From Osher Doctorow
Now I pointed out in a recent Section of this thread that if T = L^2
in the very early Universe, a plausible possibility under unification,
then we easily obtain an equation of the form:
1) Fg^a Fem^b Fs^c Fw^d = k
We could also obtain this equation from an entirely different
direction, namely let the 4 Fundamental Forces be taken as 4 variables
with MLT dimensions (3 Fundamental Dimensions), so there are 4 - 3 = 1
dimensionless product k.
But there is NO solution of (1) unless two pairs of forces are
inverses of two other pairs of forces up to a constant, since every
force in the MLT system has dimensions MLT^(-2), and a product of four
such dimensions is M^4 L^4 T^(-8) which is not dimensionless.
So it is very likely that Fg, the force of gravity, is the inverse of
either the strong or weak force, in consideration of the fact that
their ranges are "almost" inverses for example, and similarly Fem, the
electromagnetic force, is the inverse of either the weak or strong
force, unless multiplication itself in dimensional analysis is only an
approximation to a deeper +/- or "additive" representation such as
Probable Influence/Causation (PI) advocates. In the latter case, we
would replace multiplication in (1) by addition or subtraction in
various orders depending on the actual situation, and k would simply
be a constant like 1 or -1 or some other real number from Probable
Influence/Causation, for example under optimal conditions (Probable
Influence/Causation equal to 1).
Osher Doctorow
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