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

Eckard,

Now I think we are getting back to the mathematical fundamentals of what Joy Christian has demonstrated.

"While you and others consider C, H, and O indispensable, I see basic adequacy in the opposite direction, i.e. with just R."

Personally, I reserve my opinion on whether the hyper numbers (H,O) are indispensable to describe physical phenomena, though I know they are indispensable for solutions to Joy's framework, and to Rick Lockyer's octonionic construction.

The real positive integers, though, are reversible only to describe locally discrete, not globally continuous, events -- while the loss of commutativity (H) and associativity (O) guarantee global reversibility (which is the crux of the dot product result -a.b). Topology is all about global continuous functions. Joy's remarkable result is that the global function *does not differ* from the local continuous function -- a result that is now extremely difficult to argue with, since it has been simulated five different ways in a local computer model.

My personal hope is that the simulation will lead to a simpler model on C*, where the algebra is closed and compactification leaves only one simple pole at infinity. That is, the 2-dimensional complex plane in which the Hilbert space lives, may be entirely adequate for physical events up to and including the 8 dimensions of the division algebras. Then there will be absolutely no escape for Bell loyalists claiming that continuous function physics is not foundational. Hilbert space continuity will have been demonstrated independent of the axiom of choice. The choice function, just as Joy has demonstrated, will have been invested in nature's choice of space for the physical events we observe.

Forgive me for not getting into the rest of your post dealing with mathematical philosophy -- perhaps some other time and place.

All best,

Tom

Eckard, if the forum will indulge me, I would like to re-post in one spot a puzzle (from an episode of the American TV detective show "Columbo") and the solution, each of which I posted separately elsewhere:

1. "Imagine you are in a sealed room with sacks of coins -- three sacks filled with as many coins as you wish. All of these sacks except one are real gold coins of uniform weight. One sack is full of fake coins of uniform weight differing from the real coins by some slight measure -- any difference you choose, so long as it is slight enough to be undetectable by holding the bags in your hand.

"The problem is, you have a penny scale -- and you have only one penny; you can therefore make only one weight measurement. How do you tell the real from the fake?

2. "I made the solution easier, because I specified 3 bags -- I could have said choose any number of bags you please, with any number of coins in them that you please. The small finite number, though, makes the solution easier to explain:

"Label the three bags, A, B, C. From bag A, remove one coin. From bag B, remove two coins. From bag C, remove three coins. Place all six coins on the scale.

"Suppose the weight you assign to the real gold coins is 1 oz, and to the fake coins, .90 oz.

"If the scale reads 5.1 oz, the fake coins are in bag A. If 4.2 oz, the fakes are in bag B, if 3.3 oz, in bag C.

"Rob is absolutely correct that the quantum theorists don't know what information to look for. They assume that of an infinity of 'bags' there are in each a uniform number of uniformly entangled 'coins' so that no matter which bag is 'weighed,' it will always be a uniform multiple of the finite number of coins prepared for the weighing. In our puzzle example, the scale will always read 6 oz.

"Assume on the other hand, that one has a number of bags of space and one bag of time. The bag of time, like the bag of fake coins, has to differ in weight from the bag of space (explained in relativity by a change of sign in the metric signature), such that for a continuous weighing of cumulative units chosen from an infinite number of bags of space, there will be somewhere a bag of time that tells us the single true measure of time we're looking for in any *finite* observation. This bag of time will be present in every finite measure, because if it weren't we chould not choose units of space discretely; we couldn't assign any weight to units of space, because it's the move of time that facilitates the choice function.

"The Bell-Aspect choice function assumes entangled units of space and no time parameter (T = 1, a constant). The finite measure of a continuous function, however, acknowledges the move of time that in fact forces the measure to be finite. Only continuous spacetime guarantees a *scalar* result - a.b from n number of measures in the N finite set of measurements -- because the weight of the time vector differs from the weight of the space vector. Without a time parameter in fact, no scalar result is possible. And because there is only one true time measure in any sequence, the correlated 'quanta' of continuous measurement functions in spacetime have minima and maxima that are self similar at every scale."

Tom

To try and make the last post a little more numerically formal, this is how the bags A, B, C appear:

A. 6 - (1).9 = 5.1

B. 6 - (2).9 = 4.2

C. 6 - (3).9 = 3.3 ...

for n iterations:

6 - (n).9 ~ 0 epsilon

This epsilon term is present in every finite measure. It falsifies the assumption of Bell's theorem that time is unitary ( = 1) for quantum measurement, rather than continuous with the measure space at every scale, with no boundary between quantum and classical domains.

Therefore: no wave function collapse.

Tom

Tom,

It is not logically permissible to use the completeness of the real numbers in their own construction. Furthermore, modern topology is even unable to perform a logically acceptable cut between R- and R. For such reasons I don't trust in pebble-set topology. My last essays did further elaborate my criticism and suggested a way out while it is not my business to purify topology from set-theoretic burden.

You are certainly prudent when reserving your "opinion on whether the hyper numbers (H,O) are indispensable to describe physical phenomena though ...".

Functions of radius or of elapsed time don't have support for negative abscissa. Such semigroups fit completely to R. Of course, for those like you who used to see the world from the perspective of C, there are several seeming deficits.

I appreciate your effort to explain.

Regards,

Eckard

" ... final nail in the coffin of theories seeking to recover quantum from classical mechanics ..."

Few object to the inability of classical mechanics to recover quantum mechanics, Florin. Classical mechanics subsumes the quantum. The real question is whether conventional quantum theory describes anything real independent of a human mind. As you say,

"Physically the invariance of the laws of Nature under tensor composition means that the laws of Nature are the same regardless of how we partition in our mind a physical system into subsystems."

If this were true -- there would be no need for a quantum mechanics distinct from classical mechanics. The quantum universe would conform to the metric tensor that describes a 4-dimension continuous spacetime in a uniform local realistic domain. As it is, though, special relativity limits an infinity of domains to natural subsystems ("All physics is local") without relying on a mind-created mystical nonlocality to beg the question of what "quantum" means.

Just as you imply, if there is no reality independent of mind, quanta are not distinct natural phenomena; they are creations of discrete perception rather than elements of a continuous spacetime physics. Classical mechanics accommodates every one of your composability classes of positive, negative and zero spacetime curvature in each of its relativistically distinct and locally correlated quanta.

Tom

Someone didn't like my last reply, showing that if reality is independent of mind, your conclusions ("Quantum mechanics is unique, cannot be generalized, has nothing to do with classical mechanics, and Nature is quantum at core.") do not and cannot hold.

1. The "core" of your description of quantum mechanics is only in the discrete parsing of events by probabilistic interpretations in the mind of the observer. That's called "thinking." It has nothing to do with classical mechanics, because it has no connection to the classically continuous and objectively described functions ubiquitous in nature.

2. Conventional quantum theory is based on no physical first principles.

3. Your argument for composability classes is a red herring, since all of the classes of spacetime curvature (parabolic, elliptic, hyperbolic) are incorporated into continuous function physics and easily accounted for.

Tom

Inspired by Tom's recommendation earlier, I am reading Donal O'shea's popular book about the Poincare conjecture. The book is a bit too popular for my liking, but it has some accessible discussion about the topological subtleties of the 3-sphere, which are not only central to the Poincare conjecture and its confirmation by Grigory Perelman, but also to my hypothesis about the classical origins of the quantum correlation.

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I'm suprised that no more dialogue has been generated over Lucien Hardy's five reasonable axioms of quantum theory.

The fifth -- "There exists a continuous reversible transformation on a system between any two pure states of that system" -- Hardy allows is the only one inconsistent with classical probability theory (classical randomness). And that hinges on only one word -- "continuous."

My opinion is that probability measure is not and cannot be independent of mind and therefore cannot be a physical first principle.

In other words, the reversibility of a continuous measurement function is independent of the discrete processing of measurement information propagated by wave mechanics.

Joy Christian's measurement framework is the only one I know of, that allows correlation of quanta independent of discrete mental processing using the classically random functions that Hardy identifies.

Tom

    Joy, I'm glad to hear that. I will take my copy of O'Shea's book home with me over the holidays, and perhaps comparing notes in the forum will shed more light for some, on the torsion issue. It wasn't easy for me to understand, and I like your distillation, "quantum correlations are a measure of torsion within our physical space." Right on.

    All best,

    Tom

    Tom,

    Probably because human nature and its subcategory of academic disciplines, does not go in reverse.

    When a particular concept becomes accepted, subsequent work is built on and around it, so if someone is to later go back and with the hindsight of broader knowledge, point out where it is wrong, this doesn't simply put the model in reverse and effortlessly turn it back to what was the starting point. There is the combined inertia of all that other work radiating out from it.

    What's the old saying; Open a can of worms and you need a bigger can to put them back in.

    Models are closed, but reality is not.

    Regards,

    John M

    Post returned approved, thank you:

    " ... final nail in the coffin of theories seeking to recover quantum from classical mechanics ..."

    etc.

    "... if there is no reality independent of mind, quanta are not distinct natural phenomena; they are creations of discrete perception rather than elements of a continuous spacetime physics. Classical mechanics accommodates every one of your composability classes of positive, negative and zero spacetime curvature in each of its relativistically distinct and locally correlated quanta."

    Is wave/particle duality being dismissed above?

    James Putnam

    Tom,

    The concept of torsion in Riemannian geometry is less intuitive than that of curvature. I am attaching a paper which is somewhat technical, but it brings out the concept of torsion rather nicely.

    Best,

    JoyAttachment #1: 0805.0846.pdf

    Tom,

    As you may know, Lucien is a friend of mine and he is familiar with my work. In fact, we have had extensive discussions about it during past few months. He is thinking about my point of view.

    Best,

    Joy

    Tom,

    As you may know, Lucien is a friend of mine and he is familiar with my work. In fact, we have had extensive discussions about it during past few months. He is thinking about my point of view.

    Best,

    Joy

    Hi Joy,

    Hopefully the message that I am replying to or this one won't be deleted by your cyberstalker. I am wondering if you have had any pertinent discussions with Lucien about his 5th axiom and if so, anything thing important to mention here?

    I have been thinking about his 5th axiom in relation to your work but so far I haven't thought of a way obtaining the continuous reversible transformation with your model. Thought I suspect it should be able to be done.

    Best,

    Fred

    Hi Tom,

    I'm not so sure measurement is a problem here. It's the idea that quantum probabilities can have a continuous transformation between pure states and classical not. Whether or not they can actually be measured.

    Best,

    Fred

    Hi Fred,

    I haven't had any discussion with Lucien about his axioms, but we have indeed discussed the role of probabilities in my framework versus that in the orthodox quantum theory. In this regard your question about continuous and reversible transition between states is a very important question. It essentially means deterministic time-evolution of classical expectation values, or probabilities, without any funny business of wave-function collapse. Since my local-realistic framework is entirely classical (without a measurement problem), in principle continuous and reversible transition between states is not a problem. But of course I must demonstrate this mathematically, which I haven't done as yet.

    Best,

    Joy

    Hi Fred,

    Ditto what Joy said.

    I think that any classical program comes up against a built-in prejudice in favor of discontinuous particle reality. A continuous measurement function, however, is time dependent; i.e., continuous from the initial condition, such that one thinks of points of spacetime as particle manifestations after a measurement event is recorded. As Professor Bel in Joy's link of this thread concluded, "A bricklayer does not need a time-keeper as much as he needs a plumb line and a T-square, therefore we shall end this paper with some notes about the space geometry of space-time models."

    The "bricks" of topology, IOW, are not what the wall is built of; continuous measurement results recorded by "the plumb line and the T-square" which reveal how the contours of the wall change over time, depend on where in the continuum the tools are applied. What Joy's simulation shows is that no matter what local configuration of the wall one chooses to plumb and square, the global state corresponds to it in a deterministic way. Conventional quantum theory says the local measurement *creates* the corresponding global state, without having to show or prove anything about it -- it's simply "nonlocal" and in a state of linear superposition before the measurement tools create the "reality."

    Topology, though, is all about the global properties of spacetime -- which is where the torsion issue comes in, because non-vanishing torsion forces a self-similarity of quantum correlations independent of scale. As Prof. Kiehn explains:

    "The mathematical ideas of torsion can be put into two general categories:

    1. The category of geometric torsion produced by continuous deformation of a metric. The mathematical description has been called fiber bundle theory.

    2. The category of topological torsion which does not depend upon metric. The mathematical description has been called twisted fiber bundle theory."

    This obviously ties into Joy's explanation. Something that most find hard to understand about topology when first introduced to it, is that conventional ideas of distance, of metric measure, don't apply.

    Sorry this is getting so long. Forgive me if I am distracting from the main message. However, I just want to add one more thing -- I have thought (and written) for a long time, that topological quantum field theory would be the next big thing in particle physics, because it takes the pressure off the notion of "particle" in favor of the continuous functions (albeit nonlocal) that string theory promises. Never until I was introduced to Joy Christian's measurement framework had I even conceived that a classical schema -- manifestly local -- would converge on these globally continuous functions.

    In my Email today, I find a paper uploaded to academia.edu by Nathan Seiberg giving the strongest hint that local symmetries are dependent on global configuration space; i.e., local gauge symmetries whose curvature is everywhere zero, may be driven by a nonzero torsion in the global sysmmetry. This would account, I think, for the teleparalellism in Joy's framework, i.e., we might get a higher dimensional gauge theory in strictly *classical* terms. Manifestly local. Seiberg et al write in their introduction:

    "The correlation functions of local operators in R4 depend only on the choice of the Lie algebra g of the gauge group G. They are independent of the global structure of G and the different choices of line operators. So naively these subtleties are of no interest for a four-dimensional physicist. However, we will argue that they have several important consequences. First, these subtleties affect the correlation functions of line operators in the theory. Therefore, they affect the phase structure of the theory on R4. Second, these subtleties become more dramatic when we compactify the theory. For example, we will see that the choices of G and of these parameters have important consequences even for local dynamics on R3 テ--S1. In particular, these different theories can have a different number of vacua (and, in supersymmetric theories, different Witten indices) on R3 テ-- S1. The simple reason for the difference between R4 and R3 テ-- S1 is that wrapping a line operator around the S1 leads to a local operator in R3. These issues play an important role in the relation between IR dualities of four dimensional gauge theories and those of three dimensional gauge theories."

    I'm just thinking out loud here. At the least, 2014 is shaping up as a big year for theoretical physics, and I am betting that Joy's classical framework will play a central role.

    All best,

    Tom

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    Hi James,

    "Is wave/particle duality being dismissed above?"

    As a reasonable explanation for particle and wave behavior? No.

    As a foundational theory of particle and wave behavior? Yes.

    What I mean is, the wave function propagates information continuously, so we can derive discrete particle-like information from wavelike behavior in a measure of physical events in any finite interval. The converse is not true -- discrete particle trajectories do not give up information of their wavelike properties in finite time; therefore, wave and particle phenomena cannot be dual in the sense that one theory can be derived from the other.

    Best,

    Tom

    Tom wrote;

    "discrete particle trajectories do not give up information of their wavelike properties in finite time; therefore, wave and particle phenomenon cannot be dual in the sense that one theory can be derived from the other."

    I would say that is so at present, but not impossible to propose. Consider that the wave-particle duality of EMR is consistently proven experimentally and that so is the curvature of starlight by large gravitational masses. We are simply missing something.

    Given Maxwell invariance, for the sinusoidal curve evidenced by electromagnetic

    response in detectors to occur, something has to be accelerating both positively and negatively in the span of each and every wave event. If velocity across the wave lambda were constant so would be the output of the receiver. The particle might well be in that wave event, but only momentarily. Time is local by SR, so would it not also be local to the discrete wave event?

    It's okay, people, I got a good supply of burn ointment, cheers. John R. Cox