Hitoshi Kitada (hitoshi@kitada.com)
Sun, 11 Apr 1999 12:33:28 +0900
Dear Stephen,
----- Original Message -----
From: Stephen P. King <stephenk1@home.com>
To: <time@kitada.com>
Sent: Sunday, April 11, 1999 11:51 AM
Subject: [time 217] Re: [time 215] How to define length using LSs
> 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,
> the
> shortest one, and it would be possible to develop a universal time for
> the
> Universe."
>
> > >
> > > 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...
Even for the outside of an LS, the time coordinate of the LS can be used to
define the mesh (coordinate system) for seeing other LS's. Just metric looks
different as the definition of length outside the LS is different from the
inside as below.
>
> > >
> > > 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"?
Light speed c in vacuum and the time of an LS are used to measure the length
of the path (outside the LS) through which the light passes from the begining
to the end, under the situation that the path is stationary with respect to
the LS. Thus c (speed of ligh in vacuum) is assumed as an absolute constant.
The length of a path moving with respect to the LS is defined by relativistic
change of coordinates (e.g. Lorentz transformation).
>
> > >
> > > 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...
Outside an LS, 4) is true.
Best,
Hitoshi
>
> > Hitoshi
> >
>
> Later,
>
> Stephen
>
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