WHAT FOLLOWS IS PROBABLY NONSENSE. BUT LET
ME POST IT ANYWAY.
What is a meaningful gravitational analogy of epsilon?
First I thought it was a silly question. But perhaps it is not so
silly. Consider a sphere of radius R, made from styrofoam,
in otherwise empty space. It is an analogy of a sphere which
is negatively charged (because gravitational field lines are
directed toward the center). We can calculate the gravitational
potential V1 at the surface (with respect to V=0 at infinity).
Then we replace styrofoam with wood, keeping the same R.
This gives us a bigger potential, V2 (in terms of its absolute
value). Next we use, Al, Fe, Pb and Au to get V3, V4, V5
and V6. Let us stop here; I do not want to deal with black
holes in this thread. The unit of V is J/kg or (m/s)^2. What
prevents me from writing M=C*V, where M is the mass of
the sphere and C is a constant? By analogy, let call this
constant gavacity (or gravitational capacity). The unit of C
is kg*(s/m)^2; it can be called garad or gravitational farad).
We know that the amount of electric energy per unit space
(in every small region) decreases when empty space is
replaced by a dielectric material. Why? Because molecules
of that material are polarized. If molecules were not
polarizable then the presence of a dielectrical material
would have no effect on energy stored in the electric field.
In other words, the dielectric constant of the material, as
defined by Faraday, would be 1. Right?
Back to the gravitational capacitor. Suppose the space
surrounding the sphere is not empty. Gravitational
polarization does not exit because masses are always
positive. Therefore, by analogy, one may think that
presence of mass in space has no effect of gavacity
and the value of the "gravitational epsilon" is 1. But
this is not true. Presence of additional mass in space does
increase the amount of energy per unit volume. Therefore
the gravitational epsilon must be smaller than 1; the actual
value depends on the mass density in space which was
initially empty.
.
Please note that I am deliberately avoiding epsilon_zero,
a quantity whose unit depends on the unit of electric
current. A gravitational analogy of epsilon_zero would
be meaningful only if a flowing mass generated a force
field proportional to velocity (like magnetic field). I am
posting this message with a lot of hesitation.
Ludwik Kowalski