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From: gwyn@Brl-Vld.ARPA
Newsgroups: net.physics
Subject: Re:  Curvature of space due to presence of matter.
Message-ID: <1169@sri-arpa.UUCP>
Date: Thu, 24-May-84 10:58:16 EDT
Article-I.D.: sri-arpa.1169
Posted: Thu May 24 10:58:16 1984
Date-Received: Fri, 1-Jun-84 03:09:01 EDT
Lines: 46

From:      Doug Gwyn (VLD/VMB) <gwyn@Brl-Vld.ARPA>

The idea of general relativity (1914 version), which is still
considered our best theory of gravitation after 70 years, is
that gravitation is a manifestation of the curvature of space-time
(not just space).  The curvature can be considered to be caused
by matter (mass-energy-stress-momentum), or one can take the
equivalent view that what we call matter is just curved space-time.

The technical expression of this (in Einstein's original terms) is:
	Rik = Tik - 1/2 T	where T = gikTik (summed on i,k)
or
	Tik = Rik - 1/2 R	where R = gikRik
Here, T is the matter tensor density and R is the curvature tensor.
The above are field equations; i.e., they apply at each point of
space-time.  There will be different curvatures and different matter
densities at different points of space-time.
(I am skipping over several details but these are the main ideas.)

Additional standard general relativity ideas include the rule that
a gravitational test particle will follow a geodesic (think of
this as a "shortest" path in curved space-time, although it is not
really) and that light will follow a null geodesic.  A point mass
such as the sun (well, it's a fat point) generates a curved space-time
described by the "Schwarzschild solution" of the field equations;
such a mass is parameterized by a number M which represents the mass
(e.g. in grams) of the body generating the curvature.  Planets are
modeled as test particles following geodesics in the curved space-time
generated by the sun, and so forth.  If one computes what happens to
light from a distant star passing near the sun, he finds that it is
deflected from the path expected if the sun were not there.  This
effect has been measured many times (I think 1917 was the first time
but am not sure about the exact date), and it agrees with the
general-relativistic prediction.  Although a similar effect can be
derived from Newtonian physics, the observed deflection of starlight
by the sun differs from what such an approach would predict.

I hope this explanation has been sufficiently clear.  The calculation
of the predicted planetary orbits, light deflection, and so forth is
straightforward but tedious.  For normal laboratory-sized objects it
agrees pretty well with what the Newtonian theory predicts.  For
very fast (near the speed of light), very dense (neutron star), or
very large (cosmological) objects, the Newtonian theory is hopeless
and general relativity is normally used instead.

So, yes, it is "just a theory", but it is well corroborated.