Joy, shut up and derive. :-)
Is Quantum Theory As Fundamental As It Seems? by Michael James Goodband
Michael,
Here is a better quote, from Michael Atiyah:
"Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine."
Sorry, Rick. I couldn't resist (I know; I am being frivolous).
Tom, I can both drive and derive at the same time!
Joy
[deleted]
Joy,
With the response I am getting in this essay contest, I am sure many yelled out "Blasphemer. Stone him, stone him" as soon as they got to the word "Octonion" in the abstract, no need to read further. I am happy Michael is doing as well as he is, but he should be doing better.
Rick
I had not heard that quote of Atiyah, and I absolutely love it! It fits to a "t" Wheeler's information-theoretic view, imbedded in our classical world experience of continuous functions.
Tom
Attached is a talk given by Sir Michael at Princeton a year or so ago.
It seems appropriate to attach it here, for he too is one of us---namely, an octonion.Attachment #1: AtiyahTalk.pdf
Joy,
That's a wonderful quote! I have to admit that I was a reluctant octonion, but not accepting one's own conclusions would just be bad form.
Coming from a QFT view, my natural way to accommodate QT not being fundamental is to just accept it as an approximate descriptive form with illusions, and not try to interpret them literally. Your experience seems to indicate an attachment by some to the illusions being literal. Since to me it is just about description, I accept that there may be another way. Proponents of geometric algebra have to my mind clearly demonstrated that in some sense it is the natural way to describe space, as the descriptive form is free from the illusions - such as in your work.
Tom,
Before you get too excited about the idea of dealing with particles without having particles, a hidden domain enclosed by a small radius S2 looks somewhat like a particle itself, or a type of multi-particle containing any number of correlated particles. It is also only a non-relativistic view that doesn't include particle reactions that change particle numbers ... yet?
What the octonion view of such a 2D surface (homeomorphic to S2) does give you, is an easy explanation of colour confinement. With coloured particles being topological monopoles with unbroken symmetry group (Spin(3)*U(1))/Z_3 the same topological unwinding arguments as for topological defects in field theory can be applied, with conclusions:
1) a monopole/anti-monopole pair are connected by a colour string
2) the Z_3 means that the colour field of 3 coloured monopoles with no net colour charge can be unwound outside of the S2 domain
Energy minimisation then implies the S2 is shrunk to the smallest size possible, giving colour confinement in classical physics - because the monopoles come from S7. This adds to the suspicion that the conclusion is going to be, in the words of Clinton: it's the octonions, stupid ;-)
Michael
Michael,
I too have been a reluctant octonion. "Extra dimensions" were anathema to me until my own investigations in the origins of quantum correlations persuaded me otherwise. There is no way to reproduce all of the observed quantum correlations local-realistically without embracing the octonionic 7-sphere fully. All other attempts to understand quantum theory will eventually hit a brick wall. In this context my attitude towards the octonion algebra is very much the same as Rick's.
On the other hand, you are right to think that the proponents of geometric algebra have got it right. The credit for their insight, however, must go to Hermann Grassmann first before anyone else (cf. the attached slides).
Joy
[deleted]
Joy,
Sounds like you want to have your cake and eat it too: non-associative Octonion Algebra and associative Geometric Algebra.
Rick
Absolutely, Rick. That is exactly what I want, and can have it too.
I use Clifford algebra for octonions following Lounesto (cf. the first attached paper), with an additional trick I learned from string theory and super-symmetry folks. I trade the non-associativity of S7 in for variable torsion (i.e., different torsion tensor at each point of S7). Full details can be found in Section IV.E of the second paper attached. This is very convenient and well suited for my work.Attachment #1: Lounesto.pdfAttachment #2: 6_1101.1958v1.pdf
Hello. This is group message to you and the writers of some 80 contest essays that I have already read, rated and probably commented on.
This year I feel proud that the following old and new online friends have accepted my suggestion that they submit their ideas to this contest. Please feel free to read, comment on and rate these essays (including mine) if you have not already done so, thanks:
Why We Still Don't Have Quantum Nucleodynamics by Norman D. Cook a summary of his Springer book on the subject.
A Challenge to Quantized Absorption by Experiment and Theory by Eric Stanley Reiter Very important experiments based on Planck's loading theory, proving that Einstein's idea that the photon is a particle is wrong.
An Artist's Modest Proposal by Kenneth Snelson The world-famous inventor of Tensegrity applies his ideas of structure to de Broglie's atom.
Notes on Relativity by Edward Hoerdt Questioning how the Michelson-Morely experiment is analyzed in the context of Special Relativity
Vladimir Tamari's essay Fix Physics! Is Physics like a badly-designed building? A humorous illustrate take. Plus: Seven foundational questions suggest a new beginning.
Thank you and good luck.
Vladimir
Hi Joy,
Can any physical significance be attached to the torsion variation of the trick you describe?
I ask because in conceptual terms the correlation of observables is due to the torsion of the parallelised spheres, so variable torsion would conceptually be associated with some variation in observable correlations. I have yet to get to grips with how the trick works its way through to observable correlations. Since it is just a trick, any such variation would be equivalent to the effect of the non-associativity of the octonions.
Michael
Hi Michael,
Yes, the variability of torsion within S7 is a measure of the non-associativity of the octonionic observables (which, in statistical terms, are the standard scores corresponding to the raw scores +1 or -1). So, indeed, variable torsion is associated with the variations in the observable correlations, and these variations are indeed due to the non-associativity of the octonions.
Now suppose the variation in the torsion happens to be zero in some special case. Then we would still observe quantum correlations as long as this torsion is non-zero, but they would not be due the non-associativity of the octonions. For example we could observe quantum correlations even when all of the observables are confined to a single fiber of S7---namely to some S3---despite the fact that the torsion within any S3 is always constant, because the quaternions that make up S3 are associative. To put it differently, when we have variations in the torsion we have variations in the observed correlations that are in addition to those arising from the non-commutativity of the quaternions.
Perhaps these additional variations can be understood as purely gravitational effects (as opposed to, say, strong or electro-weak effects) within your 11D GR?
Joy
Hi Joy,
If the S7 in question was the particle symmetry space, then such additional variations would almost certainly be inter-family correlations - e.g. between electron, muon and tau - which are outside the domain of strong and electro-weak interactions. The Z_3 of the monopole homotopy group PI_6(S^2) = Z_3*Z_4 gives 3 particle families, which is due to: the fibre-bundle structure of S7; the non-associativity of the octonions; and is presumably related to the triality discussed in the Lounesto paper.
In correlations between particles with spin (S3) and electromagnetic charge (S1), could the condition of the 3 particle families being entering into the analysis to require S7 and consequently these additional variations? This would appear to square with the origin of particles in my 11D GR. Unfortunately, my theory has the handicap on this issue of apparently saying that the CKM and PMNS inter-family transition matrices are not calculable (a further consequence of incompleteness).
Michael
Michael,
There is another issue which may be worth keeping in mind here. In the context of Milnor's discovery of the exotic spheres I noted above, it is worth keeping in mind that there are in fact 28 distinct classes of differential structures possible on S7, compared to just one unique differential structure on S3. If we are to view S7 as a differentiable manifold with variable torsion, then this fact may be important. It is also worth keeping in mind that S10 admits 6 distinct differential structures, and S11 of your 11D GR admits 992 distinct differential structures. I would think that each choice of a differential structure on S11 would give rise to different physics, at least in principle.
Joy
Joy,
Your point about there being 6 distinct differential structures on S10 is an excellent one. My 11D GR starts with a physicality assumption that an initial S10 manifold is the "fabric of space" - there is no S11, the full scenario is cyclical in time.
Actually there are 6 different types of physics in my model. The electroweak map of S7 to S3 has 2 possibilities (PI7(S3)=Z2) which can be given chirality labels {L, R} - electroweak interactions say we are in the L version. This leaves 3 possibilities per {L, R}, which would seem to correspond to the physics of the 3 particle families, where gravity, strong and electroweak interactions are equivalent for each family, yet must be different in some sense otherwise there wouldn't be 3 families.
I note that this chiral-family correspondence on 6 is only possible for unification of spatial S3 and compactified S7 into S10.
Michael
Note: My full model is cyclical in time because closed universes must expand and contract in GR, so time occurs as S1 and the universe has existed forever. The S10 expands and contracts in this "unified" phase, then goes through a topological transition S10 -> S3*S7 to a "broken" phase. A radiation driven compactification-inflation see-saw inflates the S3 universe and it carries on expanding to a maximum size, and then contracts; at the same time the S7 compactifies and reflates, so is not of a constant size as is artificially assumed in Kaluza-Klein. For me, this resolves the conceptual problems I had with extra dimensions - the size of S7 defines the scale of *all* physical measurements (the Planck scale), including measuring the scale of S7 relative to itself to give a constant scale in a physical (relativistic) theory. My physicality assumption is critical for this dynamics, and my other results, but does constrain the possible interpretations for features of the theory.
Michael,
Very good!
Let me make a note of few things and ask a few questions:
(1) You mention that there are 6 different types of physics in your model. Perhaps these are indeed connected to the 6 possible differential structures on S10 as you seem to think. It would be nice, however, to bring out this connection more explicitly. I don't know the details of the 6 differential structures admitted by S10. I only know the number. It would be interesting to explore how closely these structures are connected to the 6 types of physics in your model.
(2) Another open question is what you have already been puzzling about. In my analysis S3 and S7 appear as spaces of all possible measurement results. Because measurement results are simply events in spacetime (a click of a detector is an event in spacetime), I tend to think of S3---and more generally of S7---as the actual physical space where these events are occurring. In your analysis, on the other hand, S3 and S7 are symmetry spaces. The connection between these two facts is still an open question.
(3) One of the things I would like to understand is the status of the equivalence principle within your model. Does it remain an exact principle in S10? How do you account for the strong equivalence principle? If it does not hold as an exact principle, then how does it hold as an approximation? Any thoughts on this matter would be useful for me to understand your overall picture.
(4) Have you followed Roger Penrose's recent work on cyclical universe? I myself have not followed it, but I know he is very excited about it. It would be interesting to see how his work squares with the cyclical conception of time and eternally existing universe of your model.
Joy
[deleted]
It is what your probelm Mr Spindel and Mr Milnor, you are not skilling to understand my works, so ....., you lacks of credibility and funds , it is that?. You want the nobel in fact. Let me laugh.Your sciences are limited and not general, so why you insist with your strategy.
You know what ? You can all keeping your monney dear band of limited scientists. I am laughing in seeing the pseudo sciences, really. even with my bad english , I give you courses all the times. And the milnor prizes
It is what the probelm dear bad band. You need funds and an international credibility or what ?. Put the balls in the spheres dudes. You can all keeping your money.Milner and Milnor, forget me and also you know what? .like that you can still focus on strategies. ok . Now put the balls where I think in the spheres and publish for the nobel band of comics. I dislike the corruptions.Me I have made my works, I am a real searcher me.
Just for you and for the evolution of physics, I will continue to share my works.Me I improve band of comics, you no. The abel prize, nothing to do.The milnor mentoring, nothing to do.The Milner prize, still less to do. Mr Spindel , still less to do.and what ? all is said band of pseudos startegists lacking of generalism. Make all what you want, all is said, between us you know the truth .Ironical no? Exotic spheres ahahahah and what after? multiverses also.and after the balls inserted in the spheres. let me laugh, I have pity spiritually speaking.
Regards
[deleted]
yes of course , and some monney after the nobel, of course of course. your strategy shows in fact your lack of skillings for the gnerality.
In fact you think really that you are going to share the nobel dear Hopf and Milnor. Let me laugh !!! or kill me.But there you are not scientists but murders, me I will be always a real searcher inventor of the therory of spherization. You shall not be in the books. Me yes, I have already spoke a lot before fqxI since more than 9 years. If you knew the number of persons knowing my theory in all countries of these planets. Kill me, it is better you know. You do not merit the nobel.
Regards
Hi Michael,
You wrote: "Before you get too excited about the idea of dealing with particles without having particles, a hidden domain enclosed by a small radius S2 looks somewhat like a particle itself ..."
Well, it isn't particles per se that I'm interested in, but rather complete structural information that is tractable to analysis (continuous measurement functions). That's what motivates me to topology in the first place. The same questions that Joy asks above are inextricably bound to that view, because all except (3) involve simple network connectivity. (3) adds relativity.
Tom
Joy,
Interesting questions, only question 4 can I completely answer: short answer, it doesn't sqaure.
1) I don't know the details of the 6 differential structures on S10 either, or if they can be connected to the chiral-family physics distinction in the way I suggest. The topological transition would have to divide them in half, but the 3 remaining options would be required at the same time for the 3 families. I don't yet know if this is possible or even makes sense.
As S3/S7 are conceptually within the space of quaternions/octonions - giving a 12D space - I think I would first have to find the relation of my manifold - with its transition S10->S3*S7 - to this background - and find the time dimension in 12D - before I could consider the differential structure.
2) There is also a local-global confusion. Globally S3*S7 is a physical manifold where the spheres are curved - demanded by them being unified in S10 which isn't parallelisable. The KK identification for the construction of a local dimensionally reduced theory involves identifying the compactified space with a group space - this gives a flat S7 in the local theory, in which the rotation group space gives the other flat S3. Your analysis then requires the measurement spaces to be (flat) S3 and S7. This gives 3 types of spaces - physical, symmetry, measurement - to square with each other. If the physical curved space of my model is dropped, then the S10 "explanation" of the S7 to S3 map is lost, and so is the condition of 6 differential structures.
3) My model is simply constructed as an 11D extension of GR, with an initial radiation density of metric waves as extra-dimensional extension of gravitational waves. This requires the addition of an energy-density term with gravitational coupling, and using the same term necessarily involves the same assumptions. However, the definition of some physical quantities depends upon the number of dimensions, which changes with dimensional compactification (e.g. entropy). In 4D GR mass has a definition via the lst Casimir invariant of the Poincare group. In 11D the relation between the equivalent invariant mass and energy will be different from the 4D case, which raises questions about the relation between inertial mass and gravitational mass. The mass invariant in whatever number of dimensions will be the inertial mass, whereas the source of gravitational curvature in N-D GR is defined by the stress-energy tensor as being energy. The equivalence principle in 4D has a hidden assumption about the relation between mass and energy in 4D, but with dimensional changes the relation between mass and energy changes.
As the particle charges come from the topology of the space - including spin being a topological "charge" - they are independent of this mass issue. The incompleteness of the calculation of the reduced mass of the Planck scale particle black hole, makes mass the major unresolved issue of the model - the masses of the fermionic particles have to be added by hand from experiment, through a renormalisation process. In contrast, the W and Z boson masses are derived in terms of closed geometric formulae involving the electroweak scale - a Higgs boson mass of ½ electroweak scale is derived in the dimensionally reduced Lagrangian.
4) I hadn't followed Penrose's work of Conformal Cyclic Cosmology (CCC), but the first thing I note from is most recent arxiv paper is that the word "cyclic" is somewhat misleading - it is more iterative or recursive. My model won't square with CCC because mine is genuinely cyclic (it bounces).
Michael