John Baez explains Einstein's Gravity Eq
Jack Sarfatti
"So the "simple geometrical essence of Einstein's equation"
is this:
Take any small ball of initially comoving test particles in
free fall. Work in the local rest frame of this ball. As
time passes the ball changes volume; calculate its second
derivative at time zero and divide by the original volume.
The negative of this equals 1/2 the energy density at the
center of the ball, plus the flow of x-momentum in the x
direction there, plus the flow of y-momentum in the y
direction, plus the flow of z-momentum in the z direction.
Or, if you want a less precise but more catchy version:
Take any small ball of initially comoving test particles in
free fall. As time passes, the rate at which the ball begins
to shrink in volume is proportional to the energy density at
the center of the ball plus the flow of x-momentum in the x
direction there plus the flow of y-momentum in the y
direction plus the flow of z-momentum in the z direction.
Note: all of general relativity can in principle be
recovered from the above paragraph! Also note that the minus
sign in that paragraph is good, since it says if you have
POSITIVE energy density, the ball of test particles SHRINKS.
i.e., gravity is attractive."
Cool. Now this is a good intuitive classical picture. How
does this picture change in quantum mechanics? Use the Bohm
picture in which the small ball of comoving test particles
also have a quantum potential Q. What changes can happen?
1. The separate test particles are all independent of each
other, each with its own quantum potential in ordinary
space.
2. The separate test particles are entangled with each other
sharing a common quantum potential in configuration space.
3. The ball is a Bose-Einstein condensate (Modanese).
4. The ball is a Fermi liquid.
This all assumes a fixed curved classical space-time
geometry. Only the matter is quantized not the geometry so
it is not quantum gravity. This is semi-classical.
Exotic matter requires that the ball expand rather than
contract. Are there cases where the Bohm quantum potential Q
will enable that sort of thing to happen?