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snowflakeuniverse
2003-Sep-14, 03:48 AM
Equivalence
Those who like a little algebra may find the following relationships interesting.

One of the assumptions of Einstein’s Theory of General Relativity was the equivalence of the Force exerted on a mass associated with a change in momentum, and the force associated with gravity.

Inertial Force = Gravitational Force
F = M A = M1 x M2 / D^2

F = force
M = Mass
A = acceleration = D/ T^2
D = distance measure
T = Time
M1 = Mass of one object
M2 = Mass of second object

Not included above is the “g” term called the gravitational constant. This is a “fudge factor” experimentally derived which allows the gravitational equation to work. It carries dimensions meaning it is not a simple number like 6 but it includes a number which is dependant on the “rulers” used that is then multiplied by the following dimensions F D^2/M^2.

If mass were described by the dimensional measures of D^3/T^2 some interesting relationships develop.
If M = D^3/T^2 then

F = MA = M1 x M2 / D^2
F = D^4/T^4 = D^4/T^4
no “g” term is needed that carries dimensions, (This is kind of a big deal).

Notice this also works with the classical expression for energy and Einstein’s Theoretically derived E= Mcc
Energy = F x D = M cc
Dimensions for c = D/T so.

Energy = D^5/T^4= D^5/T^4.

Mass apparently is a function of distance and time and is not a fundamental “dimension”.

snowflake

PS. I also derive the same dimensional relationship for the description of an expanding space-time field. This means that space-time and matter conform to the same dimensional relationships.