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

The attachment didn't go through (too long). Here is the essential page again:Attachment #1: GHZ4.pdf

Michael, you wrote on December 4th;

No. The equivalence between the different octonion algebras mentioned by Rick and Jonathan doesn't take into account the physical reality of symmetry breaking. This first picks out one of the handed algebras, and then breaks the equivalence between the 8 algebras of that handedness.

In that case; I would assert that this hierarchy likely maps to the Mandelbrot Set, which in my view is the model of symmetry breaking. That is; if we assert that it is mathematical reality which provides the seed of symmetry breaking for the physical universe, it will be found in the Mandelbrot Set. One has a split of chirality at the cusp but the extent of it can be viewed as a giant thermometer.

I have been studying how the progression of forms around either edge, from the cusp at (0.25, 0i) to the tip at (-2, 0i), follows a pattern which elucidates the cosmological epochs and fundamental forces, for around 25 years now. It has taken that long for me to learn enough Math and Physics to make sense of what I was learning, though. But I can boast of a few conversations with professor Mandelbrot on this topic, way back then.

I attach a graphic of the annotated Mandelbrot Butterfly, which would have been on one of the slides shown in Udine, had I made it to FFP12 around this time last year. The wings and disks show up when you color in points where the iterand decreases in magnitude over 3 iterations. More later... JJDAttachment #1: CosmoEras.jpg

Hi Joy,

I think our newly developed failure to communicate is because we've arrived at my main result and what it means for physics: classical physics is mathematical incomplete under certain physical conditions.

I think you're trying state that the formulation you give in Ch6 (and everywhere else as well) is not DERIVABLE within my theory. I'm sure that is correct because the physical scenario is precisely the sort of scenario where mathematical incompleteness is found, but as a consequence I can't currently produce a proof that this is correct.

However, I'm equally sure that the formulations you give are STATEABLE within the domain of my theory. This gives our apparent communication failure: propositions that are STATEABLE within the domain of my theory that are not DERIVABLE within it. This is not a mathematical contradiction, but is just what mathematical incompleteness looks like. It was a shocker to mathematics in 1931, so it is perhaps not too surprising that it is a shocker to physics in 2012.

How can I be so sure that your formulations are within the domain of my theory? Because you reproduce QT results, and with the representational shift - derivable as necessary in meta-mathematical terms within the scope of my theory - I derive the QFT of the Standard Model (up to a representational colour issue). Specifically, the electroweak theory is derived EXACTLY and so all QT experimental results under electroweak QFT - pretty much all of them - are placed within the scope of my theory. This is currently dependent upon adding the experimental fact that individual particles have a wave property to the theory by hand - thus might appear to be a possible loop-hole in the theory. However, I find particles to essentially be in representations of S0, S3, S7 and waves in representations of S1, S3, S7, where the physical dynamics of the scenario leading to mathematical incompleteness conceptually looks as though it would combine S0 and S1 into the Hopf fibre-bundle and so give wave-particle duality. My theory works as though this is true, and it looks obviously true, but that isn't a derivation. I am this one result away from QFT being derived solely WITHIN my theory. As it is GR, my theory meets the conditons of local realism, even when QFT is derived. The representational shift gives the non-locality of identity of QT, but doesn't give non-locality of causation - it can't, it's within a relativistic theory.

The physical conditions giving mathematical incompleteness specifically include the physical conditions of ANY locally-realistic classical physics that attempts to account for ALL of the results of quantum theory. Specifically particle reactions, and the experimental results indicating vacuum polarisation, such as the Casimir effect. Vacuum polarisation is a virtual-radiation effect, which is specifically a relativistic effect, and not QT. ANY locally-realistic classical physics theory must be based upon Relativity, and to account for the Casimir effect etc. the theory MUST include virtual-radiation as well as particle reactions. These conditions alone are sufficient to guarantee that the theory will be mathematically incomplete (general case here). Adding terms of some imagined new physics won't make any difference when those terms are also constrained to be locally-realistic - this is by a corollary to Gödel's incompleteness theorem. My theory displays mathematical incompleteness precisely BECAUSE it is a locally-realistic classical physics theory that includes the physical conditions of QT. Every imaginable locally-realistic classical physics theory would be exactly the same, there's no way out of it.

When I saw your hidden variable work, I noted that it specifically only requires all states to be within L, and NOT actually derivable within L. The non-specificity of the hidden domain L is sufficient to allow the domain of a theory to be L. All the undecidable propositions that cannot be derived within my theory are nonetheless within the domain of the theory, and thus within the hidden domain L. So the fact that those features cannot be derived - such as the specific locally-realistic formulation you refer to - is actually irrelevant to the hidden variable framework - that's the beauty of it.

Our failure to communicate revolves around the fact that mathematical incompleteness is real in physics. But it is not the road-block it appears to be, just an irritating obstacle that you can go around. I find QT to just be a trick to get around mathematical incompleteness, and it's weirdness is what going around the obstacle looks like. But a further implication appears to be that the hidden variable framework is possibly the only other trick to achieve the same thing.

Best,

Michael

mjg AND ANON GRAVITATIONAL LENSING RELATES TO THE RED-SHIFT.

Hi Folks,

I've more to say, and another image to attach, on how M induces symmetry breaking - and how this might pertain to the way the 8 left-hand or right-hand Octonion algebras can be sorted hierarchically. I will append those comments to the thread above, where Michael made his statement regarding how that sorting takes place because of symmetry breaking induced by the Physics - and I asserted it could arise from the pure Math. So see above for my fanciful wild idea.

Regards,

Jonathan

Regarding broken symmetries in M;

One can make the computer display the Mandelbrot Set such that what would ordinarily be the interior becomes the surface, by having it calculate concentric circles, and then showing them as lines across, with each larger circle being the next line down. This helps to visualize what I was talking about, regarding the symmetry breaking properties of M. I have attached a graphic of this. The thing is; broken symmetry in M extends to the quaternion and octonion cases, leading to a situation a little like what Geoff Dixon spells out in his theory based on T = C x H x O, because it splits the figure into two identical branches of opposing chirality, and the asymmetry in M is along the Real axis - so it is invariant over the R, C, H, and O number types.

Like Dixon's construction, and like the Spontaneous Inflation theory of Carroll and Chen, the way symmetry is broken in M suggests there is an antimatter universe, going the other way in time - somewhen/somewhere out there. That is, the first syymetry breaker is the cusp at (0.25, 0i), which appears near the center top of the attached image. For reference; I state that the point (-2, 0i) appears at both the lower left and the lower right corners of this figure. But again I have run out of time for descriptions, so I leave you to ponder this new post. This is in reference to Michael's earlier statement about a hierarchy among the 8 left-hand or right-hand algebras of the Octonions; I assert that there is very likely a connection with the symmetry breaking in M, if the sorting is via broken vs conserved symmetries.

I submit that if the facts about S3 and S7 influence the Physics we observe then the geometry of M also has some role in shaping observed form. I'll have to get back to this later.

All the Best,

JonathanAttachment #1: UnfurlMandelBig.jpg

Hello Michael, Joy, Tom, et al,

I agree with Joy's sentiment that some of the interesting Physics you are propounding, Michael, is more because of the interesting properties of S7 and S3, rather than in spite of those geometric realities. In this regard; I think my comments above about broken symmetry from M are very much germane to the discussion as the rules of geometric evolution are key to both the emergence of, and understanding, Physics.

I've been reluctant to share some of these results with this group, as on the surface it may appear that a Cosmology based on the Mandelbrot Set is a crackpot notion. It may well be true; but after 25 years of cautiously investigating the prospect there is such a connection, I still end up finding interesting evidence or proof some of my conjectures were right. But all I'm suggesting here is that; just as with Joy's comments about the properties of S7, it may be that the observed symmetry breaking is because of geometric considerations, rather than in spite of them.

I'd just be talking about the geometry of M, as the inducer of broken symmetries - which are observed in Physics. So if I appear to be talking past either of you (or anyone); I apologize. But I think I'm offering an insight that could help to break the impasse. Of course; I could be wrong and it's unrelated, but automatic broken symmetry is a big deal either way.

All the Best,

Jonathan

A parting thought.

Might the whole macro vs micro issue be resolved by acknowledging that growing and shrinking are the exact same operation in opposite directions of time, and that the same object appears either micro or macro depending on whether you are the time reversed observer or not. The thing is; there is no way to tell, as the time sense of any individual observer is associated with the direction of process evolution - which implies forward motion through time. This is also akin to Tom's observation that observers see only information coming toward them.

Perhaps it is this ambiguity over whether we are time-reversed observers ourselves - that creates the confusion between the micro and macro universe - or geometric objects associated with the Physics. This pertains to the relations spelled out in Michael's comments on 2nd and 3rd order relativity. Now I really do need to break away and get on to other stuff.

Regards,

Jonathan

Since I have a moment;

On the topic of interesting properties of S3 and S7 that inform the Physics; I note that in Joy's book, he 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). 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.

A few years back; I came to the insight that - as the Planck scale is approached - geometry becomes non-associative as well as non-commutative. In William Orem's blog asking "Does Math Evolve" he suggests that at the Planck density the existence of distinct or separate objects is not possible - and so familiar mathematical relations cannot exist or have not yet emerged. I suggest that this condition is identical to saying that geometry is non-associative at or below that scale. This could be Michael's S7 at work.

Anyhow; could the S7 in Michael's formulation appear like a superfluid vacuum near the Planck scale?

More later,

Jonathan

Jonathan,

I think in terms of evolutionary need, the hemispheres of the brain are like a thermostat(right) and clock(left). Basically one is evalutating the situation(thermostat), while the other is calculating a path through it(sequence/clock).

My observation about time being past to future perception of future becoming past process connects to this. Think in terms of a factory; While the product goes from initation to completion, the process points the other way, consuming raw material and expelling finished product. In a sense, this is the dichotomy of the mind/brain. Being physical, the brain is constantly absorbing sensory input and producing thoughts, while the mind, being the collection of these thoughts, is a record of the events. So the brain, being physically extant and going from one event to another, goes past to future, while the mind is a record of the events as they recede into the past, ie.future becoming past. The logical, linear, sequential, clock side of the brain is going from past events to future ones, while the thermal register of the right side is absorbing the dynamic process of change, as the flow of events go future to past.

On a side note, much of the conversation about symmetries, reversed time, etc. reminds me of staring into a mirror; We seem to see our world in reverse, but it is simply a reflection. If time is simply an effect of action, similar to temperature, this changes the entire question of what space is. I keep arguing it is both absolute, as an equilibrium state and infinite. (Consider centrifugal force is not due to outside reference determining spin, but spin in relation to inertia. Where does inertia come from, other than space itself? I also make the point that expanding universe theory overlooks the fact it needs a stable speed of light as a yardstick. Where does that come from?)

So if we consider space as such a form of background, might it have a form of mirror effect on the physical world and we are not really dealing with an opposite reality, but a form of reflection?

Hi Jonathan,

" ... the way symmetry is broken in M suggests there is an antimatter universe, going the other way in time - somewhen/somewhere out there."

I think this is almost certainly true. We can live without parity conservation at short nonrelativistic distances, but if spacetime is not conserved, I don't see how the world would be comprehensible at all. Even in Joy's framework as in Einstein's, all correlated quanta are indifferent to distance -- implying that particle-antiparticle pairs are also correlated from creation to infinity.

Tom

" form of mirror effect on the physical world"

In that as infinite, it is the void pulling out and as equilibrium, stability holding everything still. So in a sense, not just a reflection, but the "surface" on which existence is, with everything both pulling and holding.. Not making this clear, but it seems as possible as a reversed reality.

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