exists that - because size/distance or interiority/exteriority is reversed in sense of direction - constraints in the higher-d spaces may translate into freedoms in spaces where coordinates commute and associate directly.

Specifically; if the constraints appear in terms that anti-commute or anti-associate, their direction is reversed. A Physics example would be the asymptotic freedom of quarks in a quark-gluon plasma, which are free to move at will within the constrained region - but not to exit that region unbound.

All the Best,

Jonathan

Granted that the measure space is a subset of the complete physical space. However:

Unless free will applies over the complete physical space, it does not apply anywhere. It can't -- since the metaphysically real physical space subsumes the space of real measurement events.

This is another of those times when treating quaternions and octonions as if they were physical things makes me uncomfortable. Physical things are only measurement events; EPR, Bell, and Joy Christian all agree on that.

If some event in physical space were the random cause of an event in measure space, then the probabilistic measures of conventional quantum theory would apply both to the physical space and the measure space. On the other hand, if classical randomness (coin-toss probability) is a property of both the physical space and the measure space -- the world is deterministic; as Joy's framework shows, nonlinear random input to the continuous measurement results in a smooth function. This could only hold if the randomness of the metaphysically real physical space were equal to the randomness of the real physical measure space.

The difference between "random" and "probabilistic" is critical. Binary random events imply perfect information, as if nature and observer independently posses a qubit and are free to choose one value or the other for any measurement event. Nature's choice is the hidden variable -- and because it is equally random with the observer's choice, the continuous sinusoidal function is smooth with probability 1. "Relative becoming" is a deterministic schema, as is chaos theory.

That the observer is also part of the complete physical space makes the case for deterministic randomness. Both free-will-determinism, and no-free-will determinism, are absolute. In neither case can probabilism apply. ("Either everything is a miracle, or nothing is a miracle.")

Best,

Tom

I must contemplate this further...

I agree with you up to a point, Tom, but I feel there is something still unexamined or not recognized to be an implied assumption. In the example above, the QGP could be considered a pre-topological form of matter. That is; if the individual quarks are not topologically complete, surface-bearing objects, in a 3-d space - then their combination is the birth of topology. So asymptotic freedom of quarks is limited because once there is enough (3-d) space for them to spread out into, they MUST link up in order to exist within that space.

The sticking point (regarding your argument) comes in mainly in such extreme cases, be it the quark-gluon plasma, the primordial origin of the universe, the rim of a black hole, or other regimes where energy greatly dominates matter. If the energy bath is hot enough, this forbids the formation of the familiar particle families. My main question at this point is whether it is the effusiveness and incompressibility of energy, in the matter free regime, that 'pushes things out' into the 3-d realm, or is it the linking up of sub-units which creates a quenching effect on the available energy which does the trick.

Regards,

Jonathan

Tom,

"it preserves free will against the mystical conspiracy of superdeterminism; i.e., individual free will is hidden in plain sight, covariant with the free will of nature. That is, randomly covariant, such that nature on every scale participates in every event bifurcation -- which is exactly what we observe to happen on the classical scale, by a sensitive dependence on initial condition which characterizes deterministic chaos."

"So nature's free will is precisely equal to observer free will; i.e., classical randomness free of domain and range dependence, and without the assumption of a singular fixed cause("absolute being"), consonant with Joy's earlier work regarding relative becoming, which is also full of insight on breaking down the local-global distinction without sacrificing the free will hypothesis which necessitates "the experimental metaphysics of time.""

" On the other hand, if classical randomness (coin-toss probability) is a property of both the physical space and the measure space -- the world is deterministic; as Joy's framework shows, nonlinear random input to the continuous measurement results in a smooth function. This could only hold if the randomness of the metaphysically real physical space were equal to the randomness of the real physical measure space."

" Nature's choice is the hidden variable -- and because it is equally random with the observer's choice, the continuous sinusoidal function is smooth with probability 1. "Relative becoming" is a deterministic schema, as is chaos theory."

When I posit something similar, that time is the effect of change, turning future probabilities into past certainties and that while the process may be deterministic, the input is random, so the output cannot be fully determined prior to the event, you hold rather tightly to the spacetime model, which is deterministic, since past and future are not differentiated and there is no preferred direction, yet here you argue for a model that is much more realistic.

"In neither case can probabilism apply."

I would argue that the future, or at least the near future, is probabilistic, rather than random, since the range of potential outcomes become further constrained the nearer an event becomes. Input can be random, but momentum and inertia limit the effect truly random input can have. Its 'space' is being limited, thus the approaching events become more probable and less random.

Jonathan,

"If the energy bath is hot enough, this forbids the formation of the familiar particle families. My main question at this point is whether it is the effusiveness and incompressibility of energy, in the matter free regime, that 'pushes things out' into the 3-d realm, or is it the linking up of sub-units which creates a quenching effect on the available energy which does the trick."

Why not extend this dichotomy of energy and structure to the processing of the entire universe? Energy does expand outward, until it becomes subsumed into structure and then compresses until such time it heats up and breaks the structure down, radiating back out. Think on just how much it creates and defines life processes, as new energy is constantly growing up and out, while old structure is holding onto form and pressing it down and inward. Then onto convective processes that form geological and stellar currents, than galactic structures, pulling in form and radiating away energy. Could it be that in the intergalactic deep, even light cools enough that it 'crusts' and becomes a gas? Such as at 2.7k?

Try linking it up with complexity theory, with 'energy' as chaos and 'structure' as order. Then this complex reality is that dynamic of energy/chaos/randomness, pushing out, while structure/order/deterministicness, ie. probability, is compressing inward. Then time is the effect of this relationship, with the past as what is ordered/determined, while the future is the energy constantly pushing out this ordered form in all its weak spots, such that the new arises, either by motivating the old, or squeezing through the cracks, as either evolution, or revolution.

Regards,

John M

"I would argue that the future, or at least the near future, is probabilistic, rather than random, since the range of potential outcomes become further constrained the nearer an event becomes."

Where did you get this information, John? Psychic vision?

Tom,

Have you ever heard of weather reports???

It is easier to make predictions about tomorrow, then it is about what will happen a year from now, because the range of probabilities has been narrowed. There are logical, physical reasons for this.

Regards,

John M

I am glad I added the final nail in the coffin of theories seeking to recover quantum from classical mechanics: http://arxiv.org/abs/1311.6461

Quantum mechanics is unique, cannot be generalized, has nothing to do with classical mechanics, and Nature is quantum at core.

It is not everyday C* algebras are generalized and vast new mathematical landscapes are revealed. I'll submit this for publication in a very respectable journal, and I have more results in preparation. The fireworks is just beginning.

John, the "logical, physical reasons" that weather reports are more accurate for a near future than for a far future, are not the ones that you think they are.

Weather forecasting(Lorenz)is based on chaos theory, which is deterministic, not probabilistic. A sensitive dependence on initial conditions ensures that information supporting the forecast is *not* a result of prior probabilities; it is the result of built-in randomness that changes global initial conditions which feed back to local initial conditions.

Best,

Tom

Tom,

When was the weather ever "initial?" As I keep saying the process is deterministic, but the input cannot be fully determined, prior to the event. Yet as the event gets closer, potential input gets clearer.

While I'm sure I'm not using all these terms exactly as the book requires, I do notice you are not arguing my point that what is proposed above is not compatible with 'spacetime is physically real.'

Instead we are discussing minor points about a side issue.

Regards,

John M

"Yet as the event gets closer, potential input gets clearer."

As I asked before, John, did you get this by psychic impression? You didn't get it from the actual science.

John, maybe this will help.

For more clues on the physical reality of spacetime, see my post in "Fighting noise with noise: simulation of motional averaging with a superconducting circuit."

Best,

Tom

Jonathan,

Sure, we agree on a lot, in principle and in fact.

It's important to me, though, that I understand Joy's framework to be fully relativistic, with no hedging in terms of domain/range, or in the translation of algebraic terms into the complete spacetime of continuous functions.

If these principles of relativity are compromised, so is domain/range coherence, because there is no guaranteed smooth simply-connected path between points of the complete spacetime. Now, I do understand the theoretical cosmological signficance of a pre-spacetime; however, there is no mechanism to assure that the phase space of transition from pre-spacetime to the complete measure space is continuous. For this reason, I take n-dimension (n > 1) spacetime to be absolute and Joy's measurement framework free of singularities; therefore, the cosmological problem is resolved *within* that framework, and continuous spacetime is free from compromise.

As I have tried to make clear, I think that the imposition of algebra is an explanatory scaffolding that may be removed once the mathematical techniques are improved. The big and original idea in Joy's research is explaining in terms of continuous functions (classical physics) the same phenomenon (strong quantum correlations)that had long been thought the result of discrete measures in disconnected (before measure) and multiply connected (after measure) spaces. These quantum configuration spaces *require* the assumptions of linear superposition and nonlocality to make the measure results coherent. That is very much begging the question. Joy showed that no such assumptions are either necessary or desirable in a mathematically complete theory.

You write:

"When discussing action from spaces that are non-commutative and non-associative; the possibility exists that - because size/distance or interiority/exteriority is reversed in sense of direction - constraints in the higher-d spaces may translate into freedoms in spaces where coordinates commute and associate directly."

Maybe. But not in the measurement framework of an n-dimension spacetime, complete and simply connected.

Algebraic properties (commutativity, associativity) lose their meaning in a coordinate-free language. There has been a lot of confusion over the correlation of points of a parallelized 3-sphere; these are not points of a discrete algebra, they are points of a topological continuum.

All best,

Tom

Tom,

Both those links deal with thermodynamic processes and we recently had that conversation about thermodynamics being incompatible with spacetime being any more than coordinating measures of distance and duration. These are dynamic situations, in which change and thus measures of it, are effects. Past and future are quite distinct, opposing projections of current conditions, not some metaphysically real dimension along which events exist. There is no blocktime in thermodynamics. Even the past is no more than residual information. Change and thus time, is not some directionless scalar dimension, but a very dynamic process of a dynamically evolving state.

Regards,

John M

John, sooner or later it had to come to this. I don't understand a single word you wrote. You'll have to run it by someone who does.

Tom,

We can hope for an outside opinion.

Jonathan, can you, or anyone else, make sense of my point that a thermodynamic medium doesn't need blocktime to explain change and the measure of its frequency, ie. time and that blocktime is nothing more than a static model of a dynamic process, since the idea seems to be outside Tom's cognitive box?

Regards,

John M

" ... blocktime is nothing more than a static model of a dynamic process ..."

That means absolutely nothing, John, since every model is static.

The issue, really, is between linear and nonlinear relations of dynamic processes. While you (and Bell loyalists) have no difficulty dealing with the simple linear relations, it's the nonlinear dynamics that have you flummoxed.

Tom,

"every model is static."

Does that mean you are willing to accept four dimensional spacetime is a static model of a dynamic process? That there is no physically real 'fabric of spacetime,' in which time is a scalar dimension?

"it's the nonlinear dynamics that have you flummoxed. "

I don't feel particularly flummoxed by thermodynamics. I just see it as a dynamic process that is incompatible with the notion of blocktime. Blocktime is non-linear, but it is not dynamic. It is a static modeling of transitory events.

Regards,

John M

Tom,

You might be flummoxed. I consider my R model indeed the perhaps first non-static one in the sense it does not refer to an arbitrarily chosen point of reference but to the actual now. You might speculate whether or not there was something before an assumed act of Genesis/BigBang or whatsoever. I consider it more important to accept the now and scrutinize theories that arose from merely postulated symmetries.

Thank you John M for not giving in. Your arguments are justified. Don't expect support from Jonathan who also lives in a world of static models.

Regards,

Eckard