[time 217] Re: [time 215] How to define length using LSs

Stephen P. King (stephenk1@home.com)
Sat, 10 Apr 1999 22:51:25 -0400

Dear Hitoshi,

Hitoshi Kitada wrote:
> Dear Stephen,
> ----- Original Message -----
> From: Stephen P. King <stephenk1@home.com>
> To: Time List <time@kitada.com>
> Sent: Sunday, April 11, 1999 10:10 AM
> Subject: [time 211] How to define length using LSs
> > Dear Hitoshi,
> >
> > I am jumping the gun in our discussion of Weyl's idea. :) By fibering a
> > Riemannian manifold with no a priori connection with quantum mechanical
> > systems having a Euclidian geometry do we assume:
> By this, I assume you think the inside of _one_ LS in the following questions.
> >
> > 1) that there is a Euclidian metric over each LS?
> I think so inside an LS, at least as the current working hypothesis.

        Yes... Quoting from time [201]
"It is known that under the influence of gravitation, GR bends the
timespace in such a manner that clocks (in general) cannot be
syncronized by Lorentz tranformations, due to the fact that in the
curved Lorentz
space there is no unique path to make the time conversions along.
However, with a Euclidian metric, there is always such a unique path,
shortest one, and it would be possible to develop a universal time for
> >
> > 2) that each LS's clock can be used to define both a temporal and
> > spatial co-ordinate (mesh) system for each?
> Yes, in the same sense as above.

        Here I am thinking _outside_ the LS, as what an LS observes...
> >
> > 3) that the propagation of photons with in a given LS's mesh system
> > follows a Minkowskian light cone structure, if we consider only
> > massless particles?
> I do not know how photons behave, but at least light propagates with speed c
> _as a wave_ associated to photons. This does not prevent instantaneous forces
> inside an LS.

        Again I am thinking in external terms. How is the "speed c" defined for
a group of LSs communicating to each other? Do we assume an absolute
interval for all? How do we get around the need of a invariant interval
such as is assumed in GR? An LS defines a local clock, do they also
define a local "length"?
> >
> > 4) would massive particles follow such a Minkowskian structure if
> > gravity is very weak?
> I am not sure enough, but at least by my working hypothesis any particles do
> not follow Minkowskian structure if considered inside an LS.

        I am speaking here of the outside situation...
> Hitoshi



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