From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: STRUCTURE OF TIME
Organization: Whole Earth 'Lectronic Link
Date: Thu, 8 Oct 1992 04:07:29 GMT


In Newton's classical mechanics of the 17th century F = ma and a force law
for F gives an ordinary differential equation second order in time that can
be solved from an initial condition by giving both initial position and
initial speed. This is why we used to say that the least action principle
of the calculus of variations is not teleological. However, we see that we
were too hasty and that the nonlinearity of classical general relativity
forces us back to teleology in that ther is no analog to the local initial
data x(0) and dx(0)/dt. Rather we must go to nonlocal x(0) and x(1) since
dx(0)/dt is meaningless in the general relativity case. Thus, gravitation
demands final cause or destiny even on the classical level. The same is
true on the quantum level because the Heisenberg uncertainty principle
tells us that x(0) and dx(0)/dt cannot be simultaneously specified to
arbitrary precision. Einstein, Podolsky and Rosen showed that real faster
than light quantum action at a distance - different from influence of known
forces- is required to maintain Heisenberg's principle and Feynman's Ph.D.
thesis on the influence functional in Lagrangian path quantum mechanics
confirms it.

The details for general relativity follow:

p.131 Zeh:"In Einstein's theory, a homogeneous and isotropic universe is
described by the Friedmann-Robertson_Walker metric ... the Weyl tensor
vanishes identically, this metric may be continued to the big bang at a = 0
in accordance with the Weyl tensor hypothesis

[Friedmann metric has form, for proper space-time separation ds between two
neighboring events, is ds^2 = -dt^2 + a(t)^2{ 3d spacelike metric different
for open,flat,closed universes depending on mass density. There is a simple
"zero total energy" classical mechanical looking eq. of motion for a(t)
scale factor with an effective potential V(lna)/2 of the form

E =[(d(lna)/dt)^2]/2 + V(lna) = 0

V has 3 terms : one depending on matter energy density which is different
in inflationary (where it simulates a false vacuum cosmological constant),
radiation dominated and matter dominated epochs, the second term is an ad
hoc cosmological constant, and the third is a spatial curvature term p.132
Zeh - JS]

"The finite age of the expanding universe leads to the result that two
events in the universe need not necessarily possess intersecting backward
light cones, and therefore may have no common causes at all ...
the homogeneity of the visible universe cannot be explained by a cause ...
The inability to causally explain the homogeneity of the universe in a
purely matter-or radiation-dominated universe is called the horizon
problem. It was the essential motivation for the hypothesis of a phase
transiton of the vacuum ... By means of the resulting exponential
expansion.... the universe may in an extremely short time (10^-33 sec)
inflate in size sufficiently so as to let the [causality] horizon cover
that part of the universe which is observable by means of the 2.7K
background radiation." p.133

".. the [classical] Einstein equations are of second order in the time
coordinate, and therefore in general determine the [4D spacetime] metric g
from two bountary conditions - for example at [past] t(0) and [future] t(1)
p.135 ... the time coordinate is physically meaningless .. after also
eliminating the dependence on the arbitrary space coordinates ... [the
Einstein gravitational field equations] describe two coordinate-free [3D]
spatial geometries (or three-geometries) 3G(0) and 3G(1) (i.e., the
intrinsic curvature of these space-like (outside light cone at every point0
hypersurfaces). If no singularities arise, the Einstein equations then fix
the complete four-dimensional spacetime geometry, and therefore the
distances in proper time [not the same as coordinate time!] along all
[subluminal] time-like orbits between the hypersurfaces [slices of
spacetime] defined by 3G(0) and 3G(1).p.136 [Notice how the classical
Einstein theory of gravity requires that the present is co-caused by both
the past 3G(0) and the future 3G(1) - JS].

The connection ... between the three-geometry 3G and the four-metric g on a
space-like surface [coordinate time] t = constant [a frame-dependent non-
objective slice] can be explained by means of" a {2x2 matrix whose 11
element is NiNi - N^2, 12 element is Nl, 21 element is Nk and 22 element is
the three-geometry metric 3Gkl, where k,1 range over the three space axes,
Nl and Nk is the shift function and N the lapse function describing
arbitrary increments of space ant time coordinates respectively. The four
lapse and shift functions are unphysical gauge variables as are three
functions in 3Gkl. The three remaining physically relevant functions
correspond to the two spin degrees of freedom of the massless graviton 'and
to 'many-fingered' physical time i.e., the increase of proper times between
all pairs of orthogonally connected points on two neighboring space-like
hypersurfaces." p.136

".. the three-geometry 3G as the coordinate-free dynamical variable of
general relativity is the 'carrier of information about physical time'...By
means of the Einstein equations it determines all [subluminal] time-like
distances from some initial 3G(0) along all possible orbits of clocks...
3G(0) by itself is not a complete initial conditon which would determine
the solution [of Einstein's field equations] .. a velocity of three-
geometry would be as tautological as a 'velocity of time' "p.136

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