The Critical Rationalist Vol. 03 No. 02 ISSN: 1393-3809 23-Sep-1998

Bibliography

There Are No Limits To The Open Society

Technical Appendix:

* (46)* Astrophysical black holes almost certainly exist, but
Hawking has shown that if black holes are allowed to exist for
unlimited proper time, then they will completely evaporate, and a
fundamental quantum law called "unitarity" will be
violated. Unitarity, which roughly says that probability must be
conserved, thus requires that the universe cease to exist after
finite proper time, which in turn implies that the universe must
be closed in space, with the universe ending in a finite proper
time at a final singularity (Tipler, 1987).
The Second Law of Thermodynamics
says the amount of entropy--the amount of disorder--in the
universe cannot decrease, but the amount of entropy already in
the cosmic background radiation will eventually contradict the
Bekenstein Bound near the final singularity unless there are no
event horizons, since in the presence of horizons the Bekenstein
Bound implies the universal entropy must be less than the square
of the radius of the universe, and the radius of the universe
goes to zero as the final singularity is approached. Roger
Penrose showed how to define the shape of a singularity by using
the number of horizons that terminate in that singularity. The
absence of event horizons in Penrose's construction by definition
means that the shape of the final singularity is a single point,
call it the Omega Point (Tipler, 1986,1992).
The British physicist Malcolm MacCallum
has shown that a closed universe with a single point final
singularity is very improbable; technically we say "of
measure zero". The English astronomer John D. Barrow has shown
that the evolution of a closed universe into its final
singularity is chaotic. The American physicist James Yorke has
shown that a chaotic physical system is likely to evolve into a
measure zero state if and only if its control parameters are
intelligently manipulated. Thus life (which in the far future is
more appropriately thought of as intelligent computers) almost
certainly must be present arbitrarily close to the final
singularity in order for the known laws of physics to be mutually
consistent at all times. The American physicist Charles
W. Misner has shown in effect that event horizon elimination
requires an infinite number of distinct manipulations, so an
infinite amount of information must be processed between now and
the final singularity. The amount of information stored at any
given time diverges to infinity as the Omega Point is approached,
since the total entropy of the universe diverges to infinity
there, implying divergence of the complexity of the system that
must be understood to be controlled.

* (47)* When a closed universe collapses into its final
singularity, the average temperature of the universe increases
without limit. So in order to survive, life must transfer its
information into some other medium besides carbon, a medium which
can withstand the arbitrarily high temperatures near the final
singularity. The ability of life to transfer its information has
several implications. First of all, the density of the universe
must be great enough to close the universe. This means that the
"density parameter" which cosmologists call
"Omega-naught" (

* (48)* In the body of this paper, I mentioned another
prediction: the mass of the most important elementary particle,
the Higgs boson. The successful transfer of life's information
from its current basis to a high temperature basis implies that
the Standard Model Higgs boson mass must be within 20 of 220 GeV,
where "GeV" is a measure of mass used in particle
physics (Tipler, 1994

Bibliography

There Are No Limits To The Open Society

The Critical Rationalist Vol. 03 No. 02 ISSN: 1393-3809 23-Sep-1998

Copyright © 1998 All Rights Reserved.

TCR Issue Timestamp: 1998-09-23