Re: Determining metric tensor

From: DRLunsford (antimatter33_at_yahoo.com)
Date: 01/27/05 

Date: Thu, 27 Jan 2005 21:01:29 +0000 (UTC)

qmagick@yahoo.com wrote:

> Anyone know off hand how you experimentally determine
> the contravariant or covariant metric tensor of GM?
> Seems like a simple question but I don't know the
> answer...

There isn't a simple answer to this. One assumes the idea of arc-length
and the idea of metric is needed for its invariant description. The
natural invariant objects to use as reference are then light cones - so
you'd expect something like using the world-lines of massless objects.
This turns out to be true - see Shapiro's radar delay experiments. But
it can't be all - light cones are conformally invariant structures and
the world is (apparently) not conformally invariant. We throw in a
normalization of the metric as a tacit assumption. (A well-justified
one it would appear, but an assumption nevertheless.)

Thus experimentally one determines the metric divided by a "natural
volume element", 9 numbers. The 10th is given by the normalization.
This is a kind of reducibility of the metric and was mentioned here by
A. Jadczyk I believe.

-drl

-drl