Re: Gravitational Confusion

Posted by ronron on December 07, 19100 at 13:33:36:

In Reply to: Re: Gravitational Confusion posted by Brian on December 06, 19100 at 13:15:11:

brian, i think the reason you are talking about gravity in
terms of mass is that you are still thinking in terms of
newtonian action-at-a-distance gravitation where two material
bodies have inertial mass and are attracted by the inverse square
law F = Gm1*m2/r^2 (more or less). this law stated that the
force of attration for two
bodies was instantaneous. when you move into general relativity,
the mass acts on the fabric of spacetime itself to alter the
geometry from the flat 4-dimensional manifold of special
relativity (which ignores forces) to the curved geometry of
GR which depends on the local masses.

in GR, an object will follow the best straight line it can (called
a geodesic). one of the first verified predictions of GR
was the bending of light by the sun. you could calculate how
much the sun's mass would deform spacetime locally, then predict
what trajectory light would follow when moving near it.
it follows the straightest possible path, which is determined
by the sun's mass.

so mass in relativity is not something that acts on other
material objects, it just deforms spacetime fabric and
objects moving in spacetime move according to the curvature
of the local spacetime. when you walk on the earth,
you are really walking on a curved path, although it is
because of the orientation of the surface in the 3-D
euclidean geometry. you would not be aware of it unless
you could examine the surface with respect to the 3-D space
it's embedded in. see "intrinsic vs extrinsic curvature."

pretty much the light ray will bend as it approaches the
sun because the sun's mass has deformed the local spacetime
in much the same way as the earth has constrained you to
move in a circle as you walk around the earth. it's at
least the same idea. you think of the earth as "attracting"
you to keep you from falling off, but you're really just
following your normal worldline as caused by the earth's
mass.

as noted
in earlier post, Misner, Thorne and Wheeler describe the
situation as "mass tells geometry how to curve, and
geometry tells mass how to move."

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