composite from articles by Prof. Frank J. Tipler, taken from:
http://xxx.lanl.gov/abs/astro-ph/0104011
http://www.eeng.dcu.ie/~tkpw/tcr/volume-03/number-02/v03n02.html
http://math.tulane.edu/~tipler/why.html
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Astrophysical black holes 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 [1]. The Second Law of Thermodynamics says the amount of entropy--the amount of disorder--in the universe cannot decrease, but it can be shown [2, pg. 410] that the amount of entropy already in the CBR (i.e., cosmic background radiation) will eventually contradict the Bekenstein Bound [3] near the final singularity unless there are no event horizons, since in the presence of horizons the Bekenstein Bound implies the universal entropy S must be equal or less than that constant (i.e., the Bekenstein Bound) times the radius of the universe squared, and general relativity requires the radius of the universe to go to zero at the final singularity. 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 by definition means that the shape of the final singularity is a single point, call it the Omega Point [4,5]. The British physicist Malcolm MacCallum has shown that a closed universe with a single point final singularity is of measure zero in initial data space (i.e., infinitely improbable acting on just blind and dead forces). The English astronomer John D. Barrow [6] has shown that the evolution of a closed universe into its final singularity is chaotic. The American physicist James Yorke [7] 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 near the final state, is really collectively 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 [8,9] 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 (i.e., S) diverges to infinity there, implying divergence of the complexity of the system that must be understood to be controlled.
References:
[1] Tipler, F. J. (1987), "An Achieved Spacetime Infinity," Nature 325, 201-202.
[2] Tipler, F. J. (1994), The Physics of Immortality, (New York: Doubleday).
[3] Schiffer, M. and J. D. Bekenstein (1989), "Proof of the Quantum Bound on Specific Entropy for Free Fields," Physical Review D39, 1109-1115.
[4] Tipler, F. J. (1986), "Cosmological Limits on Computation," International Journal of Theoretical Physics 25, 617-661.
[5] Tipler, F. J. (1992), "The Ultimate Fate of Life in Universes Which Undergo Inflation," Physics Letters B286, 36-43.
[6] Barrow, J. D. (1982), "Chaotic Behaviour in General Relativity," Physics Reports 85, 1-49.
[7] Yorke, J. A. et al (1992), "Using the Sensitive Dependence of Chaos (the 'Butterfly Effect') to Direct Trajectories in an Experimental Chaotic System," Physical Review Letters 68, 2863-2866.
[8] Misner, C. W. (1968), "The Isotropy of the Universe," Astrophysical Journal 151, 431-457
[9] Misner, C. W. (1969), "Mixmaster Universe," Physical Review Letters 22, 1071-1074