> 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 1dim 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 Mtheory?
> 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 nonBohmian 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 4dim 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 11dim
> spacetime.
>
> >
> >
> > 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 11dim spacetime  like KaluzaKlein.
>
> >
> >
> > 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 spacedimensions
> 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 sumoverhistories 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, YangMills, 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 8dim vector rep of Spin(8)
> >
> > (3) firstgeneration fermion particles on M represented
> > by 8dim +halfspinor of Spin(8)
> >
> > (4) firstgeneration fermion antiparticles on M represented
> > by 8dim halfspinor of Spin(8)
> >
> > In that way, the gauge bosons of the are represented by the
> > 28dim adjoint representation of Spin(8), as follows:
> >
> > Standard Model  12 infinitesimal generators = SU(3)xSU(2)xU(1)
> > This gives you the standard model "... YangMills, 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 4dim
> > physical Minkowski spacetime.
> > By gauging the Conformal Group, you get an EinsteinHilbert
> > 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, SpringerVerlag 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 bosonsD4
> >
> > " " spacetime plus internal symmetry spaceD5 / D4 x U(1)
> >
> > " " fermion particle and antiparticlesE6 / D5 x U(1)
> >
> > Q has all states M for Quantum SummationE7 / 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 firstorder quantum theory of my model.
> >
> > You can extend the chain at least to E8 / E7 x SU(2) to get
> > higherorder 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 EulerLagrange equations for the "wave" or the Qlandscape, and a
> second set of equations for the "particle" or M. In case of quantum gravity, for
> example, the "wave" equations is the WheelerDewitt 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 3dim
> "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 toytype example that is simpler
> > than
> > the fullblown 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 trialand
> > 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 24cell,
> > which
> > is the unique regular polytope in ANY dimension that
> > is both centrally symmetric and selfdual.
> >
> > 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 errorcorrecting codes that SaulPaul
> finds? One is a 24code, and then the Hamming8 code, and obviously 3x8 = 24 = 4!
> of S4 permutation group which is at the Galois limit of solvability of
> polynomials. ????
>
> >
> >
> > (and my trialanderror 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 1dim harmonic oscillator is one of
> > the basic models taught to physicists, and that makes
> > it hard for some to think outsidethebox of
> > canonical quantization of such a model,
> > but (it seems to me after much trialanderror) 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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