The Algebra of \"Everything\" by Rick Lockyer

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

ahahah weak like always, make surf really. It is cool the people making surf.ahahah me I like soccer and I play well. I am going to create a song in honor of your bad team ahahah and hop on the net.

ahahah the poor strategists, the poor thinkers. Mr Witten , forget these pseudos, it is better for the credibility at my humble opinion. But it is just a suggestion of course.

octonions ahahaha and surf ahahah and the toe ahahah wawww impressing the strategy, you are so strong wawwww.ahahah the maths they say. if your maths are correct , me I am the queen of England.

Regards

The maths are the sister of physics.They dance together. It is time to stop confounding things. A real pity for your team.Edwin, you know what? you have not a consciousness you and your friends, so don't speak about things totally unknown.You are neither scien,tists nor generalists.Don't teach but learn dear badteam. You do not merit it !!!

You are really not skilling, just a little for the strategy, the rest frankly Let me laugh.

MIT wake up please , what are these pseudos ???Jonathan, change of job or make surf, I don't know me. You think what? that New york is to you or what? It is the country of the freedom dude. And what you fear for your credibility poor strategist. You are right, so kill me poor dude. But I am persuaded that you cannot make it alone. Buy people dude and pray if you have faith of course.

Delete now Brendan , just like that I can thinking that I am not checked on this platform. ahahah ironical your strategy since the begining with the two books. Ironical.

Regards

Rick,

I have closed geometric formula for Planck's constant, Weinberg angle, the coupling constants - including the Higgs coupling - in terms of the fundamental constants G, c and the compactification scale. When combined with the charge eigenvalues these give quantitative values for *all* the particles known to exist - and they agree to the level of experimental error. The quantitative calculation of the particle masses is proven to encounter the issue of mathematical incompleteness. This can be by-passed by changing maths represenation because maths is not the same as physics - this change *is* the origin of Quantum Field Theory.

My position is as quantitative as it is mathematically possible to be. The barrier to greater quantitative results is mathematical incompleteness - maths stands in the way of physics, but that maths barrier can be overcome by using experimental results. It has been said many times before, and it is still true: the map (maths) is not the territory (physics).

Michael

Hello crazy planet,

:) REVOLUTION SPHERIZATION OF HIGH SPHERES :)

without real universal meaning.

You are not really mathematicians.At my knowledge the mathematicians help to build for example a machine, an engeniering, or a technology. You build what with your octonionic strings of extradimensions ?

Answer: nothing.

In fact you do not respect the universal domeins and its limits. You utilize an ocean of pseudo theorems mixed with some rational.How can you have a correct conclusion. The probelm in fact is simple. You confound the computing 2d and the 3D realism.Furthermore you integrate bizare, you derivate without determinism, you substitute without sense and reason, ...in fact your maths do not improve, they are just lost these maths in an ocean of physical determinism.

and you speak about G,c and h. is it a circus from false mathematicians? if yes it is time to learn the real foundamental books you know.

Insist now, make the obliged strategist, delete, arrange like you want, make what you want dear badteam. It is not a problem for me. Mr Wilszec, what is this circus??? Mr Witten,you agree with this you ? I am persuaded that no.

Sad is a weak word.Just due to their vanity and the jealousy and the hate and the money.

Ironical.

signed the crazy spherical Jedi

Rick,

As a fellow physicist you know that the line between Maths and Physics was drawn by Galileo - Physics only existed after he set the experimental standard of applying a mathematical theory to reality. It's not my definition of Physics, it's Galileo's. Every theory starts as *just* a mathematical theory until experimentally verified and shown not to contradict known experimental results. Reproducing known theories by different means - which both you and I have done - meets the Galilean standard of Physics as the known experimental results are entailed (question answered).

In the Standard Model, the spectrum of particles and their coupling constants are added by hand from experimental results. Dimensional compactification defines a whole class of mathematical theories that seek to derive the particle coupling constants from the GR constants and a compactification scale. The 11D GR theory referenced in my essay is one of this class of theory and succeeds by *deriving* the full spectrum of particles so that they do not have to be added by hand - this is not present in the Standard Model or any associated principles. The GR scenario is uniquely defined mathematically by the occurrence of the spheres S0, S1, S3, S7 as physical manifolds and this is directly linked to the successful reproduction of known physics without any additional features that conflict with known physics. This includes the derivation of the correct Standard Model Lagrangian and QFT. These characteristics *are* unique.

The acknowledgement of "if and only if" in Godel's mathematical incompleteness is PRECISELY my point. It is conditional on integers, which is the case in classical physics for particle numbers. The calculation of the rest mass of the particles derived in 11D GR as topological defects is subject to Godel's mathematical incompleteness because of this "if and only if" condition. A mathematician would be stumped at this point, but as physicists who know that maths is just a formal language for describing reality, we are free to drop the "if and only if" condition of strictly using integers to denote particle numbers and switch to real numbers instead - the wave-function - mathematical incompleteness then vanishes. If you trace the mathematical consequences of this shift in the theory, you find that it is of the form of quantum theory. Hence, QT is not fundamental because I can derive it!

This implies that mathematical incompleteness is not so much a red herring, but the elephant in the room.

Michael

In the film spherewars by Spielberg,Steve the young Jedi has found an important thing, the force is with him. But the empire of the bad is there. The son of Yoda is his friend.

About the post:here is my humble point of vue of spherewalker.

all false !!! mike badteam ,the octonionic obliged comportment will not change the algorythms, deterministic. The aim is not to superimpose the maths without a real universal domain. In fact it is a good tool for computing.

you think what ? that you are going to insert balls now.Let me laugh band of comics.You are not skilling to ponder this kind of works.So what is the probelm. Mr Wilcszec is an universalist. Mr Tegmark also, Mr Guth also, Mr Penrose also, Mr Hawking also,Mr Witten also.so why you insist on the pseudo works,you do not respect the real searchers, you just imply strategy of strategical steal. In fact you know what ? I beleive that you do not permit the truths.Just because you confound a lot of things.It is simply an unconsciousness comportment.In fact you think that you are right. But no, there are a lot of probelms.

and you,Mr Witten , are you going to continue to act like that ? You fear for your 11d or what ??? If some persons of your team utilize several roads for the confusions about ball and sphere, frankly it is sad.and But perhaps that you do not know that they act like that?

Spherically yours