**Hitoshi Kitada** (*hitoshi@kitada.com*)

*Mon, 15 Mar 1999 13:55:50 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 18] Reformulating Weyl's Unified Field Theory"**Previous message:**Stephen P. King: "[time 16] Re: God"

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:

-----Original Message-----

From: Stephen P. King <stephenk1@home.com>

To: Time List <time@kitada.com>

Date: Sunday, March 14, 1999 12:57 PM

Subject: [time 15] eformulating Weyl's Unified Field Theory

*>Here we go!
*

*>
*

*>http://www.phys.ndsu.nodak.edu/mrm8/titles.htm
*

*>
*

*>
*

*>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,
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*>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
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*>(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
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*>4-potential are related via a simple gauge transformation under this
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*>program.
*

*>
*

*> Density Transformations in a Gauge Unification of Gravity and
*

*>Electromagnetism
*

*>
*

*> 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
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*>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
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*>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.....
*

*>
*

*>http://smatc.fcc.cc.md.us/staff/mjm/index.htm
*

*>
*

*>searching further...
*

*>
*

I think there arises a problem when we consider quantum-mechanical aspect of

things as we discussed:

-----Original Message-----

From: Hitoshi Kitada <hitoshi@kitada.com>

To: stephenk1@home.com <stephenk1@home.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 <stephenk1@home.com>
*

*>To: hitoshi@kitada.com <hitoshi@kitada.com>
*

*>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 <vesselin@baton.phys.lsu.edu> 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
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*>>>saved from collapse by quantum mechanics. Because momentum and position
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*>>>don't commute, the electron can't have both a definite position and
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*>>>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
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*>>>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
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*>>>I no longer think the trick is to make different components of position
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*>>>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
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*>>>are not really observable quantities. We don't just go out and measure
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*>>>the x coordinate of something. Fundamentally, what we do is measure the
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*>>>relation of one physical object to another. Since the components of
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*>>>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
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*>>>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
*

noncommutative,

*>>>they break the diffeomorphism symmetry down to a much smaller group.
*

*>
*

*>
*

*>Exactly! He seems to have noticed the defect of the present activities of
*

*>physicists.
*

*>
*

*>>>
*

*>>>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
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*>>>with it too great.
*

*>>>
*

*>>>>It seems that they have an argument for this but it is not too appealing
*

to

*>>>>me:
*

*>>>>
*

*>>>> "...the smaller the cube the bigger the energy... generates a black
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*>>>>hole...
*

*>>>> ... Thus it is reasonable to assume that the operators corresponding to
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*>>>>the
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*>>>> 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,
*

*>Hitoshi
*

*>
*

How do you think of the problems which arise when we consider

quantum-mechanical aspects of things in the context of Weyl?

Best wishes,

Hitoshi Kitada

**Next message:**Stephen P. King: "[time 18] Reformulating Weyl's Unified Field Theory"**Previous message:**Stephen P. King: "[time 16] Re: God"

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