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

Another way of explaining it would be that we are seeing the parts reflected in/connected to the whole and the whole reflected in/connected to the parts, as opposed an opposite set of parts, to create balance.

Thanks Michael,

My Mandelbrot Cosmology has been in the toy model phase until recently, because the Octonions and not the more familiar Complex numbers are proposed to be the playground for the full theory. Or rather; I see the Mandelbrot Set as a structure that resides equally in R, C, H, and O algebras, and displays the maximal symmetry breaking catalog of any of the related figures based on other polynomials.

The 2-d example in the Complex domain has been tractable on home computers since the introduction of the IBM PC, which was actually the machine I first used to create images of M. And I happened on the Butterfly figure as part of my attempts to find a shortcut. One would think that if the variable decreases in magnitude over 3 iterations - the function is converging. But no; I got a crazy butterfly and discs instead.

Having just taken a course in Astrophysics and Cosmology, when I found my butterfly; my first reaction was 'OMG - It's the Big Bang, and cosmological eras.' That was quite a few years ago (~ 25), but I had a lot to learn about Math and Physics before I could figure out why and how some of the things I was learning might be significant. In addition; a certain amount of progress needed to be made in those fields for some of my more conclusive results to become possible.

Notably; there had to be a fair amount of work by Baez and Huerta, Rick Lockyer, Geoff Dixon, P.C. Kainen, and also Alain Connes with his NCG program. Connes notes that with NCG, a lot of the foundational discoveries were not made until the 70s or later, and I daresay that most of what pertains to the role of the Octonions in Physics has a much younger vintage. A lot of the best material has only been written in the last 5 years or so.

In any case, I'm glad there is a workable proposal with (S0, S1, S3, S7) in it.

Regards,

Jonathan

Gee John,

That last comment sounded a little like Frank, perhaps more than a little, but I love the 'clock' and 'thermometer' comment. Until now; I never thought of the time and temperature display in front of the bank as a left brain/right brain sort of thing. Maybe that explains the almost universal attraction of such institutions (go figure). What a clever marketing ploy!

Thanks for the thoughtful comments.

All the Best,

Jonathan

Jonathan,

Frank's crazy, not stupid.

Another way of thinking about the whole vs, parts, is top down, vs. bottom up. Physics is focused on the bottom up, components adding up to a complex network, but it really is a yin/yang relationship. You don't have bottom up without top down. I tried making that point to George Ellis, in his admirable effort to defend top down causation. It is a constant feedback loop, with the more a structure pushes out, in energy and complexity, there is an equal pushback. Yet the tendency is to only see one side of the coin at a time.

Now I'm just offering up some vague thoughts on symmetry, but the one example of this tendency to see such processes in isolation, rather than in the larger context, was an observation that first led me to question physics, cosmology actually; When I first heard that the expansion of space is inversely proportional to gravitational attraction. If they balance out, the universe isn't expanding. Geometrically you might say the space being created between galaxies is falling into them. When they talk about space between galaxies expanding, the galaxies themselves seem to be treated as inert points of reference, but, according to relativity, they are gravity wells! Space is falling into them.(Or the measuremnt thereof is contracting.) This first occurred to me in the late eighties and the only theoretical answer seemed to be a cosmological constant, as the balancing of gravity as first proposed by Einstein. Since then it seems the more logical solution is that light is only a point particle when detected, but expands when released, such that an absorbed quanta is a sampling of the wave front. This goes to Eric Rieter's loading tests of light. That a quantum of light is not an indivisible particle, but the smallest measurable amount, so by energizing the detectors, he tripped more than one atom with only one quantum of light released. Here is another example of how quanta of light are more complex than assumed.

My observations about time grew out of trying to figure that out. The idea of the intuitive side of the brain came from an observation by E.O.Wilson, that an insect brain is a thermostat. The left, linear side is quite definitely a serial function, with narrative cause and effect as the result. In fact, I once read of a test, using these large desert ant, that showed they could count footsteps as a navigation tool. The brain evolved for the purpose of navigation, which means assessing the environment and charting a path through it. Parallel processor and serial processor. Time is a serial function, just as temperature is a scalar function. We only model it as a vector, but duration doesn't transcend the present. It is the state of the present between the occurrence of events.

Hi Folks,

I was forwarded a slide set from a presentation at Brookhaven and Stonybrook on chiral superfluidity in quark-gluon plasmas. I commented above on smooth flows on S3 and S7 extending to cover the entire object (which I learned from Joy's book), and remarked that this resembles the behavior of a superfluid. I conjecture that Kalaydzhyan and colleagues may be detecting a quaternionic or octonionic phase in the QGP, which appears in the form of a chiral superfluid. It was too big to upload, so I made a space to link to.

Holography and chiral superfluidity for the quark-gluon plasma

So does a chiral superfluid on o holographic boundary resemble a smooth flow on the 3-sphere or 7-sphere? Does this constitute evidence for some of the dynamics Michael is talking about? Or does the chirality indicate the torsion induced by parallelization of the spheres? Broken symmetry perhaps? Inquiring minds want to know!

See also the paper on arXiv:

Chiral superfluidity of the quark-gluon plasma

This appeared to be relevant. Let me know what you think.

Regards,

Jonathan

Hello Michael and Friends,

In the thread above, I had mentioned smooth flows on S3 and S7 resembling a superfluid, as a smooth flow initiated anywhere will come to cover the entire surface of the object (which is elucidated in Joy's book). I had previously mentioned that the geometry of spacetime seems to change, as we approach the Planck scale, becoming first non-commutative and then non-associative, conjecturing the appearance of an octonionic phase. I'm thinking this will be relevant to your work, Michael.

I have provided a link in the long thread above, to a set of slides from a talk given at Brookhaven and Stonybrook, about a Chiral Superfluid on a Holographic Boundary in the Quark-Gluon Plasma. I think this work will be of interest. My guess is that the parallelized spheres in Joy's construction would induce a chiral flow, because they are twisted to encode a torsional component. But thinking further; I also imagine that eddys will never close to a point on the surface - which seems quizzical - so the relevance of these thoughts, and the properties of the QGP, to the theories of Michael and Joy deserve discussion.

Regards,

Jonathan

Jonathan,

What gets me is the extent to which temperature is a far more complex and varied dynamic than time, but time seems the more mysterious. Why? Are we missing something?

Hello again,

I note that the comment on a superfluid phase in the QGP, and the links above, considerably extend what I said on Dec. 6 at 18:14 GMT. I remarked that in his book, Joy explains "that a smooth flow initiated on the 3-sphere or 7-sphere will cover or come to involve the whole surface (as it is simply-connected)." Then I commented "This is analogous to the behavior of a superfluid. A recent paper by Bonder, Sudarsky, and Aguilar, suggests that a 'hydrodynamic' treatment of spacetime leads to a formulation of gravity that is Lorentz invariant. I think there should be a superfluid phase, however." The linked work of Kalaydzhyan certainly delves into that subject.

Does the analogy of a smooth flow on 3-sheres and 7-spheres with a superfluid make sense? Would Joy's non-trivial twist in the topology of the parallelized 7-sphere induce chirality? Does the notion from my Mandelbrot Cosmology - that chirality comes from the symmetry breaking induced by choosing a direction in time - serve to explain things, or does it complicate the picture? It is to be noted that cosmologies based on M predict that there is a maximal extent and minimal temperature of the cosmos - making it a closed universe. It leaves open the question of whether it is terminal or cyclical, but tends to imply the latter.

At this point; I am unclear whether my work with M has a definite connection with the ideas of Michael and Joy discussed here (so far as they are concerned). But I thought I'd put the idea out there, when I saw a clear connection with the discussion on symmetry breaking, as I am certain it will be a subject of active research for me.

Kind Regards,

Jonathan

Wow Michael!

Your comment above at 16:44 GMT is awesome and much appreciated. I'll have a few things to say. First; I want to cross-reference it to the Baez paper - which I've probably already read - once I sign off on this comment. Thanks greatly for providing such an excellent road map.

All the Best,

Jonathan

Hi Michael,

I don't think it's just a matter of being man enough to deal with incompleteness, and tackle it you do, but you may be the first to notice that the doors have signs that says "Pull" and everyone before you has been trying to "Push" instead. I like the way use use Gödel's result as a door, rather than a window. To my view; you exploit incompleteness as a way to define the existence of essential degrees of freedom, where others view it as a limitation on possibilities only.

This is decidedly a different way to proceed.

All the Best,

Jonathan

Hi Michael,

Thanks for the nice summary. If what you say is true, and if arguing against your conclusion is arguing against the fundamental fermions and the structure of the normed division algebras, then I am somewhat disappointed. Because I am convinced that despite your insistence and your overall philosophical justifications to the contrary your theory is manifestly non-local.

It can be made to be local, I hope, by tweaking it somewhere to accommodate my framework in such a manner that you can explicitly write down the four local functions, namely A(a, L), B(b, L), C(c, L), and D(d, L), for the four-particle GHZ state. The latter is of course just a simplest non-trivial example. What I mean is that if and only if you are able to accommodate the nested S7 of the kind both Rick and I are advocating (differently) can your theory be local. That is my claim in any case.

I think it would be worthwhile if you reconsidered a theory based on S15 instead of S10. For S7 is uniquely linked to S15 octonions through a Hopf fibration of the latter by S8 (see, for example, the attached paper). Just a thought.

Best,

JoyAttachment #1: 1248.pdf

Michael, Jonathan,

Just a simple, basic thought here, but it seems math is inherently dynamic, while we look for static structures in it.

Add, subtract, multiply, divide, etc. are verbs, not nouns.

What seems to be, is this scale of complexity, that as you proceed upward, gathers ever more rules and structures. In the real world, this would make them more brittle, static and unstable. Could there be mathematical feedback loops occurring that our linear thought processes are not perceiving?

That is an excellent comment John,

And in my view, all of the static structures arise out of the dynamism of Maths. I tend to think that the dynamic number types octonions, and then quaternions, appeared first - and then this ultimately made the static Reals possible. People are used to numbers that just sit there, from normal Arithmetic, but this is atypical in higher Maths and as you point out - even the simple operations of add, subtract, multiply, and divide, bespeak the dynamism of Mathematics instead.

And yes; that was my comment above, but I guess my login expired.

All the Best,

Jonathan

Hi Michael,

R, C and H are subalgebras of O, so if one "listens to the octonions", they very much are also listening to R, C and H. There is no preferential treatment for O over R, C and H at all really. There are however preferential choices made out of the clear vision both of us have on the supremacy of the division algebras, with O being the mother of all. I assume this position without apology.

On H being "real space" and O being "particle space" I am OK with "particle space" if it is a statement of the fact it is the fundamental space (for me more *algebra* requiring the *space*) of reality. But I have shown gravitation to reside within an H subalgebra and electrodynamic observables reside within what John Baez calls a basic triple, which is not not an H triplet. O has 7 H subalgebras, and we can't assign all to be physical xyz triplets. Any of the 7 may be taken as one side of the physical space coin, so there is no *preferred* choice but we must make a choice none the less. Once again after this free choice is made we have 4 free choices of which 3 of the remaining 4 basis elements also map to the other side of the physical space coin. Traditionally, physical xyz is taken to be a "polar" representation, so it more closely (parallel projection) aligns with the basic triple than it does the chosen H triplet, which has multiplicative closure as do "axial" types. The left over basis element forms a C subalgebra and if we require everything to be analytic in this subalgebra, the 8D stuff cleanly partitions into the sum of what looks like 2 4D similar structures.

I see your approach as not bothering with reading Nature's book from start to finish, but jumping ahead to the last few chapters. You fill in what you missed in the middle with fanciful notions like force = particle exchange, and reality *is* the symmetry groups rather than *descriptive of*, in order to make sense out of what you find. But I listen to your perspective with great interest, for it helps me put into context what I read as I progress one paragraph at a time to the same conclusion.

Rick

Jonathan,

What's the old saying, "The opposite of small truths are false, while the opposite of large truths are also true."

While I see math as inherently dynamic, I would also see the static as inherent as well. Above you made the following observation;

"I think time has the fewest rules, needing to adhere only to the nature of process. Space needs to follow rules of geometrical evolution. Energy drives evolutionary dynamism, but must follow rules of propagation and circulation. And matter must follow a few more rules, or is the most constrained."

I would ask; Why are the rules of geometrical evolution foundational to space? What if we were to consider the opposite, that space is foundational to the rules of geometrical evolution?

To space I would assign only two properties, equilibrium and infinity. The absolute and the infinite. With gravity, we have the attraction of equilibrium and with radiation, we have the attraction of the void, the infinite. All other properties of matter and energy, circulation, interaction, attraction, repulsion, etc. could be considered as being defined by the interactions of these two polarities of space. Matter is constrained because constrainment defines form. To limit is to define, as to define is to limit.

Consider the assumption in this observation;

" I tend to think that the dynamic number types octonions, and then quaternions, appeared first - and then this ultimately made the static Reals possible."

If anything is "first," then the sequence of real numbers would have to be. So even there, you have that foundational dichotomy of "being" and "doing."

Or as Frank Sinatra so eloquently put it, "Dobedobedobedo."