From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: ORIGIN OF TIME'S ARROW
Organization: Whole Earth 'Lectronic Link
Date: Mon, 5 Oct 1992 04:43:19 GMT


excerpted from The Sarfatti Lectures for Star Fleet Academy Cadets.

Zeh in Ch.5 writes:"In the framework of general relativity, gravity is
described as an effect of the curvature of spacetime. Its global structure
may define an arrow of time which is then reflected by the dynamics of all
matter. p.110 ...Already in Newton's theory, gravitating systems are
thermodynamically peculiar in possessing a negative heat capacity. This is
a consequence of the universal attractivity of this force."

Zeh points out that the classical virial theorem that the mean kinetic
energy equals minus one half the mean potential energy equals minus the
mean total energy for bound states of attractive inverse square force does
not hold if there is a coherent superposition of energy eigenstates.

"The negative sign between kinetic and total energy has the consequence
that, for example, satellites speed up as the result of friction in the
earth's atmosphere, [ Sarfatti explanation - note that friction means that
the total energy of the satellite is not a constant of the motion. As the
satellite gets closer to surface of earth its negative gravity potential
energy varying inversely as distance to center of mass of earth is
increasing since said distance is decreaseing, therefore the positive
kinetic energy which is negative one half of negative potential energy is
increasing. QED!] or that stars heat up by radiating energy away .. in so
far as the quantum mechanical zero-point energy is negligible... This
negative heat capacity has the unusual consequence that the heat flux from
hot to cold objects causes a thermal inhomogenity to grow. .... An
homogeneous universe therefore has to be considered as extraordinarily
improbable "... [amplification of thermal inhomgenities means work can be
done by Carnot engine effect , it also mean living far from thermal
equilibrium dissipative structures pumped by the expanding universe.] Zeh
points out limits to this negative classical Newtonian negative gravity
heat capacity placed by quantum degeneracy of electrons in solid matter of
planets and in white dwarf stars; repulsive short range forces, and black
hole trapped surfaces. When the mass is high enough the first two cannot
prevent collapse to a black hole. Fermions will gravitationally compress
into bosons which cannot stop the collapse. Blackhole collapse is
irreversible.

Causality without causality - Feynman-Wheeler:
The local classical Einstein second rank tensor gravitational field
equation is G = 8piT where G is the Einstein tensor and T is the energy-
momentum stress tensor. This equation has the same form under all possible
changes of the local coordinate systems (i.e., covariance). G is formed
from R the second rank Ricci tensor which is the trace of the fourth rank
Riemann curvature tensor. This trace is analogous to the wave operator
(i.e. d'Alembertian of the electromagnetic field). The second rank metric
tensor g defining frame-invariant "proper" spacetime distances between
neighboring events replaces the Newtonian gravity potential. "Aside from
the nonlinearities responsible for the self interaction of gravity, the
Riemann curvature tensor is given by the second derivatives of the metric
tensor" p.113  The trace of the 4th rank Riemann tensor is determined
locally by the matter sources described by T, but the trace-free part of
Riemann is determined by the degrees of freedom of the matter-free part of
the gravity field - this is called W the Weyl tensor. Roger Penrose
suggested that W = 0 in the initial moment of the creation of the universe.
He thinks W = 0 is a minumum of gravity entropy. There is an anlogous
condition for the electromagnetic field. In this picture both gravity and
electromagnetism (hyperbolic eqs. in real time) are "retarded" with
"causes" in the form of "advanced sources" (i.e. Feynman-Wheeler "absorber
condition" in far future) p.113 Note the effect of Destiny here! In order
that waves propagate causally from past to future now - they must be
absorbed totally in the far future. In the Feynman-Wheeler picture we have
"Causality without causality."!

Penrose postulates vanishing of W for all time-like past singularities of
the spacetime curvature.  More anon.
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