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Re: my model is NOT 1-dim harmonic oscillator

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  • Jack Sarfatti
    ... -
    Message 1 of 1 , Jan 2, 2001
      Jack Sarfatti wrote:

      > Tony Smith wrote:
      >
      > > Jack, you say
      > > "... In order for me to understand your idea here,
      > > I would have to first see how you apply it in a simple example
      > > where the structure for Q and M are completely known
      > > as in the linear 1 dim harmonic oscillator. ...".
      > >
      > > I am NOT trying to constuct a model of a 1-dim harmonic oscillator.
      >
      > I understand that. I am saying I do not understand the physical motivation for
      > invoking all that advanced math. You have to start from some recognizable physics
      > and then show the advantage of these methods.
      >
      > I cannot understand in what sense Q has 27 complex dimensions, for example. Not
      > all Q? What is the M for which Q has 27 complex dimensions? Let's start there.
      > What material system M are you talking about? First state the physical problem.
      >
      > You seem to be trying to make some kind of TOE? Correct? Something like M-theory?
      > Something that in some limit gives standard model of cosmology and
      > U(1)xSU(2)xSU(3). This something uses E7. beyond that, I do not understand where
      > you are coming from in a physical way.
      >
      > Standard non-Bohmian way is to construct a classical action i.e. M, then put it
      > into the Feynman integral to get what is effectively Q. That's the basic method
      > in Kaku's advanced M theory text book for example. So start from that standard
      > place. The classical action (M) is the phase part of the Feynman path amplitude
      > from which Q can be constructed in principle. So, you have some kind of classical
      > action that has some kind of E7 symmetry group? Is that correct?
      >
      > So what I am saying is the M is where to start. From the symmetries of M one
      > constructs a classical action. The symmetries of Q will be essentially the same
      > as the symmetries of M.
      >
      > >
      > >
      > > I AM trying to construct a model of physics at the elementary particle level.
      > >
      > > A swinging pendulum (which itself is only approximately modeled in
      > > some circumstances as a harmonic oscillator) is made up of a lot
      > > of molecules and atoms, which in turn are composed of what are
      > > conventionally called elementary particles.
      > >
      > > My model is designed to explain behaviour at the elementary
      > > particle level, NOT at the swinging pendulum level.
      > >
      > > The basic ingredients of M are:
      > >
      > > 1 - a 4-dim spacetime (a bunch of points, each of which corresponds
      > > to a particular point in space and time in time);
      >
      > OK so you do not accept hyperspace.The basic ingredients should be an 11-dim
      > space-time.
      >
      > >
      > >
      > > 2 - for each point in spacetime, its own internal symmetry space
      > > (a representation space to carry representations of standard
      > > model gauge groups, acting as local (independent at each point
      > > of spacetime) gauge groups);
      >
      > OK, I think the idea of hyperspace is that the internal symmetries are in the
      > compactified 7 extra space dimensions of 11-dim space-time - like Kaluza-Klein.
      >
      > >
      > >
      > > 3 - for each point in spacetime, a representation space for
      > > fermion particles (electron, neutrino, rgb up quarks, rgb down quarks)
      > > so that, at each point of spacetime, there can be a fermion particle;
      >
      > Do you mean N extra fermion dimensions (Grassmann numbers) at each bosonic point?
      >
      > >
      > >
      > > 4 - for each point in spacetime, a representation space tor
      > > fermion antiparticles, so that, at each point of spacetime,
      > > there can be a fermion antiparticle;
      > >
      > > Of course, M looks like classical physics, that is, a bunch of
      > > classical states.
      >
      > This means some kind of classical field theory, perhaps in 10 space-dimensions
      > which will project to U(1)xSU(2)xSU(3)xDiff(4) with local O(1,3) tangent space in
      > some limit - this excludes torsion that violates Diff(4). So something other than
      > Diff(4) for a UFT rather than 1915 GR.
      >
      > The classical action A will then be some functional of the fields? Correct?
      >
      > So I guess I am asking what is the A and how does E7 fit into A's structure?
      >
      > >
      > >
      > > To get quantum structures, follow the example of conventional
      > > gauge field theory and do sum-over-histories path integral quantization.
      > >
      > > The geometry of Q is the geometry of all the possible M states,
      > > and how they fit together.
      >
      > OK fine. So how does one do that?
      >
      > >
      > >
      > > --------------------------------------------------------
      > >
      > > You also ask
      > > "... how in a certain limiting case one derives
      > > conventional classical physics e.g. GR, Yang-Mills, EM etc. ...".
      > >
      > > In order to do that, I found (by trial and error, many years ago)
      > > that everything fits together nicely if you let:
      > >
      > > (1 and 2) spacetime of M plus internal symmetry space of M represented
      > > by 8-dim vector rep of Spin(8)
      > >
      > > (3) first-generation fermion particles on M represented
      > > by 8-dim +half-spinor of Spin(8)
      > >
      > > (4) first-generation fermion antiparticles on M represented
      > > by 8-dim -half-spinor of Spin(8)
      > >
      > > In that way, the gauge bosons of the are represented by the
      > > 28-dim adjoint representation of Spin(8), as follows:
      > >
      > > Standard Model - 12 infinitesimal generators = SU(3)xSU(2)xU(1)
      > > This gives you the standard model "... Yang-Mills, EM etc. ..";
      > >
      > > Gravity - the other 16 generators = U(4) = SU(4)xU(1),
      > > and then note that SU(4) = Spin(2,4) = Conformal Group of 4-dim
      > > physical Minkowski spacetime.
      > > By gauging the Conformal Group, you get an Einstein-Hilbert
      > > action (plus cosmological constant plus torsion). This gives
      > > you (as an approximation) the "... GR ..." that you wanted.
      > > To see details of how this part works, you can for example
      > > read section 14.6 of Mohapatra's book
      > > Unification and Supersymmetry, 2nd edition, Springer-Verlag 1992.
      > > The mechanism was developed by MacDowell and Mansouri at Yale
      > > in the 1970s (Phys. Rev. Lett. 38 (1977) 739).
      >
      > OK I would need to see the above in detail. Do you have it as a .pdf with the
      > equations conventionally written? That would be good.
      >
      > >
      > >
      > > Since all this stuff works very well if you start with everything
      > > being based on representations of the D4 Lie group Spin(8),
      > > I have constructed my larger structures M and Q by starting
      > > with D4 and going up the following chain of symmetric space
      > > coset spaces:
      > >
      > > D4
      > >
      > > D5 / D4 x U(1)
      > >
      > > E6 / D5 x U(1)
      > >
      > > E7 / E6 x U(1)
      > >
      > > Here is roughly what you get at each level of that chain:
      > >
      > > M has gauge bosons---------------------------------D4
      > >
      > > " " spacetime plus internal symmetry space-------D5 / D4 x U(1)
      > >
      > > " " fermion particle and antiparticles----------E6 / D5 x U(1)
      > >
      > > Q has all states M for Quantum Summation------------E7 / E6 x U(1)
      >
      > What do you mean by Q here? Simply the Feynman path integral generated by M
      > forming the classical action?
      >
      > >
      > >
      > > This chain, in which D4 is inside D5 is inside E6 is inside E7,
      > > is the basis for the first-order quantum theory of my model.
      > >
      > > You can extend the chain at least to E8 / E7 x SU(2) to get
      > > higher-order quantum theory.
      >
      > How do we make this Bohmian? I can see this as a conventional Feynman path
      > theory. But the Feynman path integral is basically for the Q, we also need
      > equations of motion for the paths of M.
      >
      > We need something generalizing
      >
      > dX/dt = (h'/m)(dS/dx)|x = X(t)
      >
      > in addition to the Schrodinger equation.
      >
      > I suppose, this means we need two actions!
      >
      > Action(wave) and Action (Particle)?
      >
      > We then have Euler-Lagrange equations for the "wave" or the Q-landscape, and a
      > second set of equations for the "particle" or M. In case of quantum gravity, for
      > example, the "wave" equations is the Wheeler-Dewitt eq
      >
      > Hwdw [Wave Function of Universe] (over Wheeler super space) = 0
      >
      > Giving the pseudo "problem of time".
      >
      > But as Shelly Goldstein showed there is also and equation of motion for G3 (space
      > geometry = Bohm point) with a "time" (arc length of path of actual material 3-dim
      > "bubble" universe through Wheeler superspace). So there is no real "problem of
      > time" in quantum gravity.
      >
      > >
      > >
      > > When you try to go to very high orders,
      > > you see that
      > > at very high energies (at least above Planck),
      > > all these symmetries get merged into a huge Simplex in which
      > > everything is connected to everything else (really maximal symmetry),
      > > but that is too hard for humans to work with or think about easily.
      >
      > Well since we may be able now to make huge Planck lengths in machines, this
      > problem of the Big Simplex may be more practical than you think! :-)
      >
      > >
      > > --------------------------------------
      > >
      > > There is another point to be made with respect to your request
      > > that I start my description with a toy-type example that is simpler
      > > than
      > > the full-blown theory
      > > with realistic spacetime, internal symmetry space, and particles.
      > >
      > > The reason that I do not do that is that everything only
      > > fits together (as far as I can see, having done a LOT of trial-and-
      > > error work many years ago) in the special case of starting
      > > with structures based on the D4 = Spin(8) Lie algebra.
      > >
      > > This (empirical for me) fact is probably related to
      > > the fact that the root vector diagram of D4 = Spin(8)
      > > is the 24-cell,
      > > which
      > > is the unique regular polytope in ANY dimension that
      > > is both centrally symmetric and self-dual.
      > >
      > > If you try anything larger or smaller,
      > > you lose some of the special symmetry that seems to
      > > make things work out right in my model.
      >
      > OK, does this have anything to do with the error-correcting codes that Saul-Paul
      > finds? One is a 24-code, and then the Hamming-8 code, and obviously 3x8 = 24 = 4!
      > of S4 permutation group which is at the Galois limit of solvability of
      > polynomials. ????
      >
      > >
      > >
      > > (and my trial-and-error process of many years ago
      > > had a lot of trials, most of which were errors,
      > > so my comments in this part are based on some experience).
      > >
      > > Tony 2 Jan 2001
      > >
      > > PS - Jack, I know that the 1-dim harmonic oscillator is one of
      > > the basic models taught to physicists, and that makes
      > > it hard for some to think outside-the-box of
      > > canonical quantization of such a model,
      > > but (it seems to me after much trial-and-error) that
      > > such a model is really very badly suited for
      > > describing elementary particle physics on a fundamental level.
      > > Of course, that is only my opinion, but it is my opinion.
      >
      > --
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