Nonrenormalization vs Renormalization 83: Quantum Gravity First Riccati PI Equation
- From: "OsherD" <mdoctorow@xxxxxxxxxxx>
- Date: 4 Jul 2006 16:27:39 -0700
From Osher Doctorow mdoctorow@xxxxxxxxxxx
Looking at the exponential type braneworld models in Varun Sanhi (2004)
discussed in one of the last few Sections, the idea of searching for a
Riccati Differential equation occurs to us in combination with Probable
Influence/Causation (PI).
Since Probability and Sets --> time --> energy and time --> space -->
mass and energy --> mass (with reversibility "in theory" for the latter
but not so much cosmologically), the Riccati Differential equation
should arguably have as its main variable y of dy/dt = A(t) + B(t)y +
C(t)y^2 the quantity P (Probability), which later will be argued to be
Probable Causation/Influence (PI). The remaining variables should be
those above, namely time, energy, space, mass, or these relative to
volume (densities). In what follows, I refer to mass and energy even
when mass density and energy density are meant.
One simpification will be made, namely that energy and mass and space
involve arguably some redundancy, so a separate space variable will not
be inserted.
The following equation system is proposed:
1) dP/dt = P + P/t = P(1 + t)/t, d(EM)/dt = -2EM, E energy, M mass
We could actually obtain this system from:
2) P = t/(E^(1/2)M^(1/2)), d(EM)/dt = -2EM
Probability, or to anticipate results Probable Causation/Influence P,
is increasing with time and decreasing with energy/mass (or energy
density/mass density).
Remarkably, the acceleration of P is nonnegative:
3) Dtt(P) = (2 + t)/(EM)^(1/2)
So that the 1 of (1 + t) in (1) has become 2 and the denominator t is
gone.
If we regard the early Universe of inflation as low density on a
"relative" scale (relative to the present volume of the Universe, or
even to infinity coded as 1), then (3) could account for both Inflation
and the recent acceleration of the Universe in terms of Probability.
Osher Doctorow
.
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