Stephen P. King (firstname.lastname@example.org)
Mon, 15 Mar 1999 11:36:29 -0500
Re: [time 17] Re: Reformulating Weyl's Unified Field Theory
Mon, 15 Mar 1999 07:20:11 -0500
"Stephen P. King" <email@example.com>
Hitoshi Kitada <firstname.lastname@example.org>
Hitoshi Kitada wrote:
> Dear Stephen,
> I agree that Weyl's book "Space-Time-Matter" is a beautiful book. However, it
> is concerned only with classical aspect, not with quantum mechanical aspect as
> you quote:
I agree, but we must take Weyl, and these others contextually. I
firmly convinced that only a few have an understanding of the flaw
inherent in the classical model, and it has, unfortunately, not been
purged from most QM formalisms. Only Dewitt's MWI and Cramer's
Interactional Interpretation come close, Bohm was very close but, no one
The main point of my bringing Martin's ideas to the forefront is
shine a light on what others are thinking about and to try to establish
a raport with them to filter out the noise and better build a workable
model of QG. No individual's model can ever hope to be complete...
> -----Original Message-----
> From: Stephen P. King <email@example.com>
> To: Time List <firstname.lastname@example.org>
> Date: Sunday, March 14, 1999 12:57 PM
> Subject: [time 15] eformulating Weyl's Unified Field Theory
> >Here we go!
> >Michael J. Martin, University of Missouri
> > Reformulating Weyl's Unified Field Theory of 1919
> > In 1918-19, Hermann Weyl introduced the first classical unified
> >field theory, a theory that united electromagnetism and general
> >relativity into one geometrical framework. This theory, the forerunner
> >of modern gauge theory, involved transforming the metric 2-tensor with a
> >"scale factor" that, in turn, transformed the line element, causing
> >lengths of parallel transported vectors, as well as their orientations,
> >to change. This length dependence was later dismissed, and reformulated
> >by London and Fock as wave function phase dependence. We attempt another
> >reformulation, whereby the volume element varies on parallel transport
> >(volume instead of length) unless it is transformed into a tensor
> >density. This transformation introduces a gauge potential, the
> >contracted Christoffel symbol, which maintains invariance under
> >covariant differentiation.
> > The electromagnetic potential, in pure gauge form, is shown to be
> >equivalent to a constant multiple of the contracted Christoffel symbol.
> >The gravitational field is introduced into wave mechanics via the
> >contracted Christoffel symbol, which appears as an integrable phase
> >factor. The contracted Christoffel symbol and the electromagnetic
> >4-potential are related via a simple gauge transformation under this
> > Density Transformations in a Gauge Unification of Gravity and
> > The Lagrangian which describes an electron wavefunction in QED
> >remains invariant under local phase transformations through a gauge
> >transformation of the electromagnetic 4-potential, which is the gauge
> >connection appearing in the QED covariant derivative. We postulate that
> >similarly, the Lagrangian which describes the electron wavefunction in
> >both an electromagnetic and gravitational field remains invariant under
> >local phase transformations of the wave function density, via the
> >introduction of the contracted Christoffel symbol as gauge connection in
> >the covariant derivative. The resulting transformations, of the QED
> >Lagrangian density, are explored. The quanta of the gravitational field
> >would appear to be both massless and of infinite range, as the
> >transformations are nearly identical to U(1). We explore the case of
> >wave function --> wave function density, and wave function
> >density-->wave function density, where a density is defi.....
> >searching further...
HK >I think there arises a problem when we consider quantum-mechanical
> things as we discussed:
> -----Original Message-----
> From: Hitoshi Kitada <email@example.com>
> To: firstname.lastname@example.org <email@example.com>
> Date: Saturday, March 13, 1999 2:41 PM
> Subject: RE: Quantum groups (was: Re: Poisson groups/actions)
> >Dear Stephen,
> >I seem to have underestimated John Baez.
> >-----Original Message-----
> >From: Stephen Paul King <firstname.lastname@example.org>
> >To: email@example.com <firstname.lastname@example.org>
> >Date: Saturday, March 13, 1999 12:24 PM
> >Subject: Re: Quantum groups (was: Re: Poisson groups/actions)
> >>Dear Hitoshi,
> >> John Baez himself seems to be agreeing with your arguments! :)
> >>On 12 Mar 1999 20:33:28 GMT, you wrote:
> >>>In article <36E692F5.A8CDCB86@phys.lsu.edu>,
> >>>Vesselin Gueorguiev <email@example.com> wrote more or less this:
> >>>>I have had problems convincing myself that x,y,z should become noncommutative.
> >>>Me too - at least now. Back when I was a grad student, I was really
> >>>excited about this idea. This is how I thought: the hydrogen atom is
> >>>saved from collapse by quantum mechanics. Because momentum and position
> >>>don't commute, the electron can't have both a definite position and
> >>>a definite momentum. This keeps it from falling into the proton.
> >>>Now in general relativity we have a problem similar to electron collapse:
> >>>the singularity that occurs when a large mass collapses. So maybe we
> >>>can solve this problem too using quantum mechanics. How? Well, maybe
> >>>we should go a bit further and say, not just that momentum and position
> >>>don't commute, but that the diffferent components of position don't
> >>>commute! Then nothing can even have a definite position. So there's
> >>>no way for matter to collapse down to a single point!
> >>>It sounded convincing to me back then. I still believe that quantum
> >>>mechanics will eliminate the singularities in general relativity. But
> >>>I no longer think the trick is to make different components of position
> >>>commute. Here's why I think this idea is wrong. In general relativity,
> >>>the components of position depend on the coordinate system you use. They
> >>>are not really observable quantities. We don't just go out and measure
> >>>the x coordinate of something. Fundamentally, what we do is measure the
> >>>relation of one physical object to another. Since the components of
> >>>position are not really physical observables, we shouldn't quantize them!
> >His point agrees with my standpoint.
> >>>More precisely, since they depend on an arbitrary choice of coordinates,
> >>>we shouldn't quantize them unless we can do so in a way that doesn't
> >>>depend on our choice of coordinates. But there appears to be no such
> >>>way. I tried to find one and I couldn't. Recently lots more people have
> >>>been playing this game, and none of them has succeeded in this either.
> >>>Whenever people quantize spacetime by making the coordinates
> >>>they break the diffeomorphism symmetry down to a much smaller group.
> >Exactly! He seems to have noticed the defect of the present activities of
> >>>Now of course this is not a definitive argument. The final test is
> >>>experiment. But I've decided that the motivation for making the
> >>>components of position noncommutative is too weak, and the problems
> >>>with it too great.
> >>>>It seems that they have an argument for this but it is not too appealing to
> >>>> "...the smaller the cube the bigger the energy... generates a black hole...
> >>>> ... Thus it is reasonable to assume that the operators corresponding to the
> >>>> coordinates x, y, and z do not commute..."
> >>>Right, that's kind of how the argument goes. The problem with this
> >>>argument is that there's a huge logical gap right before the "Thus".
> >>>Why should we assume this? Why not something else? I've never seen
> >>>a plausible answer.
> >Best wishes,
> How do you think of the problems which arise when we consider
> quantum-mechanical aspects of things in the context of Weyl?
Weyl's ideas seem to get into how LSs "appear" to each other, or more
directly, how the dynamics of LSs, considered from the "external"
perspective, behaive. I believe that the experimental evidence for this
is in the Hubble red shift data (COBE, etc.). Robert and I last night
discussed how LSs act as adaptive antennas internally and like broadband
transmiters externally. What we see in Weyl's gauge variability is that
there is a dependence on the "history" or chronological ordering of a LS
with respect to what aspects of other LSs it can observe. We are also
thinking of LSs as adaptive filters, or Wegner's MIM's.
It is easy to see the connectionof gravity with consciousness when we
think in these terms.
Onward to the Unknown!
> Best wishes,
> Hitoshi Kitada
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