Is Quantum Theory As Fundamental As It Seems? by Michael James Goodband

Michael, Tom,

"These can only be metaphysically real, i.e., independently objective though fundamentally "distant.""

I think that even as we peer into that abyss, the shadows do have some faint dimensionality. I don't see why time and temperature wouldn't be in the same category. What is more fundamental than the background radiation, or quantum fluctuation and they are both explicitly thermal functions, rather than temporal. Once a system reaches it final entropic state of distribution, there is no more order, therefore it cannot change and thus no measure of time, but it is not thermally inert, since it didn't theoretically loose the actual energy causing the distribution. If I can get time demoted, then I'm going to try to get temperature promoted.

More news on the daughter; $52,000 early decision grant!!!!!! Counting Pell, etc, we have to come up with all of about 3000. Lot of back story on that. Too non-linear to explain...

Michael,

Just as Rick provides insight into Octonion algebra and its connection to gradient, divergence, and curl, your explanation of spurious mathematical degrees of freedom and Fadeev-Popov ghosts is insightful. I knew they were figments of QFT but otherwise would have trouble explaining them.

I find this relevant to your belief in 11D. Yang-Mills 1954 paper was essentially a self-interacting version of electrodynamics, perfectly suited to gravitomagnetism. It was ignored for 20 years because gravitomagnetism was believed too weak and its essential dependence on density was unrecognized. Eventually, a way for quanta to acquire mass through symmetry breaking was invented. The path integral approach to quantization of the theory foundered on 'excessive' gauge freedom until Fadeev-Popov introduced (unphysical) 'ghost fields'. About 1964 'color' was invented and by 1974 a formulation compatible with YM was put forth. Even today QCD cannot prove quark confinement and is one of the Millenium problems. QCD fails in many ways, as I've repeatedly noted, and simplistic lattice models are usually good for only a few percent. People hoped SUSY would rescue QCD but that's not happening. I think your own problems with color symmetry might give you a hint. I don't believe you should be so quick to count 3 dimensions for color. You might be double counting. Although you insist that Physics trumps Maths, your counting is based on a very specific Maths-based formalism. For example isospin is an abstraction based initially on the idea that proton and neutron were essentially similar to 'spin up' and 'spin down' states of one particle. No matter how convenient this formulation, it is certainly more mathematical than physical, ignoring quarks and lifetimes and more. This entire discussion of multiple dimensions and exotic topologies is far more Maths- than Physics-based. And I agree with Susskind (and, I believe, Dirac) that "the paradigm of relativistic quantum field theory almost certainly has to be replaced." When it is the dominance of symmetry over dynamics may disappear, or at least be diminished.

Rather than 11D my own bet is on 8D split electromagnetism and gravitomagnetism co-existing in 4D space and time. I think renormalizable Lagrangians imply 4D since operators of dimension larger than 4 have coupling constants with negative mass dimensions.

Your ingenious model is unique and inspired, but your interpretation of experimental physics leading you to 11D is just exactly that, *your interpretation*. As Joy says:

"The [interpretation of] experimental evidence is in the eye of the beholder."

To a group that is so ready to overthrow orthodoxy in terms of Bell's theorem, the topological nature of the universe, and other aspects of orthodox physics, I say don't be so certain that orthodox QCD will survive much longer [except through the sheer force of the orthodoxy-enforcing institutions.] The fact that nothing beyond the Standard Model has been found does not fix the many problems of the Standard Model.

Best,

Edwin Eugene Klingman

Hi Michael,

It turns out that my results can be interpreted purely microscopically after all, without involving any macroscopic extra dimensions. Here is how this may work:

I refer to equations (113) to (116) of the attached paper where the standard scores corresponding to the measurement results A = +/-1 etc. are given by the functions A(n1, L) etc., which are bivectors defined in equation (105). Now the question is whether the co-domain of these functions---which is necessarily S7---can be interpreted purely microscopically, even though the actual measurement events (the results A = +/-1 etc.) are macroscopic events occurring at macroscopic distances apart (cf. Fig. 2 of the second attachment). Well, we can certainly view the bivector A(n1, L) as representing a point of a microscopic S7 attached to a point of a macroscopic S3 by using Planck units for the length of the vector n1. And although the actual measurement events A, B, C, and D are occurring at macroscopic distances, nothing prevents us from evaluating the expectation value (118) as a computation of the correlation among the points of a microscopic S7. In fact in Planck units the distinction between microscopic versus macroscopic is meaningless.

Intuitively this is not too difficult to visualize. Although A, B, C, and D are occurring at macroscopic distances from each other, the bivectors A(n1, L), B(n2, L), C(n3, L), and D(n4, L), viewed as standard scores in the statistical sense, can be moved and brought under the integral (118) for the purposes of computing the correlation among the results A, B, C, and D. In other words, we can view the measurement events A, B, C, D both as occurring macroscopically within S3 as well as microscopically within S7 at the same time. The GHZ correlations are then correlations among the points of this microscopically parallelized S7.

So I now think that it is possible to view your theory as a Locally Unified Theory.

Having said this, I still think the manifold S15 is much more natural from a mathematical point of view, and it would be premature to abandon it. I also remain convinced about my macroscopic experiment for reasons that have more to do with the orientation-entanglement property of the physical space than our present concern. So I am now going to concentrate more on my experiment, leaving you in peace with your theory.

Best,

JoyAttachment #1: 8_1101.1958v1.pdfAttachment #2: 1_GHZ4.pdf

Michael,

I would also point out that temperature isn't just an abstract measure. Since all the components are moving about and bumping into one another, they are physically trading energy around and creating a uniform level of energy. The end result of entropy.

My oh my,

First off; as Fred suggests, there must be compactified topology in S15, as the sphere's (hyper-) volume is maximal in 5-d (theoretical limit ~5.25695) and surface in 7-d (also rounded). But as Michael suggested, in the space of S15, all the dimensions have an equal footing. I mentioned this could be thought of as maximally uncorrelated. Another way to say it might be the figure is directionless or has no preferred orientation.

This would allow the property Joy described of ex nihilo creation to be emergent, and this is attractive indeed. I've given considerable thought to the idea that the quaternions and octonions are dynamic rather than static. Connes talks about non-commutative measure spaces evolving with time, and possessing 'God given' automorphisms. P.C. Kainen talks about the Octonions having a procedural aspect, as well as this evolutive quality Connes speaks about. Complex numbers have some semblance of this aspect, but perhaps it actually comes from the Sedenions.

Maybe the magic of S15 is that once it is formed, it is automatically systematic in the sense of being likely to evolve into something else, and equally likely to explore any of the four fibrations, all of the above, or neither. So maybe we should think of the Sedenions as the mother of all division algebras. I would echo Fred's recommendation that there is useful info on Tony Smith's page "Why not the Sedenions?" which pertains to the discussion above. I alerted Tony about this thread, as well, and he has expressed interest.

More later,

Jonathan

Further thoughts,

This thread has seen may twists and turns, and has been full of surprises with always something interesting to learn. I think there are ways to deal with the apparent ambiguities or frustrations seamlessly. Perhaps in the case of the initial Sedenion algebra, we can indeed view it's Real component as the initial arrow of time - in a geometrical or mathematical sense. But from the moment there is any evolution of form beyond this initial state, or once there is any relevant Physics to speak of, time takes on a different meaning.

I think that what role S15 plays is to provide a blank slate of sorts. It is an equalizer or normalizer by virtue of the equal footing it gives all dimensions. When we were considering the physical attributes of octonionic space, Ray Munroe thought the imaginaries had to be space-like, and the Real component time-like. And this makes sense up to a point. But if the Octonions are not the Master algebra - but only one of the component algebras - then it's the Real dimension of the Sedenions that determines the initial timeline.

I don't know if the 'extra' Reals are a problem either. As a component of a higher algebra they are part of a package deal, where you can't necessarily break them out. But there is the alternative that time is multi-dimensional. Alex Mayer talks about how Minkowski got the idea for spacetime right, but Einstein did not grasp the full intent of viewing space and time as a unified entity. If time is volumetric instead of linear, this changes some things, but leaves others apparently unchanged. And it does seem that the arrow of time can vary direction with scale - yet appear invariant.

Have Fun!

Jonathan

Congratulations to John!

Good luck to your daughter in her studies at Johns-Hopkins. May all go well in the transitions involved in this process.

I have enjoyed this branch of the conversation too.

All the Best,

Jonathan

Hi All,

Yes Joy, you should definitely concentrate on your experiment. I never thought there was any problem with your framework related to how microscopic quantum object behave through space. The big question to answer is if it works with macroscopic objects also.

Jonathan, I think you are now seeing what I was talking about earlier with math rules. Sedenions have the least amount of rules that I guess you can still consider to be math. And the surprising thing is that S15 contains all the others that successively have more and more rules. And also what Joy said about something from nothing. Well... math-wise anyways. Nature has to start with something physical I would think. But the math should be very simple at the beginning.

I forgot to warn everyone about Tony Smith's website; you can spend hours on there since there are so many links to interesting things. :-)

Best,

Fred

Jonathan, Fred,

Doing your part to uphold the rich insight-density of this thread, you two have contributed the link to Tony Smith's page "Why not the Sedenions?"

I found the treatment of Clifford algebras (geometric algebras) on pages 17 and 18 to be as succinct as any I have seen. Wow!

Best,

Edwin Eugene Klingman

"Connes talks about non-commutative measure spaces evolving with time, and possessing 'God given' automorphisms."

Thanks, Jonathan. I hadn't heard it put that way, though it seems almost certainly true that a finite measure space of infinite quantum correlations allows infinite time evolution.

In the discussion section of my ICCS 2006 conference paper I showed that the trivial zeros of the Riemann zeta function (the negative even integers) monotonically increase by the same interval as the real part of the nontrivial zeta zeros. In other words,

n = sqrt inclusive - 4/4 = m

n = - 2, - 4 , -6, -8 ...

m = -0.5, - 1, - 1.5, - 2.0 ...

So part of the argument I had with Ray Munroe over the role of time on R is that if he were correct, intervals of time actually move in the negative direction of R by a constant interval (making imaginary any measure off the real line). This might be true if we conceive that the irreducible unit of time = 0.5 = 1 second applies backward and forward on the line to infinity -- which is actually how we think of time independent of space, in our limited experience of time units.

The nontrivial zeros of Riemann's function are not so ordered. The singular 1/2 ix infinite zeros within the critical strip tend to "thin out" with approximately the same spatial regularity as one finds in the prime number theorem. My prime number research has come a long way since, though I am not yet ready to talk about it publicly.

Related to the present discussion, Joy's model of compact simply connected topology completes the measure space without obviating his elegant philosophy of a "relative becoming" universe. Such a spacetime world preserves continuous measure functions while giving time permission to evolve -- differing not only from Newton's absolute time but from the conventional blocktime universe most widely accepted today. At the end of the day, we profit by getting order from disorder, something from nothing ("The resulting theory abhors any form of preferred structure ... "). If that's not the basis for "'God given' automorphic functions," one is hard put to reduce it further.

Tom

There are different types of definitions of entropy. If one is speaking about the original discovery of thermodynamic entropy as defined by Clausius then: "...they are physically trading energy around and creating a uniform level of energy. The end result of entropy." is not true if it includes the assumption that a non-uniform level of energy existed, more than an infinitesimally small variation, prior to the end result. The other forms of entropy are sufficiently distant from Clausius' definition that the statement is true in most cases. They can be haphazard in their re-adjustment process.

James Putnam,

Michael,

"In physical terms, how does one particle wave? Think of an electron travelling in a magnetic field and you have your answer."

That of course is exactly the model I develop in my essay, based on Einstein's gravito-magnetic field equations, with the same helical result. Even if you attribute it to a spin topological defect, I'm glad to see you arrive at a 'particle AND wave' model versus the 'particle OR wave' favored by so many.

My earlier point was that it would be amazing to me that, given such a physical particle and wave, one could not map a S0*S1 symmetry onto it, rather than taking the position that the existence of S0*S1 symmetry somehow implies particle and wave (if that is what you are saying.) It seems to be very much in the eye of the beholder.

Best,

Edwin Eugene Klingman

Michael,

I'm not trying to un-link them, only order them. Actually I would put causation and time in the same category, as sequential, linear effects. The lightcone of input is incomplete prior to the occurrence of any event. So since causation is a transfer of energy, the total range of energy input can't be known before the event occurs. It is only after the fact that we can fully deduce cause. All we can really say about causation is that energy is conserved.

Thanks Tom and Jonathan. I only mentioned this on Georgina's thread, but her mother was killed in a traffic accident October 24th and this has been an extremely traumatic month and a half. We were still married, but had been separated for the last ten years. For the last four, I'd been working afternoons for her, mostly as child support, so now I'm in the process of having to wind down her riding school. It was focused on beginning riders, since it combined her master's in education and horsewomanship and was quite successful. No one could manage ten kids on Shetland ponies like she could. Lots of unhappy kids. Barbara Ann, our daughter, gave the eulogy. Among many other things, the funeral was delayed for two days by Hurricane Sandy.

Zitterbewegung! That is how a particle waves.

Hestenes' essay

My Essay

Best,

Fred Diether

Yeouch!

A sad story, John. It's never fun when somebody dies, and the closer they were the more it hurts. It sure seems like a lot of departures lately. My sympathies for your loss, and the delayed resolution. Good luck trying to wind down her school. I hope your daughter Barbara Ann does really well at J-H. And it looks like Michael congratulated you as well.

For what it's worth; I put time, space, energy, and matter in a hierarchy in my first FQXi essay, and I still think this makes sense. Time as duration must exist for forms of any kind to persist, and time as process allows procedural evolution to proceed, potentially making space emergent. Matter can arise from energy, and energy can arise from properties of space. So ordering Michael's linked tuple as above might make sense if you assume that events happen to objects.

Regards,

Jonathan

Jonathan

"Time as duration must exist for forms of any kind to persist, and time as process allows procedural evolution to proceed, potentially making space emergent"

There is a difference between physical substance and the physically existent state thereof. The latter is what really defines physical existence at any given time, and it alters, ie become a different state. Timing measures this rate of change against a conceptual constant. But, note that difference does not physically exist, only substance in a physically existent state does, and it can only be in one such state at a time. This also point to the fallacy of space/distance, because that is a function of physically existent states, ie it is the spatial difference. Which again, as a difference, does not physically exist, and there can only be space/distance between existent states which exist at the same time, ie there is no duration in distance.

Paul