In a message dated 2/14/01 1:29:03 PM Eastern Standard Time,
David_Bowman@GEORGETOWNCOLLEGE.EDU writes:
<< When I had used the symbol 'R' in my post objecting to John Denker's
claim that there was "nothing non-Newtonian" about the CC I was
discussing a universe that was spatially *flat* (i.e. its spatial
curvature length was infinite) and had only one or two masses of any
major significance in the *Newtonian limit* of slow speeds and weak
gravitational potentials. The meaning of "R" in that context was merely
the distance between the masses or the distance from an isolated mass to
a given spatial origin. What I was discussing was the fact that a free
isolated mass will accelerate away (in the *absence* of any gravitational
effects from *anything else* in the universe *except* the CC) from that
origin according to a = B*R where B is proportional to the CC (i.e.
B = (1/3)*[LAMBDA]*c^2) and R is the proper distance of the mass from the
origin. If the CC is zero then there is no such repulsive term appearing
in the Newtonian limit of GR, and only in this latter case does the
theory really boil down to Newton's theory in the nonrelativistic limit
of the relevant speeds being slow compared to c and relevant
gravitational potentials being small compared to c^2. >>
Dave I concur with the point you made to John Denker. However I would like to
expand a little on your thought experiment to see where it goes. You
postulated a Universe with one mass. Let me postulate a Universe empty of any
mass that is spatially flat. I believe this is a formulation known as the De
Sitter Universe. General Relativity implies the following equation.
Where a is the scale factor, k is curvature, A is the cosmological constant
and p is mass-energy density. In a Universe that is spatially flat (K=0) and
has zero energy density (p=0) by solving the above equation we get the
following result:
a=ki*exp((A^.5)*c*t Where Ki is an arbitrary constant.
which suggest under the condition of a spatially flat Universe with zero mass
energy density we end up with an expodential expansion of the scale factor.
This looks a lot like inflation though this approach is really an
oversimplified example.