From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Birth of time
Organization: Whole Earth 'Lectronic Link
Date: Fri, 9 Oct 1992 04:14:56 GMT


One 'semi-classical' idea for the creation of the flow of time is that the
phase transition (from the false symmetric vacuum that drives inflation to
the our unsymmetric physical vacuum) forces the Weyl tensor (hence the
gravitational entropy of spacetime) to zero as the superposition of
physical vacua collapses. Zeh p.140 However, this is not the complete story
because the three-geometry has not yet been quantized. The inflation model
is semi-classical it is not yet quantum gravity.

"in quantum description, an objective clock-time u should correspond to a
classical property that 'emerges' through continuous measurements. p.142

In general relativity the spatial metric 3G is itself considered as a
'dynamical object' (the time-dependent state of geometry), which by its
change (or motion) defines intrinsic time as a dynamical variable....
clocks, therefore have to be dynamically influenced by the metric in order
to have their motion controlled by it. By means of their mass they in turn
react upon it... the metric ... is a physical clock p.143

the quantuzation of time becomes relevant only within the framework of the
quantization of gravity lll a stationary Schrodinger equation H| > = 0
which no longer contains a time parameter [as in ordinary quantum mechanics
of fields (with particle excitations)]...

H|F,3G> = 0 is the 'timeless" Wheeler-Dewitt or Einstein-Schrodinger
equation of quantum gravity in the eternity that gives birth to time.
F is the set of matter fields on the space-like hypersurface 3G.

"In general the wave function |  > has support on all spatial geometries.
...This wave function does not require or select specific foliations of
spacetime in contrast to the classical 3G orbits through superspace (a
configuration space of geometry and matter fields) p.143

The four-geometry is identical to the equivalence class of all orbits of
three geometries 3G which represent its deifferent foliations (slices) ..
the four-geometry is at most a quasi-classical approximation.

If time is absent in the Einstein-Schrodinger equation how do we define a
low entropy initial condition required for the arrow of time's flow once it
comes into being emerging out of the quantum gravity era into the semi-
classical inflationary expansion era which then creates the Big Bang by
quantum tunneling from the false to the physical vacuum?

Quantization of the classical Friedmann metric:
Cut off short waves give mini-superspace enabling a computable model. There
is a 'factor-ordering problem' p.145  The timeless Einstein-Shrodinger
equation for the Friedmann metric is hyperbolic because of the negative
gravity potential so that one can formulate "an intrinsic initial value
problem" p.146 of time without time!

The log expansion parameter lna is a time without time variable for
hyperbolic initial value problem. "one may claim that gravity gives rise to
time" p.146

the correlation of the expansion parameter lna with conventional clocks
(including the physiological ones responsible for the subjective experience
of time's flow) remains meaningful...

the quantized Friedmann metric in mini-superspace is non-unitary [Born
quantum probability not conserved, current density vanishes] p.147

... describe our observed universe quantum mechanically by means of a
superspace wave packet.... following a semi-classical orbit in mini-
superspace for ages bigger than Planck time of 10^-44 sec,,,,p.147 ...
these wavepackets normalizable only for certain initial conditions p.149
the remaining freedom due to the non-unitarity of the reduced dynamics
p.150

Hartle and Hawking (1983) have proposed a 'ground state' for the Einstein-
Schrodinger equation which is defined by the absence of any boundaries in a
'Euclidean' [i.e., 'imaginary time'] representation by means of path
integrals... p.154 for closed universe with a big crunch in far future of
big bang. So far evidence is that universe is open or flat but not closed.

classical orbits in mini-superspace [long wave modes only] may then be
expected to emerge because of their 'continuous measurement' by microscopic
[short wave?] variables p.155

Conventional clocks require degrees of freedom beyond mini-superspace i.e.
multipole expansions of the metric and matter fields ...including different
topologies..p.155

P.156 "There are thus two concepts of time in quantum gravity [ the lna
time and the WKB time]...The lna time controls the monopole dynamics and
the WKB time approximately controls the higher multipole dynamics p.156

It's the WKB higher multipole time that is our classical time! WKB time
controls propagation of light. p.156

the higher multipoles are the 'environment' of the mini-superspace
variables ... continualy measuring them p.158

"Hawking (1985) argued that the multipole wave functions describing the
inhomogeneity and complexity of the universe have to be in their ground
states at the beginning of the WKB era in mini-superspace i.e. at the
beginnning of the [semi-classical]inflationary phase which follows after
the [quantum gravity] Planck era  This would explain the required low
initial state of entropy in the big bang ...p.159


the emergence of quasi-classical histories.... can in fact only be
understood subjectively (relative to observers), the conventional concept
of time (as any classical concept) is then also esssentially observer-
related. It is nevertheless objectivizable with respect to different
observers [who communicate with each other-JS] because of the unavoidable
continuous measurement of the metric p.162

an intrinsic observer of the universe must always be quantum-correlated
('entangled') with the state of the spatial metric [3G] ('have measured
it'), in this way inducing the approximate concept of classical time by
hirs subjective presence as a matter of hir 'prespective' in superspace(
which she macroscopically shares with other observers with whom she is able
to communicate ... a basis of relevance ...p.163