The Algebra of \"Everything\" by Rick Lockyer

Good to see you back here too, Rick!

Thanks for your reply.

By the way, I have already rated yours (as well as Michael's) essay (as a member). You can venture a guess what marks I have given. I may be accused of bias; but, as you know, I have been accused of worse.

Happy working,

Joy

Thanks Michael, for the point of agreement;

It really depends how the subspaces relate to the octonionic background or bulk. Hans Van Leunen's 'Hilbert book model' uses quaternions to link us with the microscale and quaternions again to link us with the cosmic scale - and with other systems in general - through probability amplitude distributions. He calls them QPADs. But if in your theory; we are living in a quaternionic topological space - S3, that is embedded in or contiguous with octonionic space - S7, what does that imply conceptually? And how do things fit together? The linkage is all important.

My guess is that the orderliness of the octonions actually comes to the rescue there, or for helping reconcile your theoretical ideas with Joy Christian's, in terms of helping to sort out the way things link together and the order in which things must evolve.

I've been working for some time on a universal protocol for measurement or determination, and it turns out to have strong tie-ins with the octonion algebra's procedural aspect, as it requires precisely seven stages. I keep returning to points made by Connes, in papers from 12 years ago, regarding how we define smooth, topological, and measurable spaces. He spells out some of the precursors or prerequisites of measurability. But that's just a starting place. However; I think the octonions suggest and endpoint to that process.

More later,

Jonathan

Please note, Anonymous;

John Baez wrote a wonderful article on Octonions with John Huerta, and it was published in Scientific American - one of the sponsors of this contest. It seems ill mannered of you to invoke Baez' crackpot index here, for ideas John Baez might actually support.

Regards,

Jonathan

I think it is high time someone produces

(1) a "stuck-in-the-box" index for all the dogmatic idiots of the scientific world

and

(2) computes the so-called "crackpot indices" of Kepler, Newton, and Einstein.

Jonathan and Rick

Just to clarify. In my model the S3 of space is *not* a subspace of S7 but the two S3 and S7 form a 10 dimensional product space. This can either be viewed as a torus - if we pick the S1 fibre from the S3 - with an S7 cross-section, or a sphere - if we pick out the S2 base-space of S3 - which has a S7 surface cross-section. The absolutely critical element of my model is that there is a twist in the S7 cross-section in going around the S3 (like a higher dimensional mobius strip or twisted torus) - this is the electroweak vacuum and it picks out the sub-spheres of S7, but in a way that mixes S7 with the S3 spin space. In my model, this gives the reason for why the electroweak charges of the particles are chiral. This is also why my results with a 10 dimensional product space are *not* actually in disagreement with the S7 of Joy's correlation results. Spin (space S3) is correlated with isospin (space S3) and hypercharge (space S1) which are sub-spaces of S7, but colour charges are independent and not correlated with the other observables.

So my model says that viewing S7 as all of space - as Joy and Rick do - will work for spins and electroweak charges - which are correlated in particle physics - but that leaves the colour space unaccounted for. Joy's correlation results imply the *independent* colour space would be S3 (as S7 isn't a group space). The twist in my model of a physical gauge space S7 in going around the space of a closed S3 universe has the peculiar effect of switching S3 spaces in the *measurement* space - the S3 spin space is swicthed for the S3 colour space. The linkage of the subspaces is all important - as is the distinction between physical spaces and measurement spaces - and just how 'the orderliness of the octonions' actually does the rescuing is the piece of the puzzle I'm looking for.

Michael

Ahahahah and they insist furthermore.You are not real christians. Me yes.Don't try with things that you do not understand.

How can you converge if you have not understood the reall message.It seems not possible. In fact your goodband is just a team without real innovations. A goodband, yes of course, a goodband of businessmen yes. And you try with bad strategies.Like poor thinkers frustrated and jealous and envious and full of hate. My universal love will eat your hate. Dead or alive, I will continue. even a gun on my head, I will continue.

You know ; kill me , it is better you know and more quick for your strategy.

Aahahah I am crazy, I have god with me , Jesus Christ also is with me and Buddah. You want really to try with the faith. Let me laugh band of bad men.

Irritating that I forgive you all no?You would in fact that I discriminate people and country. Let me laugh, I love more than you the USA. the United States of the Sphere you know. No? don't worry you shall understand on the entropical arrow of times. I love USA !

A goodband, yes of course.a good band for monney yes.

Regards

Michael,

I found it interesting that you say, "Joy's encountered 'difficulties' trying to explain the simpler topological structure of S3; trying to do the same for S7 is likely to be a lot more difficult."

I see it as just the opposite -- S^7 is easier to understand than S^3, and S^n, n > 7 is easier still. Maybe this is the difference between having the knowledge of particle physics that y'all possess and that I lack.

The properties of simple connectedness and the orientability inherent in topological analysis give me comprehension of Joy's framework without invoking any specific struture; indeed, actually demanding a coordinate-free description of physical interaction. (I doubt I would have even been interested in Joy's research had not Perelman fortuitously proved the Poincare Conjecture for S^3.)

"A translation exercise between the two perspectives may prove to be useful in the long term as ... well, it seems S7 is it."

I see that as a limit, S^7 and O are compelled to be identical, as Joy has it. It's a perfect fit of discrete measurement outcomes with continuous measurement functions.

You guys -- Joy, Michael, Rick, Jonathan -- are, in the colorful vernacular of my generation X daughter, "the shit." :-)

Tom

Hi Rick,

You're leading me to understand some of the historical rivalry between analysts and algebraists that had me puzzled in the past. :-)

I just don't understand the aversion you seem to have in translating one mathematical method to another. For example, 16 degrees of octonionic freedom is identical to 16 redundant points of a Minkowski space tensor. Hestenes, with spacetime algebra, gets smoothly from the algebra to the analysis by deriving Minkowski space. If he couldn't get there, I would be prone to dismiss your arguments, because I wouldn't understand them.

I truly admire your ability to get seamlessly to your destination by letting the algebra drive, as you say. Some of us lesser mortals, however, walk on crutches, and have no chauffeur.

Tom

Rick Lockyer wrote:

"I call The 3:4 Morph Rule."

I call 3:1 Yuri Rule

See please

http://www.fqxi.org/community/forum/topic/946

http://fqxi.org/community/forum/topic/1413

Rick, Jonathan, Joy, Michael, and Tom:

As another author observed in a comment, "It's so hard to change others minds." Obviously this is related to the investment others have made in pushing their own model of understanding.

Rick described it beautifully [12 Sep @16:36]: "Many people pick one of these choices and run with it [which is optimal because] the collective will succeed faster by leaving no stone unturned."

We are all -- on Rick's thread -- admirers of Octonions. Unfortunately [or not?] each is pushing his own cart filled with his preferred goodies.

Despite yeoman's efforts Michael Goodband and Joy Christian have failed to converge. Joy's S7 is "physical space" while Michael's S7 is "particle space", which is compactified to produce a fermionic spectrum of topological defects, and *must* be added to S3, the physical [or spin?] space for a total of 10D. Although individual love of S0, S1, S3, S7 is shared, the models do not overlap in a meaningful way.

While I appreciate Quaternions and Octonions, I do not come to my theory through either symmetry groups or topology. Instead I focus on the physical behavior of physical fields implied by Maxwell's equations [he was first to write the gravito-magnetic equations that also fall out of general relativity].

This is quite a different approach than that exemplified by Lisi's E8, which, as I see it, is to find a large mathematical structure and try to show how it contains "everything", even making up new "things" to fill empty slots in the structure.

Now because of their own models [which are incompatible with each other despite a professed love of S0, S1, S3, S7] both Joy and Michael reject my model. But it does address some of Rick's concerns. Specifically, Rick claims that Octonions fully encompass electromagnetics and gravitomagnetics.

But Michael responds [6 Sep @ 18:46] that "A solely "octionic relativity" can't include both GR and the full gauge symmetries -- not enough degrees of freedom."

To which Rick responds, "It may be that ... the Standard Model actually does have too many knobs to twist" and allows himself to be guided by his intuition [as I do].

Michael responds with a "degree of freedom count" that shows 11 conserved "charges", three of which are color charges.

To which I respond: A gravitomagnetic theory of particles does not require color charges. The dynamics of the C-field achieve the purposes for which color was *invented*: Pauli asymmetric fermionic wave-function, "famous-factor-of-3", asymptotic freedom and quark confinement, and offers a way to compute the mass spectrum. Thus in this model at least 3 degrees of freedom vanish, putting us back to 8. [There are also implications for the S7 "fermionic spectrum of topological defects" but I'll stop here at 8.]

So we all agree that Octonions are important but we all disagree about the details. At this point I believe my own model actually fits within Rick's "algebra of everything".

[I don't expect to convince anyone. In three FQXi contests I've yet to see anyone give up his own model for another! And please spare me the Bell lecture.]

Thanks for fascinating discussions.

Edwin Eugene Klingman

Hi Edwin and Rick,

I think we have some agreement on "it's so hard to change others minds". That might also be in part because it is often so hard to change our own minds with our own ideas. It took me quite a while to change my own mind about the relevance of Godel to physics and bypassing it through representational change. Joy has managed to change my mind about Bell's Theorem, but then I was in a very receptive frame of mind for such a result having independently arrived at the same conclusion about QT. Mine and Joy's work are actually compatible, to what extent is yet to be agreed. For my part having read Joy's book I see no current disagreement - there is some about future direction.

Geoffrey Dixon and Cohl Furey consider R*C*H*O and get the Standard Model group eigenvalues for SU(3)*SU(2)*U(1), whereas I consider the physical manifold S0*S1*S3*S7 and get a colour group dispute - but QT not being fundamental. In either case, the octonion structure is likely to prove to be required reading, but we are going to want it from the particle physics perspective in order to present it to others - sorry, but it won't just be about us seeing it the "correct" octonion way.

Michael

Hi Rick,

I understand the appeal of maths structure, but my physics intuition won't let me go with it. I had the same issue with super-symmetry and string theory: maybe interesting maths, but they ain't physics. I'm a physicist first, not a mathematician. For me letting go of physical reality and floating free into maths is the path to insanity - I've seen the evidence, I've read string theory papers, it leads to insanity ;-) Even GR is presented as a maths map stripped of its physical territory, which gives acceptance of "constant" in a theory about the "relative"; a cosmological "constant" just ain't physics! (rant over)

The puzzlement referred to maybe because I came at S7 from a non-octonion direction. For me, QT not being fundamental means that the resolution of the physics conflict between GR and QFT, is that just leaves GR as fundamental. This is GR with a physical manifold; a physical surface you could notionally poke with a stick; a real physical territory; a physical reality to hold on to. The question was then: for a closed S3 universe what closed space can be mapped to S3 to give particles as topological monopoles (S0)? From the homotopy groups of spheres the answer is S7 - I never directly touched the octonions. As this scenario in GR is cyclical in time (S1), this gives the 4 spheres in the 4 normed division algebras in a metric field theory and defines the scenario to be unique - this is more than my belief in coincidence can take. I have a unique scenario that gives a realisation of Einstein's pure geometric unification of physics with GR, the correct electroweak vacuum, the correct particles and a derived QFT describing the particles. That's a lot of reality for a physicist to be holding on to - pretty maths just isn't tempting.

Michael

On Edwin's point about changing minds, you have had an effect on changing my mind, although the preferred phrasing is of course, refined my thinking (if not quite in the way you may have intended). Observational physics naturally divides into the world outside of hadrons, and the inner hadron world. In the outer world there is space and time with associated inner particle symmetries spin (S3) and particle/anti-particle, isospin symmetry (S3) and hypercharge symmetry (S1), but no colour symmetry, giving an 8 dimensional outer world of most observations in physics (I think this was the point that Edwin was making).

In my case, this outer world is of a cyclical (S1) closed universe (S3) with electroweak base-space (S4) forming a product space. Here, gravity in S3 is by curvature and the particle forces of S4 by torsion, which are incompatible to be embedded in the same space. BUT in a local (vicinity) theory it may be possible to construct a torsion based view of gravity and so combine S3 and S4 into S7 to give your suggested Octonion Relativity covering the outer hadron world.

Joy's 2 particle correlation analysis for observables in the outer hadron world could be viewed as reaching the same conclusion. In the Standard Model, the electroweak charges are chiral and so spin orientation in S3 is related to isospin orientation in its S3, and hypercharge S1. The conclusion that correlations are due to the embedding of these spaces in S7 requires a flat parallelised sphere with torsion. There are 3 spaces here (physical space, symmetry space, measurement space) and whereas I deal with the first 2, Joy effectively deals with the second 2 - so direct comparison is a bit confusing. This is made worse in my GR model by compactified physical spaces being identified with symmetry spaces (as in Kaluza-Klein theories) - the physical scale factor between the 2 is the charge coupling constant.

In the inner hadron world there is also colour, which is not correlated with spin or the electroweak charges. This implies that Joy's correlation analysis for 2 colour observables (C, D) can be applied independently of the spin/electroweak observables (A, B) as there is no correlation between (A, B) and (C, D). The conclusion is the parallelised spheres S3 or S7, neither of which obviously squares with the Standard Model colour group SU(3). S7 isn't a group space, but S3 is - of SO(3). 2 particle correlation (the 2 quarks inside a meson) of an S3 colour space would yield S3 in Joy's analysis, whereas 3 particle correlation (a baryon) would yield the S7 result.

For your point of view, the inner hadron world yields a second independent occurrence of an S7 measurement space, as opposed to just the one in the outer hadron world. These inner and outer S7 occurrences could have the look of being mathematically dual, but as the references of Jens say that the E8 lattice is self-dual that may be a road to nowhere.

So you have persuaded me in principle, that in the outer hadron world it may be possible to construct a form of Octonion Relativity - which would necessarily be flat and not involve curvature - that could describe the measurement space of observables and particle symmetries. However, the spaces would not be physical spaces in the sense meant by Einstein. This would be apparent in particles having to be added by hand, and the theory not being extendable to the whole universe (that would be an invalid induction from a local vicinity theory). The corresponding physical theory for such an observational theory could of course be mine. I'm sticking with Albert on his concept of physicality and specifically a physical GR, as if I abandon this point then I would no longer consider myself a physicist.

There are 3 different types of space (physical, symmetry, measurement) and we may be confusing between them. We (me, you, Joy, Jens, ...) may not actually be handling separate beasts, but different parts of the same elephant.

Regards,

Michael