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

Dear Michael,

Congratulations with your interesting essay and good luck in the competition!

You raise a very important problem whether quantum theory can be substantiated in view of the Goedel theorem. The theorem is based on the fact that a set of natural numbers is infinite. As a consequence, standard quantum theory is based on standard mathematics with infinitely small, infinitely large etc. In my papers (see e.g. http://arxiv.org/abs/1011.1076 and references therein) I consider an approach when quantum theory is based not on complex numbers but on a Galois field. Since any Galois field is finite, no problem with the Goedel

incompleteness arises. Standard theory is formally a special case of a theory based on a Galois field in the the formal limit p->infty where p is the characteristic of the Galois field. You also raise a question whether gravity should be quantized. In my approach http://arxiv.org/abs/1104.4647 gravity is

not an interaction at all but simply a kinematical manifestation of de Sitter symmetry over a Galois field.

Felix

Hi Alan

In Kaluza-Klein theories (KKT) the extra dimensions are shrunk into closed spaces, which for the case of electromagnetism basically gives the motion of light as being of the form of a spiral wave travelling along the surface of a closed tube. Such rotation around the closed dimension would give a visualisation of why a photon has spin in KKT.

The wave expansion about a particle-like compactified black hole given in my essay would physically correspond to the scenario of virtual-radiation about a particle creating a particle/anti-particle pair and then for the created anti-particle to annihilate the original particle. This gives a sort of alternation between a particle and the waves of its virtual-radiation field. The wave-particle duality comes from the time-scale of this alternation being as rapid as the Planck time, and so all interactions occur over the time scale of millions of such cycles. It is like drawing a particle and a wave on two pieces of card and then rapidly flicking between them, the net result is that you see both wave and particle at the same time. Whereas you can stop flicking the cards to see one of them at a time, the Planck time scale of the alternation means that there is no corresponding way of only seeing one at a time and so we see wave-particle duality.

This gives a scenario of an alternation between a particle with a virtual-radiation wave field, where the waves in KKT travel in a spiral fashion around a compactified tube. Accurate visualisations of higher dimensional scenarios are always slightly dubious, but you could argue that the average net effect seems to have elements of your visualisation.

Michael

Hi Michael,

Thanks very much for the clarifications and the recognition of how the Archimedes screw visualisation *does* tie-in with modern theories. Much appreciated.

Alan

Dear Felix

Thanks for your positive comments and best of luck to you too!

You're absolutely right that Gödel's theorem has a critical dependence upon the natural-numbers being infinite, where for physical theories the natural-numbers arise as the cardinality of sets. Hence your finite Galois field avoids incompleteness issues. I note that your paper http://arxiv.org/abs/1011.1076 has to make the assumption that the universe is finite in order to get finite sets of particles. I also have to impose this finite universe condition to get a closed universe with the necessary topology to get a chiral twisted space that looks like the electroweak vacuum, and a spectrum of 12 topological monopoles that look like the 12 fundamental fermionic particles.

Despite our different approaches, we agree on this finite condition and we are not the only ones. In my case the finite condition of a closed universe gives topological monopole particles with a finite radius and no point singularity. Other essays have argued against point-like particles and singularities from a different basis. So with regards to possible 'meta'-principles asked for in the contest, a meta-principle of reality being finite - as in a closed universe and no singularities - is one that is being proposed from a number of different angles.

Michael

Dear Doctor Goodband,

Due to an abysmal lack of formal education on my part, although I valiantly tried my best to read your essay several times, I did not understand a word of it. While it might readily seem to be the height of ignorant impertinence for me to make any sort of comment about your essay, as a realist whose essay Sequence Consequence fully explains my position, I would like to pose this question to you. Just as it has been physically impossible for scientists to create a perfect vacuum in the laboratory, why are scientists so confident that they can effortlessly build a perfect dark chamber? Whether or not visible light is made up of a finite number of perfectly formed identical photons or exchangeable identical particles or identical waves seems immaterial. Whatever light is made up of it is still a physical entity and as such once it comes into existence, light cannot be totally eradicated it can only be altered. It is my contention that visible light does not have a speed of motion, it is always stationary. I truly believe that once visible light strikes a surface, it stays on that surface illuminating it. If the source of the light goes out, the visible light on the surface automatically assumes the darkened appearance of the surface, but it cannot physically move away or cease to exist.

Dear Michael James

I think Quantization is imperative to describe the infinite universe with finite expressions, in that the quantization of physical noumenon of nature needs adaptations for sensing the phenomena of nature.

With best wishes

Jayakar

Hi Michael,

Your comments on the essay by Edwin Eugene Klingman led me to your own essay. You wrote on Edwin's blog:

"Models with causal linkage between the particle and wave property generally have problems with Bell-type analysis, or re-analysis. Quantum Theory has a very peculiar form of non-locality, with what can be called non-locality of identity which is confirmed by wave interference and quantum entanglement experiments. However, this is strangely not accompanied by non-locality of causation such that it could be practically used to send a signal faster than light. Unfortunately because your model has causal linkage between the wave and particle properties, when you obtain the non-locality of identity required for comparison with QT you also acquire non-locality of causation. So Joy Christian is right and the model as given in the essay does fall victim to the non-locality issue, as encountered via Bell-type analysis."

I have been trying to tell this to Edwin for some time now, but you have been able to say it much more clearly. Bell's analysis is not something that can be overcome that easily.

In any case, what I found interesting in your own essay is your comments about the four parallelizable spheres, S^0, S^1, S^3, and S^7, and their associated normed division algebras. In this context you may find my attached paper interesting (with a fuller account of my ideas in several chapters of my book).

Best of luck for the essay competition,

Joy ChristianAttachment #1: 5_1101.1958v1.pdf

Hi Michael,

Thanks again for your comments on my thread. They definitely helped my 2nd reading of your essay.

Like Joy I had noted your mention of S0, S1, S3, and S7 as the only normed division algebras, a point that Joy has repeatedly remarked on. This time I was particularly fascinated by your view of black holes as Kaluza-Klein 'particles' with empty S2 interior and 'real physical surface' as event horizon, and no singularity.

You indicate also that you derive values close to the Standard Model "despite being derived solely within classical physics." I plan to look at that reference. In the first page or so you remark there is no means in classical mechanics for a single particle to travel as a wave. Of course my model is based on the particle always traveling 'with' a wave. It is this linked state that you seem to view as a causal linkage leading to Bell-type non-locality issues. With inherently unknowable phase the abstraction 'causal' may be stronger than is actually the case, as there is also a self-interacting aspect of the C-field that may or may not allow physically real solutions to be derivable. In other words I am uncertain, according to your definition, whether to consider my wave property of the particle 'derivable' or not. [By the way, I tried to get your book Agent Physics on Amazon, with no success. Any ideas?]

Another point I did not fully appreciate the first time I read your essay is this: "Conservation laws applying to charges of particles mean that no real-number valued variables could be the cause of changes in particles numbers [with implications for incompleteness proof]." And this time through I did like your conserved charge as a limit to black hole self-immolation.

The following section on Non-physically-real terms is a tough nut to crack. I read and understood the words, but it doesn't jell. Partly because I believe particles derive from physical processes, not symmetry. Perhaps I'll understand this better after reading your reference [15]. I do agree with you about physics unification without quantum mechanics being fundamental.

In studying your 'twist' in S7, it does not sound the same as Joy's torsional twist. Is it? I did not interpret your change in metric in the ergo-region to be equivalent to Joy's change in handedness, but do you believe your solution is isomorphic to his?

I hope to have a few new questions after another reading or so.

Best,

Edwin Eugene Klingman

Michael,

Nine pages is just not enough! I doubt that anyone can understand your essay with one or two readings. I would advise anyone who wishes to better understand what you are doing to read your reference [15].

Edwin Eugene Klingman

Hi Joy,

Fascinating paper! It looks very much like you've got the other side of the story I have presented in the context of extended GR.

In my Agent Physics book - and in the review paper of the chapter presenting the theory http://www.mjgoodband.co.uk/papers/STUFT.pdf - I proposed the following meta-principle:

Physical causation will only be consistent and complete if it realises all the manifolds S0, S1, S3 and S7.

I assume that this applies to a real physical manifold - as in a real fabric of reality like the fabric concept of space-time - which when read off directly in the context of extended GR specifies a closed S3 universe with particle dimensions S7. Such a universe is necessarily cyclical S1 and to obtain the manifold S0 as physical objects requires topological monopoles - hence the given pattern S10 -> S3*S7 with the formation of a physical twist in the fabric of space which breaks the S7 symmetry in a suitable way. This gives monopoles and anti-monopoles - giving a realisation of S0 - which must be in a representation of the rotation group - with group manifold S3 - and particle symmetry representation of the manifold S7. The S1 representation would come from the monopoles having a wave property, which I have to add from observation as my derivation of QFT is based on the wave property being non-derivable.

Unless I'm much mistaken, it looks as though your work could be stated as the meta-principle:

Physically-real representation of reality (in the sense of ERP) will only be consistent and complete if it involves all the manifolds S0, S1, S3 and S7.

Would this be correct? Such a condition on mathematical representation would be the other side to the equivalent condition being applied to a real physical fabric of reality. However, the consequence of this restriction is that the symmetry breaking required to give topological monopoles must be of the form:

S7 = SU(4)/SU(3) -> (Spin(3) * SU(2) * U(1))/Z3

Which would imply that the local colour group HAS to be SO(3) and not SU(3). Once the significance of the manifolds S0, S1, S3 and S7 is recognised there doesn't seem to be a way of avoiding this conclusion. Does this seem correct to you?

Michael

Edwin is probably right. There are two interlinked parts in my essay which are both quite involved, and have been discussed carefully as they suggest a model for physics unification. See

1) http://vixra.org/abs/1208.0010

2) [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf

The first part is about the physical conditions under which Gödel's incompleteness theorem can apply to science theories constructed in strictly physically-real terms, and how this is not the end of the story as you can change the mathematical representation - to non-physically-real terms - to escape from Göde's proof. This is discussed in more general terms in a philosophy of science paper that I have posted on http://vixra.org/abs/1208.0010 to make it more available. The issues raised here are those of the relationship between physical reality and mathematical representation - as also discussed by Roger Schlafly and mentioned by others e.g. Dan Bruiger - especially how it can become problematic when a physical system forms a closed cycle of cause and effect. The problem here is specifically with the top-down causation part of the closed cycle, from effect back to cause - George Ellis discusses how we might be under-estimating all such top-down causation in science.

The second part of my essay is specifically identifying a scenario which realises the conditions needed for Gödel's incompleteness theorem to apply to a particle-like object within classical physics. This is specifically identified in a rotating black hole of the Planck scale, as the rotation drags space-time such that there-exists a region where any radiation in it would be of the form of the virtual-radiation of Quantum Theory. The calculation of the effect this virtual-radiation has in reducing the rest mass of the particle-like black hole is shown to be subject to Gödel's incompleteness theorem. The Planck mass of the object is reduced by the virtual-radiation field around it, but the reduced mass cannot be calculated in classical physics. Heuristic arguments imply that the mass reduction effect can be almost total, giving an almost massless particle-like black hole with a radius of the Planck length and angular momentum of ½ the Planck constant - such an object looks suspiciously like a real particle. I then assume that a non-derivable feature in this theory is that this object possesses a wave property, and use the change in mathematical representation discussed above to show that these objects would then be described by a Quantum Field Theory. Since QFT can be derived by a change in mathematical representation QFT cannot be fundamental; this is expanded upon in detail in [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf.

The final part of the essay then discusses how this all adds up in being able to derive both General Relativity for space-time and a Quantum Field Theory for 12 topological monopoles with the same charges as the 12 fundamental particles, where the Lagrangian has the same mathematical form as that of the Standard Model. The points discussed above with Joy Christian about the spaces S0, S1, S3 and S7 being special, imply that the extended GR model of the essay - S10 unified field theory - is uniquely characterised for the assumption that the fabric of space is a real physical surface. The theory has 2 potential conflicts: it says that the local colour group HAS to be SO(3), not SU(3); and the universe HAS to closed (S3). If these are true, and the mathematical representation change is the origin of Quantum Theory that it appears to be, then S10 unified field theory would seem to be viable a candidate for physics unification.

Michael James Goodband

Michael,

It's a breath of fresh air to see some serious understanding of modern topology, when these forums have been full of serious misunderstandings the last couple of years. Where were you when we needed you? :-)

Also, I for one very much appreciate your organization -- building from classical black hole relativity to quantum theory. Nice.

I don't think Joy Christian's mathematically complete framework has the problem of demanding a closed universe; parallelization of S^1, S^3, S^7 gives us a flat space to work in, so that conformal mapping guarantees angle preservation to infinity even in a curved space, and simple connectedness does the rest. I.e., because all real functions are continuous, and because the octonionic space of S^7 allows the geometric algebra to return all real values, the set of complete measurement results on S^3 constitutes a closed logical judgment on all the local physics, even in an open universe. (There's some peripheral discussion of this issue in my essay "The perfect first question," that I hope you get a chance to visit.) I'm not familiar with the term "particle space" that you apply to S^7; however, it seems to fit with my informal characterization of Christian's S^7 structure as "physical space" in concert with S^3 as "measure space."

Really, you've done a crackerjack job. Thanks for sharing and best wishes in the competition.

Tom

Michael,

For me the significance, or rather the inevitability of the manifolds S^0, S^1, S^3, and S^7 is necessitated by a rather innocent looking algebraic identity (cf. equation 1.53 of the attached paper). I am sure you are more than acquainted with this identity, but for a summary of my perspective on the matter please have a look at sections 1.4 and 1.5 of the attached paper.

Best,

JoyAttachment #1: 9_Origins.pdf

Hi Michael,

Nice summary. As Tom says: Where were you when we needed you? :-)

The discussion of my work, both here at FQXi and elsewhere, is usually at a very superficial level. Most people seem to get stuck at the most basic EPR correlation, when I want to talk about local causality of any conceivable quantum correlations, no matter what the underling quantum state. This can *only* be done by recognizing the exceptional properties of the parallelized 7-sphere---especially its closed-ness under multiplication, as well as that of its fibres, S^3, S^1, and S^0.

This is perhaps *the* fundamental conceptual difference between our respective uses of these spheres. While I too arrived at them through physical considerations (by analysing the conceptual arguments of Einstein, EPR, and Bell), what I ended up with are the *parallelized* spheres, which are---so to speak---as flat as a sheet of paper. More precisely, their curvature tensors vanish identically, while torsions within them remaining non-zero. Thus the theory of gravity more appropriate in the context of my work is the teleparallel gravity, not the usual general relativity. It turns out that without parallelization local causality cannot be maintained for all conceivable quantum correlations, or even for the basic EPR correlation. Parallelization is the *only* way to meet Bell's challenge. Unfortunately this fact is not yet widely appreciated, even by some supporters of my work.

Best,

Joy

As the potential skunk at the picnic, and the possibly alluded to deluded 'supporter' and one who is minimally familiar with both of your work, it is not clear to me that a shared appreciation of S0, S1, S3, and S7 doth a marriage make. I too believe that these normed division algebras are important and, with Rick Lockyer's view of Octonions, see them as applying to my own work. Just sayin'.