[time 13] Re: Gravitational Aharonov-Bohm Effect

Hitoshi Kitada (hitoshi@kitada.com)
Sun, 14 Mar 1999 10:32:40 +0900

Dear Stephen,

I had overlooked Eric's suggestion at the end of his message. Although I do
not understand his point, it is interesting if we could hear his further


-----Original Message-----
From: Stephen Paul King <stephenk1@home.com>
To: time@kitada.com <time@kitada.com>
Date: Saturday, March 13, 1999 12:37 PM
Subject: [time 7] Re: Gravitational Aharonov-Bohm Effect

>This applies to Local Time theory!
>Eric Forgy <forgy@uiuc.edu> wrote:
>On 13 Mar 1999 00:11:17 GMT, you wrote:
>>A while back, I asked about a relation between vector potentials and
>>connection coefficients. I then learned that this is at the heart of
>>gauge theory. I was interested in Weyl's unification of gravitation and
>>electromagnetism. While reading about Weyl's theory in the book "The
>>Dawning of Gauge Theory" by O'Raifeartaigh, it gave an argument (one of
>>many) why Weyl's theory was incorrect. One argument that comes to mind
>>is it mentioned that the conformal rescaling of the metric would lead to
>>a so-called "gravitational Aharonov-Bohm" effect. To quote directly
>>"...one can summarize Einstein's objection to Weyl's theory as the
>>statement that. according to atomic spectroscopy, there is no
>>Aharonov-Bohm effect for gravitation."
>>also pg.85
>>"...in effect, Weyl was assigning an (imaginary) electric charge to the
>>metric tensor. From this point of view, Einstein's objection to the
>>theory is very understandable."
>>That is a strong enough argument for me (and hopefully for anyone) to
>>see that Weyl's theory is in fact unphysical. However, the thing that
>>caught my attention is something I just read in a paper:
>>"On Gauge Aspects of Gravity"
>>-Frank Gronwald and Friedrich W. Hehl
>>In this paper, they mention the experimental results of
>>Colella-Overhauser-Werner. I should quote directly to avoid
>>"Twenty years ago a new epoch began in gravity:
>>Colella-Overhauser-Werner measured by interferometric methods a phase
>>shift of the wave function of a neutron caused by the gravitational
>>field of the earth."
>>This sounds a WHOLE LOT like a gravitational Aharonov-Bohm effect to me.
>>Was the statement "there is no Aharonov-Bohm effect for gravitation" in
>>O'Raifeartaigh wrong?
>>The absence of a measurable gravitational Aharonov-Bohm effect in atomic
>>spectra can easily be explained by the relative magnitudes of the
>>electromagnetic and gravitational forces. This is why it was observed
>>via a study involving neutrons.
>>I am speculating that the observed gravitational Aharonov-Bohm effect is
>>compatible with a conformal rescaling of the metric under parallel
>>transport. Am I making sense?
>>Thank you for any comments.

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