From Osher Doctorow
We're going to look at the old Newtonian law of universal gravitation:
1) F_g = Gm1m2/r^2, subscript g being gravitation, F force
We postulate that the expansive force or the force associated with
expansion is:
2) F_e = -Em1m2/r^2, E constant > 0
Of course, the signs could be reversed - the point is that they are
opposite in direction. Now watch this:
3) 1 + y - x = 1 + (-Em1m2/r^2) - Gm1m2/r^2
where x = Gm1m2/r^2, y = -Em1m2/r^2.
The left hand side of (3) is the Probable Influence/Causation of
gravitation upon expansion, but since x and y have to be probabilities
ordinarily, we are generalizing to negative probabilities in
accordance with Feynman's well-known idea. We assume normalization
so that everything has absolute value in [0, 1].
Looking at (3), both gravitation and expansion have become (Probable)
Causes by having negative sign if we rewrite (3) as:
4) 1 + y - x = 1 - (E + G)m1m2/r^2
But what are they operating on, that is to say, what is the Effect
(usually denoted by a positive term which y ordinarily is, distinct
from 1 and from the term -x)? The Effect is arguably 1 itself
representing the Universe only in this scenario or possibly 0
representing the Observer or even the Initial Universe at the Big
Bang! For example, in the case of 0, (4) reads:
5) 1 + y - x = 1 + 0 - (E + G)m1m2/r^2
The left hand side is Probable Influence/Causation, P(A-->B), and we
obtain directly from (5):
6) As r --> infinity, or as m1m2 --> 0+, P(A-->B) ---> 1 (its maximum)
7) As r^2 --> m1m2(E + G), P(A-->B) ---> 0 (its minimum)
Notice that Probable Influence/Causation is maximized at infinite
distance and at 0 masses, precisely the situation at the "center" of
the black hole discussed in the last few threads, but also the
situation discussed earlier of ideal application of Quantum Gravity to
expansion-driven space travel. Inflation is an approximation to it.
I'll try to discuss the minimum solution next time.
Osher Doctorow
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