There are very few moments in theoretical physics that qualify as... thrilling -- moments that send shivers of excitement down the spine and make the brain tingle. It's such an abstract pursuit, you wouldn't think the effects would be so visceral. The thoughts take years to accumulate, and are often disjoint and haphazardly organized. On a very rare occasion, a new insight brings a cascade of ideas together at once -- a chain reaction in the mind. It's very cool. Of course, the idea could still be wrong. And usually one needs to set about the hard work of trying to prove it wrong, before airing it in public. But, in this case, with a recent idea I think is significant, that work will likely take me a long time -- and I want to share the main idea now. So here it is:

If we take seriously the idea that fermions may be gauge theory ghosts, there is one gauge theory in particular that stands out: that of a principal E8-bundle. The exceptional group of rank 8 is the largest of the exceptional Lie groups, and perhaps the richest in structure. Pirating an appendix from Superstring Theory, the 248 dimensional Lie algebra of E8 is described as:

e8 = so(16) + S(16)

the special orthogonal group (with 120 elements) acting on the space of 128 dimensional chiral spinors. This is remarkable as it is, since it says there's a Lie algebra in which the Lie bracket of two elements gives one element acting on another as a Clifford algebra element, B, of so(16) acting from the left on a spinor, Psi, of so(16):

[ B, Psi ] = B Psi

There is also a lesser known, equivalent description of e8 that I read about in John Baez's This Week's Finds:

e8 = so(8) + so(8) + (V(8) x V(8)) + (S(8) x S(8)) + (S(8) x S(8))

In this description, the 28 elements, H, of so(8) act from the left on three 64 element blocks, Psi1,Psi2,Psi3:

[ H, Psi123 ] = H Psi123

and the other 28 elements, G, of so(8) act on these from the right. Now, if we build a Yang-Mills theory with E8, and take the three blocks to be ghosts, the BRST extended connection:

A = H + G + Psi1 + Psi2 + Psi3

and its curvature,

F = d A + AA

= (dH+HH) + (dG+GG) + (dPsi1+HPsi1+Psi1G) + (dPsi2+HPsi2+Psi2G) + (dPsi3+HPsi3+Psi3G)

fits the standard model -- complete with three generations of fermions and gravity! This is mostly laid out in my last paper. The gravitational connection, frame, Higgs multiplet, U(1), and SU(2) fit in H, while SU(3) and another piece of U(1) fit in G. And three generations of leptons and quarks fit in the Psi's, related by triality. This is a beautiful thing -- exactly what one would hope for in a TOE!

If it's true, it would explain a lot of complicated structures in the standard model in terms of a simple E8 Yang-Mills field: exactly what and why spinors are, why the particles get the charges they do, why there are three generations, and possibly why the masses are what they are. And there's very little wiggle room. It will have to be a real form of complex E8, since we need a non-compact gauge group for gravity. But there will be only a handful of ways to consider the E8 symmetry breaking to the standard model. After all, it's just a Yang-Mills theory, with no other fancy stuff flying around. It will either clearly work, or it clearly won't.

There is a lot of work to do. I haven't gotten exactly the right particle assignments down yet. And I don't know if someone's tried this before, since the literature is somewhat obfuscated by the use of E8 in heterotic string theory, which is quite different. (I doubt it's been done before though, since it relies on my crazy idea of replacing some gauge fields with fermionic ghosts.) I expect to be working on this for quite a while -- studying the structure of E8, which is quite beautiful, and many other aspects -- trying to see if the fermions will fit properly and the KM matrix pops out of it. It's not a completed theory, which is why I didn't write it up as a paper. But I think it's interesting and exciting enough to put here, for the enjoyment and puzzlement of others.

    5 months later
    • [deleted]

    Is anything recursive/self referential in the mathematics of your theory?

    • [deleted]

    Are there any experiments that could be done in the near future that might test predictions of your theory? Or will the energies be out of reach for a long, long time, like they are for other grand theories of everything?

    • [deleted]

    Being only a humble carpenter, would this mean that since we know how weak, strong, e/m, and now gravitional forces are linked, can we now begin to learn to artifically manipulate a gravitational field?

    Because we specialize in difficult and unusual builds, I thought it might be nice to offer my clientel anti-gravity sleeping quarters on earth or maybe a house that floats.

    I apologize if this insults anyone, but I can't hang mentally with the bunch of you for long. Seriously though, can gravity now be manipulated?

    • [deleted]

    Are there any implications or unknown properties of Gravity or Magnetism that are implied by this theory? For that matter are there any other implications of this theory on other known laws or theories?

    • [deleted]

    Dear M Lisi,

    Can your interpretation of the E8 group shed some light on the "Cosmic Galois Group" conjonctured by M P.Cartier(*) which acts as an universal group of symmetries on the coupling constants of renormalizable physical theories and which is expected to solve the problem of divergences in quantum field theory.

    (*) A Mad Day's Work : From Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry.

    Bull.Amer.Math.Soc. (N.S.) 38 (2001) ,no. 4 389-408Attachment #1: 001_from_grothendieck.pdfAttachment #2: Connes_Marcolli.pdf

    Mark:

    Is anything recursive/self referential in your question?

    Stв€љВ©phane:

    It's still to early to say what they are, but the theory appears to be sufficiently restrictive that as it develops there will certainly be testable predictions, right or wrong.

    Andrew:

    We're still stuck with gravity -- just do the best you can with wood. Be creative.

    Matthew:

    The theory is built from the ground up to match what we know. If all goes well, it will continue to agree with what we know and predict some new things that we don't.

    Emile:

    I'm afraid I'm not familiar with that.

    • [deleted]

    As a long-time artist/meditator I applaud your method of study. It allowed you to spend a lot of time in altered states of consciousness (like surfing, snowboarding) so that you COULD come up with this kind of theory. Very clever of you, indeed.

    If you (or anyone reading) are not a student of sacred geometry, you might want to check into the work of Ibrahim Karim, an Egyptian architect who is studying/teaching sacred geometry from the inner chambers of the Egyptian pyramidal tombs, and further developing the studies of the French Radiethesiests. There is some VERY interesting information there. Sacred geometry is apparently how spirit creates matter.

    • [deleted]

    Your E8 theory shows that the smallest known bricks of matter and force fit a very beautiful (and complex) symmetry.

    Up in the biosphere, symmetry in shape (or a flower, a runner, etc.) is not a free gift; it is achieved by an evolutionary process.

    Is it at all conceivable that the E8-particles and their symmetry be the result, by emergence, of the evolutions of

    an exceptionally simple (maybe deterministic, discrete, computational) system, in the spirit of, say, cellular automata?

    • [deleted]

    I may ask this question clumsily, but bear with me a moment. The symmetries of the particles extend to the forces themselves which govern them. Fusion (strong nuclear) is balanced by fission (weak nuclear) and they are, in some way, inverses of one another. Aristotle coined the word for "gravity" to describe the force which causes things to sink or fall and Newton picked it up. But Aristotle coined two words for opposing balanced forces: gravity and levity. There was some talk in the past decade about an antigravity fifth force in the universe, indetectable at micro scales, but readily apparent in the macrocosm -- Einstein's Fudge Factor, the force propelling the acceleration of expansion in the universe, etc. And the famous "inflationary universe" soon after the Big Bang signals its separation from the symmetry. Does E8 allow for a missing force? Are the 20 missing elements related in some way as a family? Or are they scattered through the matrix? What is your opinion on levity?

    • [deleted]

    PS: The fellow who asked about recursive or self-referential (Mark) was asking, I think, whether E8 has the nature of a fractal or if it is fractal geometry.

    Lois:

    Wow, "altered states of consciousness"... here I thought I was just having fun. ;) Also, I do like geometry a great deal, but "sacred" seems too strong a word. It would be impossible (and arrogant) for me to say with certainty that ancient philosophers couldn't have obtained deep insights into the geometry of the universe through omphaloskepsis, but I prefer using math. If people are struck by the beauty of geometry, I would encourage them to use this as motivation to learn a bit of the related mathematics. Physics and math are the best magic I know -- most of the other kinds are fake.

    Tommaso:

    Yes, this is possible. I try to follow Occam's razor in these matters, but it's conceivable that there's a simple system for which E8 is an emergent symmetry. Though I'm going to spend more time working on the E8 Theory itself first, before I consider how it might emerge from something else.

    Bryan:

    Yes, I feel levity is very important in physics. (I think that's apparent from my paper title.) And if this E8 Theory turns out to be true about nature, it will include a few new particles, corresponding to new forces. But these are going to have to be sufficiently weak that they don't contradict the standard model, which very accurately describes the world on our human scale.

    Bryan II:

    If so, then the answer is no, E8 is a complicated (simple) Lie group, but not a fractal.

      • [deleted]

      To the extent human tropical water monkeys see randomness in events ... time is a ride exactly between quantum and astronomical. That would make self conscious life actually THE unifed field and quite a beautiful answer as well.

      • [deleted]

      Occam's razor is one of my favorite tools too (maybe not for posts, though...). After your november 2007 paper, precisely two distinguished concepts are filed in my mind under 'particles' 'beauty': one is the system of roots for the 248 symmetries of the E8 manifold; the other is Wolfram's elementary cellular automaton 110, with its amazing interacting particles emerging from basically any initial condition, including the simplest.

      While it is clear that the universe can't be a cellular automaton, one can expect a lot of beautiful things to emerge when trying to transpose the simple ideas behind them -- and the computational-universe view -- to the discrete, graph-like structures considered in LQG (spin networks, foams, knots, braids...), or just to plain, finite trivalent graphs, as suggested by Wolfram himself.

      That's what I am after, and although I well understand that your priority is still on the internals of the E8-Theory, I wonder whether you'd have at hand a 'natural' candidate for a sequence of increasingly complex symmetries X1, X2, ..., Xn, with Xn = E8, so that research and experimentation on emergence in graphs could be more realistically directed towards cracking X1 first.

      • [deleted]

      A piece of the answer hides in the Coral Castle. See you in the water sone day.TG. http://www.coralcastle.com/9tonbig.htm

      • [deleted]

      Looks like I'm going to have to go back to math school for a few years to anwer my own questions about how your idea affects cosmology. In the meantime...

      Have you considered that some of the unnasigned points on E8 could apply to "dark matter"? Does your idea rule out dark matter or make it easier to know how and what to look for?

      As an alternative to dark matter, does your idea show that the effect of gravity is not perfectly linear in its relation to space?

      • [deleted]

      Is it possible that quark spinors, emulating electron spinors in magnetism and sigma and pi chemical bonding, could be responsible for gravity and inertia?

      7 days later
      • [deleted]

      Is this related to Star Trek Voyager's episode regarding the Omega Project, where there find the ultimate element? Seven says the element is symbolic of Perfection.

      • [deleted]

      Just a few questions:

      Would not a theory of *everything* have to say something about the consciousness that created it, or through which it emerged?

      (I suggest that a theory of *everything* would have to be able to explain its own origin. This is not my idea. It was told to me by another searcher for Truth back in 1972.)

      Inasmuch as science originates in self-reflection and the thought of the 'thinker', a true theory of *everything* would have to determine whether this is the only dimension of consciousness. (It isn't. There is also the chaotic Lorentz attractor form descriptive of "psychosis", as well as the "observing consciousness" which is capable of observing the 'movement' of self-reflection in the first place.) (The 'classical' consciousness originating in self-reflection and thought cannot observe this because it does not yet exist.)

      Would not a rigid adherence to Occam's Razor result in the conclusion that there is neither a 'mind', nor a 'thinker', nor a 'self' but merely thoughts?

      If this E-8 is, in fact, a theory of everything in the physical world, how could it be related (through metaphor, archetype, synchronicity etc.) to a complete description (based upon observation, not thought or self-reflection) of the full dimensions of human consciousness?

      In other words, maybe E-8 is not a TOE but a crucial *half* of a theory of everything: a TOEBH or a theory of everything by half.

      Michael Cecil

      http://science-of-consciousness.blogspot.com/