From: seeta@eng.wayne.edu (Seetamraju UdayaBhaskar Sarma)
Subject: ... when western science dwarfs the vedaas ....
Reply-To: seeta@eng.wayne.edu
Organization: College of Engineering, Wayne State University, Detroit Michigan, USA
Date: Tue, 26 Jan 1993 00:43:21 GMT

The big bossu on sci.math from MIT (john baez) writes:

-+>Well, this week I have had guests and have not been keeping up with
-+>the literature.  So "this week's finds" are mostly papers that have
-+>been sitting around in my office and that I am now filing away.
......
-+>5)  The origin of time asymmetry, by S W Hawking, R Laflamme and G W Lyons,
-+>preprint available as gr-qc/9301017, in tex.
-+>
-+>I haven't had a chance to read this one yet but it looks very ambitious
-+>and is likely to be interesting.  Let me just quote from the introduction
-+>to get across the goal:
-+>
-+>The laws of physics do not distinguish the future from the past direction
-+>of time. More precisely, the famous CPT theorem$^{\refcpt}$ says that the laws
-+>are invariant under the combination of charge conjugation, space inversion and
-+>time reversal. In fact effects that are not invariant under the combination
-+>CP are very weak, so to a good approximation, the laws are invariant under
-+>the time reverseal operation T alone. Despite this, there is a very obvious
-+>difference between the future and past directions of time in the universe
-+>we live in. One only has to see a film run backward to be aware of this.
-+>
-+>There are are several expressions of this difference. One is the so-called
-+>psychological arrow, our subjective sense of time, the fact that we
-+>remember events in one direction of time but not the other. Another is the
-+>electromagnetic arrow, the fact that the universe is described by  retarded
-+>solutions of Maxwell's equations and not advanced ones. Both of these
-+>arrows can be shown to be consequences of the thermodynamic arrow, which
-+>says that entropy is increasing in one direction of time. It is a non
-+>trivial feature of our universe that it should have a well defined
-+>thermodynamic arrow which seems to point in the same direction everywhere
-+>we can observe. Whether the direction of the thermodynamic arrow is also
-+>constant in time is something we shall discuss shortly.
-+>
-+>There have been a number of attempts to explain why the universe should
-+>have a thermodynamic arrow of time at all. Why shouldn't the universe be
-+>in a state of maximum entropy at all times? And why should the direction
-+>of the thermodynamic arrow agree with that of the cosmological arrow, the
-+>direction in which the universe is expanding? Would the thermodynamic
-+>arrow reverse, if the universe reached a maximum radius and began to
-+>contract?
-+>
-+>Some authors have tried to account for the arrow of time on the basis of
-+>dynamic laws. The discovery that CP invariance is violated in the decay of
-+>the K meson, inspired a number of such attempts but it is
-+>now generally recognized that CP violation can explain why the universe
-+>contains baryons rather than anti baryons, but it can not explain the
-+>arrow of time. Other authors have questioned whether quantum
-+>gravity might not violate CPT, but no mechanism has been suggested. One would
-+>not be satisfied with an ad hoc CPT violation that was put in by hand.
-+>
-+>The lack of a dynamical explanation for the arrow of time suggests that it
-+>arises from boundary conditions. The view has been expressed that the
-+>boundary conditions for the universe are not a question for Science, but
-+>for Metaphysics or Religion. However that objection does not apply if
-+>there is a sense in which the universe has no boundary. We shall therefore
-+>investigate the origin of the arrow of time in the context of the no
-+>boundary proposal of Hartle & Hawking. This was formulated in
-+>terms of Einsteinian gravity which may be only a low energy effective theory
-+>arising from some more fundamental theory such as superstrings. Presumably
-+>it should be possible to express a no boundary condition in purely string
-+>theory terms but we do not yet know how to do this. However the recent
-+>COBE observations indicate that the perturbations that lead to
-+>the arrow of time arise at a time during inflation when the energy 
-+>density is about 10^{-12} of the Planck density. In this regime, 
-+>Einstein gravity should be a good approximation.
-+>
-+>[I'll skip some more technical stuff on the validity of perturbative
-+>calculations in quantum gravity...]
-+>
-+>One can estimate the wave functions for the perturbation modes by
-+>considering complex metrics and scalar fields that are solutions of the
-+>Einstein equations whose only boundary is the surface $S$. When $S$ is a
-+>small three sphere, the complex metric can be close to that of part of a
-+>Euclidean four sphere. In this case the wave functions for the tensor and
-+>scalar modes correspond to them being in their ground state. As the three
-+>sphere $S$ becomes larger, these  complex metrics change continuously to
-+>become almost Lorentzian. They represent universes with an initial period
-+>of inflation driven by the potential energy of the scalar field. During
-+>the inflationary phase the perturbation modes remain in their ground
-+>states until their wave lengths become longer than the horizon size. The
-+>wave function of the perturbations then remains frozen until the horizon
-+>size increases to be more than the wave length again during the matter
-+>dominated era of expansion that follows the inflation. After the wave
-+>lengths of the perturbations come back within the horizon, they can be
-+>treated classically.
-+>
-+>This behaviour of the perturbations can explain the existence and direction
-+>of the thermodynamic arrow of time. The density perturbations when they
-+>come within the horizon are not in a general state but in a very special
-+>state with a small amplitude that is determined by the parameters of the
-+>inflationary model, in this case, the mass of the scalar field. The recent
-+>observations by COBE indicate this amplitude is about $10^{-5}$. After the
-+>density perturbations come within the horizon, they will grow until they
-+>cause some regions to collapse as proto-galaxies and clusters. The
-+>dynamics will become highly non linear and chaotic and the coarse grained
-+>entropy will increase. There will be a well defined thermodynamic arrow of
-+>time that points in the same direction everywhere in the universe and
-+>agrees with the direction of time in which the universe is expanding, at
-+>least during this phase.
-+>
-+>The question then arises: If and when the universe reaches and maximum
-+>size, will the thermodynamic arrow reverse? Will entropy decrease and the
-+>universe become smoother and more homogeneous during the contracting
-+>phase? 
-+>
-+>[I'll skip some stuff on why Hawking originally thought entropy
-+>had to decrease during the Big Crunch if the no-boundary proposal
-+>were correct... and why he no longer thinks so.]
-+>
-+>The thermodynamic arrow will agree with the cosmological arrow for half the
-+>history of the universe, but not for the other half. So why is it that we
-+>observe them to agree? Why is it that entropy increases in the direction
-+>that the universe is expanding? This is really a situation in which one can
-+>legitimately invoke the weak anthropic principle because it is a question
-+>of where in the history of the universe conditions are suitable for
-+>intelligent life. The inflation in the early universe implies that the
-+>universe will expand for a very long time before it contracts again. In
-+>fact, it is so long that the stars will have all burnt out and the baryons
-+>will have all decayed. All that will be left in the contracting phase will
-+>be a mixture of electrons, positrons, neutrinos and gravitons. This is not
-+>a suitable basis for intelligent life.
-+>
-+>The conclusion of this paper is that the no boundary proposal can explain
-+>the existence of a well defined thermodynamic arrow of time. This arrow
-+>always points in the same direction. The reason we observe it to point in
-+>the same direction as the cosmological arrow is that conditions are
-+>suitable for intelligent life only at the low entropy end of the
-+>universe's history.
-+>


Seetamraju Udaya Bhaskar Sarma
(email : seetam @ ece7 . eng . wayne . edu)