Re: Is the Assumption Of Consistent Proper Time Throughout The Universe In GR Valid?

qchiang2_at_yahoo.com
Date: 01/09/05 

Date: 9 Jan 2005 07:59:52 -0800

Tom Roberts wrote:
> qchiang2@yahoo.com wrote:
> > 1. Einstein tensor and equation are based on the assumption of
> > consistent proper time.
>
> Not true. Proper time is not involved at all.
>
> The Einstein field equation is obtained as the Euler equations of a
> Lagrangian consisting of the curvature term (the Ricci scalar) plus
the
> appropriate Lagrangian density for whatever matter fields are
present,
> all integrated over the appropriate invariant volume element. Here
the
> metric tensor (field) and the matter fields are taken as the
independent
> functions to be determined by the variation.
>
> The energy-momentum tensor is the result of the variation of the
> Lagrangian density for the matter fields with respect to the metric,
and
> the Einstein tensor is the result of the variation of the curvature
> term. Nothing here depends on any proper time, or on any coordinates
> whatsoever.
>
>
>
> Remember that proper time makes sense only for pointlike objects. In
an
> earlier response I showed how the proper time of such objects is
> integrated over when determining their energy-momentum tensor, and
the
> result does not depend on the proper time of any object. A tensor
field
> on the manifold could not possibly do so.
>
>
> Tom Roberts tjroberts@lucent.com

There is always the problem of parameterization in Einstein theory.
The most fundamental assumption there is that the space and time scales
must be defined to let light be traveling at the same light speed any
where on a manifold. The problem is that if both space and time are
shrunk/expanded by the same proportion (say, a meter in a particular
galaxy is only one tenth a meter on earth, and simultaneously a second
there is also one tenth a second here), light would still be measured
at the same speed and nobody would know the space and time scales are
shrunk 10 fold (and mass and all 4-vectors would be expanded 10 times).
GR simply assumed that they never shrunk/expanded throughout the
universe, i.e. proper time unit remains consistent throughout the
universe. In his book "space, time and matter" Weyl claimed that
light alone is able to determine the scale units. Lorentz showed him
it's not possible and claimed massive particles would be needed to
determine it. (see, page 399 of the book "Gravitation" by Misner,
Thorne, Wheeler, Freeman, 1973). Without a spacetime scale, your
integration cannot be carried out.
I will try to repost my post again using the notation you suggested.
Qchiang

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