Re: Quantum Gravity Via Expansion-Contraction 24: Fundamental Equations of Information/Entropy

From Osher Doctorow mdoctorow@xxxxxxxxxxx

So we come to Sir Isaac Newton's:

1) F = Gm1m2/r^2

which was incorporated, potentialwise at least, into Einstein's GR as
one tensor/matrix component (the potential involves the first power of
r).

While we are here, why not also compare:

2) beta (or gamma) = sqrt(1 - v^2/c^2) (or its multiplicative inverse)

of Special Relativity.

Does anybody notice the emphasis on 1/r, 1/r^2, v^2/c^2, but NOT r,
r^2, v^2? But mv^2 could not go away from kinetic energy, and
Einstein did emphasize E = mc^2, and yet the Newtonian and Einstein
"fundamental equations" involving gravitation and/or the macroscopic
world kept emphasizing the analog of Shannon and Renyi
Information/Entropy (before the births of either Shannon or Renyi, of
course) rather than the analog of Probable Influence/Causation as
explained in the previous postings.

So what does this have to do with Quantum Gravity?

Guth's and Linde's (Stanford) Inflation suddenly emphasized the Riccati
Differential equation picture implicitly because exponential
acceleration and/or exponential velocity are Riccati, and the Riccati
Differential equation itself has two main subtypes (exponential
growth/contraction/decay and logistic) which are rational functions of
exponentials. And their insights were further "indicated" by later
accelerations of the Universe and Dark Energy/Dark Matter.

The only other class of "Gravitation" besides the Newton-Einstein
inverse pictures which emerges from all this is exponential-related or
equivalently the positive exponent rather than inverse exponent
picture. If Quantum Theory wants to carve out a niche for itself in
Gravitation, it arguably has to adopt Riccati exponential-related
expansion/contraction.

Isn't exponential behavior too "big" for Quantum Theory? Not in the
least. Photons and other virtual and/or real elementary particles are
already recognized as travelling with "big" velocities in all of
physics. Quantum-related electronics is largely exponential.
Semiclassical behavior is largely exponential. And "half" of it all
is very "small", as when exp(kt) has k < 0!

Osher Doctorow

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