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Line 78: − [[Stephen Hawking]] has proposed a solution to the black hole information issue in order to preserve unitarity but without the universe collapsing which is dependent on the conjectured string theory-based anti-de Sitter space/conformal field theory correspondence (AdS/CFT correspondence).<ref name="Hawking2005">[[Stephen Hawking|S. W. Hawking]], [http://www.physics.princeton.edu/~mcdonald/examples/QM/hawking_prd_72_084013_05.pdf "Information loss in black holes"], ''Physical Review D'', Vol. 72, No. 8 (October 2005), Art. No. 084013, 4 pages, {{doi|10.1103/PhysRevD.72.084013}}, {{bibcode|2005PhRvD..72h4013H}}. [http://www.webcitation.org/5oCZDMztm Mirror link]. Also at {{arxiv|hep-th/0507171}}, July 18, 2005.</ref>+ Line 90:
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Spelling/Grammar Check, typos fixed: additon → addition
<blockquote>To emphasize the scientific nature of the Omega Point Theory, let me state here that I am at present forced to consider myself an atheist, in the literal sense that I am not a theist. (''A-theist'' means "not theist.") I do not yet even believe in the Omega Point. The Omega Point Theory is a viable scientific theory of the future of the physical universe, but the only evidence in its favor at the moment is theoretical beauty, for there is as yet no confirming experimental evidence for it. Thus scientifically one is not compelled to accept it at the time of my writing these words. So I do not. [[Antony Flew|Flew]], among others, has in my opinion made a convincing case for the presumption of atheism. If the Omega Point Theory and all possible variations of it are disconfirmed, then I think atheism in the sense of Flew, [[David Hume|Hume]], [[Bertrand Russell|Russell]], and the other self-described atheists is the only rational alternative. But of course I also think the Omega Point Theory has a very good chance of being right, otherwise I would never have troubled to write this book. If the Omega Point Theory is confirmed, I shall then consider myself a theist.</blockquote>
<blockquote>To emphasize the scientific nature of the Omega Point Theory, let me state here that I am at present forced to consider myself an atheist, in the literal sense that I am not a theist. (''A-theist'' means "not theist.") I do not yet even believe in the Omega Point. The Omega Point Theory is a viable scientific theory of the future of the physical universe, but the only evidence in its favor at the moment is theoretical beauty, for there is as yet no confirming experimental evidence for it. Thus scientifically one is not compelled to accept it at the time of my writing these words. So I do not. [[Antony Flew|Flew]], among others, has in my opinion made a convincing case for the presumption of atheism. If the Omega Point Theory and all possible variations of it are disconfirmed, then I think atheism in the sense of Flew, [[David Hume|Hume]], [[Bertrand Russell|Russell]], and the other self-described atheists is the only rational alternative. But of course I also think the Omega Point Theory has a very good chance of being right, otherwise I would never have troubled to write this book. If the Omega Point Theory is confirmed, I shall then consider myself a theist.</blockquote>
Tipler now regards himself as a theist due to what he states have been advancements in his Omega Point Theory which occurred after the publication of ''The Physics of Immortality''.<ref name="Meddis1998">Sam Vincent Meddis, "Computers of the distant future", ''[[USA Today]]'', four parts, August 3–31, 1998. [http://www.usatoday.com/tech/columnist/ccb0803.htm Part 1: "Machines evolve"] (August 3), [http://www.usatoday.com/tech/columnist/ccb0810.htm Part 2: "A quantum leap"] (August 10), [http://www.usatoday.com/tech/columnist/ccb0817.htm Part 3: "Universal truths"] (August 17), and [http://www.usatoday.com/tech/columnist/ccb0831.htm Part 4: "Web of thought"] (August 31). See Part 1 concerning Tipler no longer being an atheist.</ref><ref name="Tipler2007b2">Frank J. Tipler, ''The Physics of Christianity'' (New York: Doubleday, 2007), ISBN 0385514247, {{lccn|2006039028}}, Chapter III: "Life and the Ultimate Future of the Universe", p. 62.</ref> Namely, Tipler now says the known laws of physics—specifically, [[quantum mechanics]], [[general relativity]], the [[second law of thermodynamics]], and the [[Standard Model]] of particle physics—require the existence of the Omega Point [[gravitational singularity|singularity]] in order to avoid their violation;<ref name="Tipler2005"/><ref name="Tipler1998"/><ref name="Tipler2001"/><ref name="Tipler2003"/> whereas in ''The Physics of Immortality'' Tipler investigated what would be necessary from the postulate that life continues forever while still keeping the analysis confined to the known laws of physics. Tipler states that these physical laws have been repeatedly confirmed by every experiment to date. According to Tipler, this constitutes a massive body of empirical evidence for the Omega Point Theory's correctness. And as indicated above, Tipler also now considers himself a Christian due to his identification of the Omega Point with the [[God]] of [[Christianity|Christian theological tradition]].
Tipler now regards himself as a theist due to what he states have been advancements in his Omega Point Theory which occurred after the publication of ''The Physics of Immortality''.<ref name="Meddis1998">Sam Vincent Meddis, "Computers of the distant future", ''[[USA Today]]'', four parts, August 3–31, 1998. [http://www.usatoday.com/tech/columnist/ccb0803.htm Part 1: "Machines evolve"] (August 3), [http://www.usatoday.com/tech/columnist/ccb0810.htm Part 2: "A quantum leap"] (August 10), [http://www.usatoday.com/tech/columnist/ccb0817.htm Part 3: "Universal truths"] (August 17), and [http://www.usatoday.com/tech/columnist/ccb0831.htm Part 4: "Web of thought"] (August 31). See Part 1 concerning Tipler no longer being an atheist.</ref><ref name="Tipler2007b2">Frank J. Tipler, ''The Physics of Christianity'' (New York: Doubleday, 2007), ISBN 0385514247, {{lccn|2006039028}}, Chapter III: "Life and the Ultimate Future of the Universe", p. 62.</ref> Namely, Tipler now says the known laws of physics—specifically, [[quantum mechanics]], [[general relativity]], the [[second law of thermodynamics]], and the [[Standard Model]] of particle physics—require the existence of the Omega Point [[gravitational singularity|singularity]] in order to avoid their violation;<ref name="Tipler2005"/><ref name="Tipler1998"/><ref name="Tipler2001"/><ref name="Tipler2003"/> whereas in ''The Physics of Immortality'' Tipler investigated what would be necessary from the postulate that life continues forever while still keeping the analysis confined to the known laws of physics. Tipler states that these physical laws have been repeatedly confirmed by every experiment to date. According to Tipler, this constitutes a massive body of empirical evidence for the Omega Point Theory's correctness. And as indicated above, Tipler also now considers himself a Christian due to his identification of the Omega Point with the God of [[Christianity|Christian theological tradition]].
==Physics==
==Physics==
<blockquote>Astrophysical black holes almost certainly exist, but [[Stephen Hawking|Hawking]]<ref name="Hawking1976" group="q">[[Stephen Hawking|S. W. Hawking]], [http://www.physics.princeton.edu/~mcdonald/examples/QM/hawking_prd_14_2460_76.pdf "Breakdown of predictability in gravitational collapse"], ''Physical Review D'', Vol. 14, Issue 10 (November 1976), pp. 2460-2473, {{doi|10.1103/PhysRevD.14.2460}}, {{bibcode|1976PhRvD..14.2460H}}. [http://www.webcitation.org/5o9PpPxNW Mirror link].</ref> and Wald<ref name="Wald1994" group="q">Robert M. Wald, ''Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics'' (Chicago: University of Chicago Press, 1994), ISBN 0226870251, {{lccn|94011065}}, Section 7.3, pp. 182-185.</ref> have shown that if black holes are allowed to exist for unlimited proper time, then they will completely evaporate, and unitarity will be violated. Thus, unitarity requires that the universe must cease to exist after finite proper time, which implies that the universe has spatial topology ''S''<sup>3</sup>.<ref name="Barrow1986" group="q">John D. Barrow, Gregory J. Galloway and Frank J. Tipler, [http://adsabs.harvard.edu/abs/1986MNRAS.223..835B "The closed-universe recollapse conjecture"], ''Monthly Notices of the Royal Astronomical Society'', Vol. 223, No. 4 (December 1986), pp. 835-844, {{bibcode|1986MNRAS.223..835B}}, CAT.INIST No. [http://cat.inist.fr/?aModele=afficheN&cpsidt=8251334 8251334]. On p. 926 of the same 2005 ''Reports on Progress in Physics'' paper, Tipler writes that "A dynamical proof for ''S''<sup>3</sup> can be found in Barrow (1986)", with "Barrow (1986)" being this reference.</ref> The [[Second law of thermodynamics|Second Law of Thermodynamics]] says the amount of entropy in the universe cannot decrease, but Ellis and Coule<ref name="EllisCoule1994" group="q">G. F. R. Ellis and D. H. Coule, [http://www.springerlink.com/content/xh785g1534074045/ "Life at the end of the universe?"], ''General Relativity and Gravitation'', Vol. 26, No. 7 (July 1994), pp. 731-739, {{doi|10.1007/BF02116959}}, {{bibcode|1994GReGr..26..731E}}.</ref> and I<ref name="Tipler1994" group="q">Frank J. Tipler, ''The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead'' (New York: Doubleday, 1994), ISBN 0385467982, {{lccn|93045046}}, {{bibcode|1994pimc.book.....T}}, Appendix C: "The Bekenstein Bound", p. 410. Said Appendix is reproduced in Frank J. Tipler, [http://arxiv.org/abs/astro-ph/0111520 "Genesis: How the Universe Began According to Standard Model Particle Physics"], {{arxiv|astro-ph/0111520}}, November 28, 2001, Section 2: "Apparent Inconsistences in the Physical Laws in the Early Universe", Subsection a: "Bekenstein Bound Inconsistent with Second Law of Thermodynamics".</ref> have shown that the amount of entropy already in the CMBR will eventually contradict the Bekenstein Bound near the final singularity unless there are no [[event horizon]]s, since in the presence of horizons the Bekenstein Bound implies the universal entropy ''S'' ≤ constant × ''R''<sup>2</sup>, where ''R'' is the radius of the universe, and [[general relativity]] requires ''R'' → 0 at the final singularity. If there are no horizons then the (shear) energy density can grow as ''R''<sup>−6</sup> which means that the total available energy grows as (''R''<sup>−6</sup> ) ''R''<sup>3</sup> ~ ''R''<sup>−3</sup>, and so the Bekenstein Bound yields ''E R'' ~ (''R''<sup>−3</sup>)''R'' ~ ''R''<sup>−2</sup> which diverges as ''R''<sup>−2</sup> as ''R'' → 0 at the final singularity.<ref name="Tipler2003" group="q">Frank J. Tipler, [http://theophysics.freevar.com/pdf/tipler-intelligent-life-in-cosmology.pdf "Intelligent life in cosmology"], ''International Journal of Astrobiology'', Vol. 2, Issue 2 (April 2003), pp. 141-148, {{doi|10.1017/S1473550403001526}}, {{bibcode|2003IJAsB...2..141T}}. Mirror links [http://www.webcitation.org/5o9QHKGuW here] and [http://theophysics.host56.com/pdf/tipler-intelligent-life-in-cosmology.pdf here]; also available [http://math.tulane.edu/~tipler/intelligentlife.pdf here]. Also at {{arxiv|0704.0058}}, March 31, 2007.</ref><ref name="Tipler1994" group="q"/> The absence of event horizons by definition means that the universe's future c-boundary is a single point,<ref name="HawkingEllis1973" group="q">[[Stephen Hawking|S. W. Hawking]] and G. F. R. Ellis, ''The Large Scale Structure of Space-Time'' (London: [[Cambridge University Press]], 1973), ISBN 0521200164, {{lccn|72093671}}, {{bibcode|1973lsss.book.....H}}, pp. 217-221.</ref> call it the ''Omega Point''. MacCallum<ref name="MacCallum1971" group="q">Malcolm A. H. MacCallum, "Mixmaster universe problem", ''Nature—Physical Science'', Vol. 230 (March 1971), pp. 112-113, {{bibcode|1971Natur.230..112M}}, {{OSTI|4048469}}. See also [http://www.maths.qmul.ac.uk/~mm/papers.html here].</ref> has shown that an ''S''<sup>3</sup> closed universe with a single point future c-boundary is of measure zero in initial data space. Barrow,<ref name="Barrow 1982" group="q">John D. Barrow, "Chaotic behaviour in general relativity", ''Physics Reports'', Vol. 85, Issue 1 (May 1982), pp. 1-49, {{doi|10.1016/0370-1573(82)90171-5}}, {{bibcode|1982PhR....85....1B}}.</ref><ref name="Barrow1998" group="q">John D. Barrow and Janna Levin, [http://link.aps.org/doi/10.1103/PhysRevLett.80.656 "Chaos in the Einstein-Yang-Mills Equations"], ''Physical Review Letters'', Vol. 80, Issue 4 (January 1998), pp. 656-659, {{doi|10.1103/PhysRevLett.80.656}}, {{bibcode|1998PhRvL..80..656B}}. Also at {{arxiv|gr-qc/9706065}}, June 20, 1997.</ref> Cornish and Levin<ref name="CornishLevin1997" group="q">Neil J. Cornish and Janna J. Levin, [http://link.aps.org/doi/10.1103/PhysRevD.55.7489 "Mixmaster universe: A chaotic Farey tale"], ''Physical Review D'', Vol. 55, Issue 12 (June 1997), pp. 7489-7510, {{doi|10.1103/PhysRevD.55.7489}}, {{bibcode|1997PhRvD..55.7489C}}. Also at {{arxiv|gr-qc/9612066}}, December 30, 1996.</ref> and Motter<ref name="Motter2003" group="q">Adilson E. Motter, [http://llacolen.ciencias.uchile.cl/~vmunoz/download/papers/m03a.pdf "Relativistic Chaos is Coordinate Invariant"], ''Physical Review Letters'', Vol. 91, Issue 23 (December 2003), Art. No. 231101, 4 pages, {{doi|10.1103/PhysRevLett.91.231101}}, {{bibcode|2003PhRvL..91w1101M}}. [http://www.webcitation.org/5o9Pa8B4M Mirror link]. Also at {{arxiv|gr-qc/0305020}}, May 5, 2003.</ref> have shown that the evolution of an ''S''<sup>3</sup> closed universe into its final singularity is chaotic. Yorke ''et al.''<ref name="Yorke1990" group="q">Troy Shinbrot, Edward Ott, Celso Grebogi and James A. Yorke, [http://link.aps.org/doi/10.1103/PhysRevLett.65.3215 "Using chaos to direct trajectories to targets"], ''Physical Review Letters'', Vol. 65, Issue 26 (December 1990), pp. 3215-3218, {{doi|10.1103/PhysRevLett.65.3215}}, {{bibcode|1990PhRvL..65.3215S}}.</ref><ref name="Yorke1992" group="q">Troy Shinbrot, William Ditto, Celso Grebogi, Edward Ott, Mark Spano and James A. Yorke, [http://link.aps.org/doi/10.1103/PhysRevLett.68.2863 "Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system"], ''Physical Review Letters'', Vol. 68, Issue 19 (May 1992), pp. 2863-2866, {{doi|10.1103/PhysRevLett.68.2863}}, {{bibcode|1992PhRvL..68.2863S}}.</ref> have 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 (≡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. Misner<ref name="Misner1968" group="q">Charles W. Misner, [http://adsabs.harvard.edu/abs/1968ApJ...151..431M "The Isotropy of the Universe"], ''Astrophysical Journal'', Vol. 151 (February 1968), pp. 431-457, {{doi|10.1086/149448}}, {{bibcode|1968ApJ...151..431M}}.</ref><ref name="Misner1969a" group="q">Charles W. Misner, [http://link.aps.org/doi/10.1103/PhysRev.186.1319 "Quantum Cosmology. I"], ''Physical Review'', Vol. 186, Issue 5 (October 1969), pp. 1319-1327, {{doi|10.1103/PhysRev.186.1319}}, {{bibcode|1969PhRv..186.1319M}}.</ref><ref name="Misner1969b" group="q">Charles W. Misner, [http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/07/036.pdf "Mixmaster Universe"], ''Physical Review Letters'', Vol. 22, Issue 20 (May 1969), pp. 1071-1074, {{doi|10.1103/PhysRevLett.22.1071}}, {{bibcode|1969PhRvL..22.1071M}}. [http://www.webcitation.org/5oFUpabxe Mirror link]. Also available as [http://www.gravityresearchfoundation.org/pdf/awarded/1969/minner.pdf an entry] in the Gravity Research Foundation's 1969 essay competition. [http://www.webcitation.org/5oFmSHFDm Mirror link].</ref> 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 time diverges to infinity as the Omega Point is approached, since ''S'' → +∞ there, implying divergence of the complexity of the system that must be understood to be controlled.</blockquote>
<blockquote>Astrophysical black holes almost certainly exist, but [[Stephen Hawking|Hawking]]<ref name="Hawking1976" group="q">[[Stephen Hawking|S. W. Hawking]], [http://www.physics.princeton.edu/~mcdonald/examples/QM/hawking_prd_14_2460_76.pdf "Breakdown of predictability in gravitational collapse"], ''Physical Review D'', Vol. 14, Issue 10 (November 1976), pp. 2460-2473, {{doi|10.1103/PhysRevD.14.2460}}, {{bibcode|1976PhRvD..14.2460H}}. [http://www.webcitation.org/5o9PpPxNW Mirror link].</ref> and Wald<ref name="Wald1994" group="q">Robert M. Wald, ''Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics'' (Chicago: University of Chicago Press, 1994), ISBN 0226870251, {{lccn|94011065}}, Section 7.3, pp. 182-185.</ref> have shown that if black holes are allowed to exist for unlimited proper time, then they will completely evaporate, and unitarity will be violated. Thus, unitarity requires that the universe must cease to exist after finite proper time, which implies that the universe has spatial topology ''S''<sup>3</sup>.<ref name="Barrow1986" group="q">John D. Barrow, Gregory J. Galloway and Frank J. Tipler, [http://adsabs.harvard.edu/abs/1986MNRAS.223..835B "The closed-universe recollapse conjecture"], ''Monthly Notices of the Royal Astronomical Society'', Vol. 223, No. 4 (December 1986), pp. 835-844, {{bibcode|1986MNRAS.223..835B}}, CAT.INIST No. [http://cat.inist.fr/?aModele=afficheN&cpsidt=8251334 8251334]. On p. 926 of the same 2005 ''Reports on Progress in Physics'' paper, Tipler writes that "A dynamical proof for ''S''<sup>3</sup> can be found in Barrow (1986)", with "Barrow (1986)" being this reference.</ref> The [[Second law of thermodynamics|Second Law of Thermodynamics]] says the amount of entropy in the universe cannot decrease, but Ellis and Coule<ref name="EllisCoule1994" group="q">G. F. R. Ellis and D. H. Coule, [http://www.springerlink.com/content/xh785g1534074045/ "Life at the end of the universe?"], ''General Relativity and Gravitation'', Vol. 26, No. 7 (July 1994), pp. 731-739, {{doi|10.1007/BF02116959}}, {{bibcode|1994GReGr..26..731E}}.</ref> and I<ref name="Tipler1994" group="q">Frank J. Tipler, ''The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead'' (New York: Doubleday, 1994), ISBN 0385467982, {{lccn|93045046}}, {{bibcode|1994pimc.book.....T}}, Appendix C: "The Bekenstein Bound", p. 410. Said Appendix is reproduced in Frank J. Tipler, [http://arxiv.org/abs/astro-ph/0111520 "Genesis: How the Universe Began According to Standard Model Particle Physics"], {{arxiv|astro-ph/0111520}}, November 28, 2001, Section 2: "Apparent Inconsistences in the Physical Laws in the Early Universe", Subsection a: "Bekenstein Bound Inconsistent with Second Law of Thermodynamics".</ref> have shown that the amount of entropy already in the CMBR will eventually contradict the Bekenstein Bound near the final singularity unless there are no [[event horizon]]s, since in the presence of horizons the Bekenstein Bound implies the universal entropy ''S'' ≤ constant × ''R''<sup>2</sup>, where ''R'' is the radius of the universe, and [[general relativity]] requires ''R'' → 0 at the final singularity. If there are no horizons then the (shear) energy density can grow as ''R''<sup>−6</sup> which means that the total available energy grows as (''R''<sup>−6</sup> ) ''R''<sup>3</sup> ~ ''R''<sup>−3</sup>, and so the Bekenstein Bound yields ''E R'' ~ (''R''<sup>−3</sup>)''R'' ~ ''R''<sup>−2</sup> which diverges as ''R''<sup>−2</sup> as ''R'' → 0 at the final singularity.<ref name="Tipler2003" group="q">Frank J. Tipler, [http://theophysics.freevar.com/pdf/tipler-intelligent-life-in-cosmology.pdf "Intelligent life in cosmology"], ''International Journal of Astrobiology'', Vol. 2, Issue 2 (April 2003), pp. 141-148, {{doi|10.1017/S1473550403001526}}, {{bibcode|2003IJAsB...2..141T}}. Mirror links [http://www.webcitation.org/5o9QHKGuW here] and [http://theophysics.host56.com/pdf/tipler-intelligent-life-in-cosmology.pdf here]; also available [http://math.tulane.edu/~tipler/intelligentlife.pdf here]. Also at {{arxiv|0704.0058}}, March 31, 2007.</ref><ref name="Tipler1994" group="q"/> The absence of event horizons by definition means that the universe's future c-boundary is a single point,<ref name="HawkingEllis1973" group="q">[[Stephen Hawking|S. W. Hawking]] and G. F. R. Ellis, ''The Large Scale Structure of Space-Time'' (London: [[Cambridge University Press]], 1973), ISBN 0521200164, {{lccn|72093671}}, {{bibcode|1973lsss.book.....H}}, pp. 217-221.</ref> call it the ''Omega Point''. MacCallum<ref name="MacCallum1971" group="q">Malcolm A. H. MacCallum, "Mixmaster universe problem", ''Nature—Physical Science'', Vol. 230 (March 1971), pp. 112-113, {{bibcode|1971Natur.230..112M}}, {{OSTI|4048469}}. See also [http://www.maths.qmul.ac.uk/~mm/papers.html here].</ref> has shown that an ''S''<sup>3</sup> closed universe with a single point future c-boundary is of measure zero in initial data space. Barrow,<ref name="Barrow 1982" group="q">John D. Barrow, "Chaotic behaviour in general relativity", ''Physics Reports'', Vol. 85, Issue 1 (May 1982), pp. 1-49, {{doi|10.1016/0370-1573(82)90171-5}}, {{bibcode|1982PhR....85....1B}}.</ref><ref name="Barrow1998" group="q">John D. Barrow and Janna Levin, [http://link.aps.org/doi/10.1103/PhysRevLett.80.656 "Chaos in the Einstein-Yang-Mills Equations"], ''Physical Review Letters'', Vol. 80, Issue 4 (January 1998), pp. 656-659, {{doi|10.1103/PhysRevLett.80.656}}, {{bibcode|1998PhRvL..80..656B}}. Also at {{arxiv|gr-qc/9706065}}, June 20, 1997.</ref> Cornish and Levin<ref name="CornishLevin1997" group="q">Neil J. Cornish and Janna J. Levin, [http://link.aps.org/doi/10.1103/PhysRevD.55.7489 "Mixmaster universe: A chaotic Farey tale"], ''Physical Review D'', Vol. 55, Issue 12 (June 1997), pp. 7489-7510, {{doi|10.1103/PhysRevD.55.7489}}, {{bibcode|1997PhRvD..55.7489C}}. Also at {{arxiv|gr-qc/9612066}}, December 30, 1996.</ref> and Motter<ref name="Motter2003" group="q">Adilson E. Motter, [http://llacolen.ciencias.uchile.cl/~vmunoz/download/papers/m03a.pdf "Relativistic Chaos is Coordinate Invariant"], ''Physical Review Letters'', Vol. 91, Issue 23 (December 2003), Art. No. 231101, 4 pages, {{doi|10.1103/PhysRevLett.91.231101}}, {{bibcode|2003PhRvL..91w1101M}}. [http://www.webcitation.org/5o9Pa8B4M Mirror link]. Also at {{arxiv|gr-qc/0305020}}, May 5, 2003.</ref> have shown that the evolution of an ''S''<sup>3</sup> closed universe into its final singularity is chaotic. Yorke ''et al.''<ref name="Yorke1990" group="q">Troy Shinbrot, Edward Ott, Celso Grebogi and James A. Yorke, [http://link.aps.org/doi/10.1103/PhysRevLett.65.3215 "Using chaos to direct trajectories to targets"], ''Physical Review Letters'', Vol. 65, Issue 26 (December 1990), pp. 3215-3218, {{doi|10.1103/PhysRevLett.65.3215}}, {{bibcode|1990PhRvL..65.3215S}}.</ref><ref name="Yorke1992" group="q">Troy Shinbrot, William Ditto, Celso Grebogi, Edward Ott, Mark Spano and James A. Yorke, [http://link.aps.org/doi/10.1103/PhysRevLett.68.2863 "Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system"], ''Physical Review Letters'', Vol. 68, Issue 19 (May 1992), pp. 2863-2866, {{doi|10.1103/PhysRevLett.68.2863}}, {{bibcode|1992PhRvL..68.2863S}}.</ref> have 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 (≡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. Misner<ref name="Misner1968" group="q">Charles W. Misner, [http://adsabs.harvard.edu/abs/1968ApJ...151..431M "The Isotropy of the Universe"], ''Astrophysical Journal'', Vol. 151 (February 1968), pp. 431-457, {{doi|10.1086/149448}}, {{bibcode|1968ApJ...151..431M}}.</ref><ref name="Misner1969a" group="q">Charles W. Misner, [http://link.aps.org/doi/10.1103/PhysRev.186.1319 "Quantum Cosmology. I"], ''Physical Review'', Vol. 186, Issue 5 (October 1969), pp. 1319-1327, {{doi|10.1103/PhysRev.186.1319}}, {{bibcode|1969PhRv..186.1319M}}.</ref><ref name="Misner1969b" group="q">Charles W. Misner, [http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/07/036.pdf "Mixmaster Universe"], ''Physical Review Letters'', Vol. 22, Issue 20 (May 1969), pp. 1071-1074, {{doi|10.1103/PhysRevLett.22.1071}}, {{bibcode|1969PhRvL..22.1071M}}. [http://www.webcitation.org/5oFUpabxe Mirror link]. Also available as [http://www.gravityresearchfoundation.org/pdf/awarded/1969/minner.pdf an entry] in the Gravity Research Foundation's 1969 essay competition. [http://www.webcitation.org/5oFmSHFDm Mirror link].</ref> 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 time diverges to infinity as the Omega Point is approached, since ''S'' → +∞ there, implying divergence of the complexity of the system that must be understood to be controlled.</blockquote>
According to Tipler,<ref name="Tipler1994b"/> during the collapse phase of the universe, life uses gravitational shear energy by forcing a Taub universe collapse (named after physicist Abraham Haskel Taub), whereby the universe collapses along one axis into the shape of an oblate spheroid by life directing trajectories of mass, thereby creating greater heating along the axis of collapse and hence a temperature differential whereby usable energy can be obtained. The Taublike collapse in one direction, and then another direction (i.e., Mixmaster oscillations) is also used to eliminate event horizons by allowing communication across the universe along the axis of collapse, which is necessary for information processing (and hence life) to continue. This mode of collapse ends (in proper time, as in computer clock time it never ends) in a single c-boundary (i.e., causal boundary) point: the Omega Point. The gravitational shear energy thereby available to life diverges to infinity as the Omega Point is approached. That is, by making the negative gravitational energy go to minus infinity, the positive energy available to life goes to plus infinity, as the total energy of the universe at all times sums to exactly zero, as physicist [[Stephen Hawking]] has pointed out.<ref name="Hawking1996">[[Stephen Hawking]], ''The Illustrated A Brief History of Time'' (New York: Bantam Books, 1996), ISBN 0553103741, {{lccn|96019732}}, {{bibcode|1988bhtb.book.....H}}, Chapter 8: "The Origin and Fate of the Universe", pp. 166-167. Hawking writes:
According to Tipler,<ref name="Tipler1994b"/> during the collapse phase of the universe, life uses gravitational shear energy by forcing a Taub universe collapse (named after physicist Abraham Haskel Taub), whereby the universe collapses along one axis into the shape of an oblate spheroid by life directing trajectories of mass, thereby creating greater heating along the axis of collapse and hence a temperature differential whereby usable energy can be obtained. The Taublike collapse in one direction, and then another direction (i.e., Mixmaster oscillations) is also used to eliminate event horizons by allowing communication across the universe along the axis of collapse, which is necessary for information processing (and hence life) to continue. This mode of collapse ends (in proper time, as in computer clock time it never ends) in a single c-boundary (i.e., causal boundary) point: the Omega Point. The gravitational shear energy thereby available to life diverges to infinity as the Omega Point is approached. That is, by making the negative gravitational energy go to minus infinity, the positive energy available to life goes to plus infinity, as the total energy of the universe at all times sums to exactly zero, as physicist Stephen Hawking has pointed out.<ref name="Hawking1996">Stephen Hawking, ''The Illustrated A Brief History of Time'' (New York: Bantam Books, 1996), ISBN 0553103741, {{lccn|96019732}}, {{bibcode|1988bhtb.book.....H}}, Chapter 8: "The Origin and Fate of the Universe", pp. 166-167. Hawking writes:
<blockquote><p>The answer [to where the univere's energy came from] is that the total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.</p>
<blockquote><p>The answer [to where the univere's energy came from] is that the total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.</p>
(3)</p>
(3)</p>
<p>This is the qualitatively unique gravitational [[Lagrangian]] picked out by [[quantum mechanics]]. Physicists do not like it because (1) it has an infinite number of (renormalizable) constants <math>c^i_j</math>, all of which must be determined by experiment and (2) it will not yield second order [[differential equation]]s which all physicists know and love. But the countable number of constants are in effect axioms of the theory, and I pointed out in an earlier section that the Löwenheim–Skolem theorem suggests there is no real difference between a theory with a countable number of axioms and a theory with a finite number of axioms. The finite case is just easier for humans to deal with, provided the 'finite' number is a small number. Further, as Weinberg<ref name="Weinberg1995" group="q">Steven Weinberg, ''The Quantum Theory of Fields, Volume I: Foundations'' (Cambridge: [[Cambridge University Press]], 1995), ISBN 0521550017, {{lccn|95002782}} {{bibcode|1995qtf..book.....W}}, pp. 499 and 518-519.</ref> has emphasized, this Lagrangian generates a quantum theory of gravity that is just as renormalizable as [[quantum electrodynamics|QED]] and the [[Standard Model|SM]].</p>
<p>This is the qualitatively unique gravitational [[Lagrangian]] picked out by [[quantum mechanics]]. Physicists do not like it because (1) it has an infinite number of (renormalizable) constants <math>c^i_j</math>, all of which must be determined by experiment and (2) it will not yield second order [[differential equation]]s which all physicists know and love. But the countable number of constants are in effect axioms of the theory, and I pointed out in an earlier section that the Löwenheim–Skolem theorem suggests there is no real difference between a theory with a countable number of axioms and a theory with a finite number of axioms. The finite case is just easier for humans to deal with, provided the 'finite' number is a small number. Further, as Weinberg<ref name="Weinberg1995" group="q">Steven Weinberg, ''The Quantum Theory of Fields, Volume I: Foundations'' (Cambridge: [[Cambridge University Press]], 1995), ISBN 0521550017, {{lccn|95002782}} {{bibcode|1995qtf..book.....W}}, pp. 499 and 518-519.</ref> has emphasized, this Lagrangian generates a quantum theory of gravity that is just as renormalizable as [[quantum electrodynamics|QED]] and the SM.</p>
<p>Since quantum field theory itself is forcing the Lagrangian (3) on us, I propose that we accept the judgement of quantum mechanics and accept (3) (and the countable number of additional terms involving the non-gravitational fields interacting with the <math>h_{\mu\nu}</math>) as the actual Lagrangian of reality.</p>
<p>Since quantum field theory itself is forcing the Lagrangian (3) on us, I propose that we accept the judgement of quantum mechanics and accept (3) (and the countable number of additional terms involving the non-gravitational fields interacting with the <math>h_{\mu\nu}</math>) as the actual Lagrangian of reality.</p>
<p>Donoghue<ref name="Donoghue1994" group="q">John F. Donoghue, [http://link.aps.org/doi/10.1103/PhysRevD.50.3874 "General relativity as an effective field theory: The leading quantum corrections"], ''Physical Review D'', Vol. 50, Issue 6 (September 1994), pp. 3874-3888, {{doi|10.1103/PhysRevD.50.3874}}, {{bibcode|1994PhRvD..50.3874D}}. Also at {{arxiv|gr-qc/9405057}}, May 25, 1994.</ref> and Donoghue and Torma<ref name="DonoghueTorma1996" group="q">John F. Donoghue and Tibor Torma, [http://link.aps.org/doi/10.1103/PhysRevD.54.4963 "Power counting of loop diagrams in general relativity"], ''Physical Review D'', Vol. 54, Issue 8 (October 1996), pp. 4963-4972, {{doi|10.1103/PhysRevD.54.4963}}, {{bibcode|1996PhRvD..54.4963D}}. Also released as [http://arxiv.org/abs/hep-th/9602121 "On the power counting of loop diagrams in general relativity"], {{arxiv|hep-th/9602121}}, February 22, 1996.</ref> have shown that Lagrangian (3) will not contradict experiment provided the (renormalized) values of the infinite number of new coupling constants are sufficiently small. ...</p></blockquote>
<p>Donoghue<ref name="Donoghue1994" group="q">John F. Donoghue, [http://link.aps.org/doi/10.1103/PhysRevD.50.3874 "General relativity as an effective field theory: The leading quantum corrections"], ''Physical Review D'', Vol. 50, Issue 6 (September 1994), pp. 3874-3888, {{doi|10.1103/PhysRevD.50.3874}}, {{bibcode|1994PhRvD..50.3874D}}. Also at {{arxiv|gr-qc/9405057}}, May 25, 1994.</ref> and Donoghue and Torma<ref name="DonoghueTorma1996" group="q">John F. Donoghue and Tibor Torma, [http://link.aps.org/doi/10.1103/PhysRevD.54.4963 "Power counting of loop diagrams in general relativity"], ''Physical Review D'', Vol. 54, Issue 8 (October 1996), pp. 4963-4972, {{doi|10.1103/PhysRevD.54.4963}}, {{bibcode|1996PhRvD..54.4963D}}. Also released as [http://arxiv.org/abs/hep-th/9602121 "On the power counting of loop diagrams in general relativity"], {{arxiv|hep-th/9602121}}, February 22, 1996.</ref> have shown that Lagrangian (3) will not contradict experiment provided the (renormalized) values of the infinite number of new coupling constants are sufficiently small. ...</p></blockquote>
One consequence of the above [[Lagrangian]] being the true description of quantum gravity, explains Tipler, would be that so long as one is within [[spacetime]], then one can never obtain a ''complete'' description of quantum gravity and hence of physics: there will always be infinitely more to learn and discover in the field of physics, including by requiring the use of experiment.<ref name="Tipler2007b3"/> He says that physics will be able to become ever-more refined, knowledgeable and precise, but never complete (i.e., within spacetime). Only at the final singularity of the Omega Point (which is not in spacetime<ref name="HawkingEllis1973">[[Stephen Hawking|S. W. Hawking]] and G. F. R. Ellis, ''The Large Scale Structure of Space-Time'' (London: [[Cambridge University Press]], 1973), ISBN 0521200164, {{lccn|72093671}}, {{bibcode|1973lsss.book.....H}}, pp. 217-221.</ref>) will the full description of physics be obtained, states Tipler.
One consequence of the above [[Lagrangian]] being the true description of quantum gravity, explains Tipler, would be that so long as one is within [[spacetime]], then one can never obtain a ''complete'' description of quantum gravity and hence of physics: there will always be infinitely more to learn and discover in the field of physics, including by requiring the use of experiment.<ref name="Tipler2007b3"/> He says that physics will be able to become ever-more refined, knowledgeable and precise, but never complete (i.e., within spacetime). Only at the final singularity of the Omega Point (which is not in spacetime<ref name="HawkingEllis1973">S. W. Hawking and G. F. R. Ellis, ''The Large Scale Structure of Space-Time'' (London: Cambridge University Press, 1973), ISBN 0521200164, {{lccn|72093671}}, {{bibcode|1973lsss.book.....H}}, pp. 217-221.</ref>) will the full description of physics be obtained, states Tipler.
In the same aforestated journal article, Tipler combines the above theory of quantum gravity with an extended [[Standard Model]] in order to form what he maintains is the correct Theory of Everything (TOE) describing and unifying all the [[force]]s in physics.<ref name="Tipler2005"/><ref name="Tipler2007b"/>
In the same aforestated journal article, Tipler combines the above theory of quantum gravity with an extended Standard Model in order to form what he maintains is the correct Theory of Everything (TOE) describing and unifying all the [[force]]s in physics.<ref name="Tipler2005"/><ref name="Tipler2007b"/>
Out of 50 articles, Tipler's said paper<ref name="Tipler2005"/> was selected as one of 12 for the "Highlights of 2005" accolade as "the very best articles published in ''Reports on Progress in Physics'' in 2005 [Vol. 68]. Articles were selected by the Editorial Board for their outstanding reviews of the field. They all received the highest praise from our international referees and a high number of downloads from the journal Website."<ref name="Palmer">Richard Palmer, Publisher, [http://www.iop.org/EJ/journal/-page=extra.highlights/0034-4885 "Highlights of 2005"], ''Reports on Progress in Physics''. [http://www.webcitation.org/5o9VkK3eE Mirror link]. See also [http://www.iop.org/EJ/journal/-page=board/0034-4885 "Editorial board"], ''Reports on Progress in Physics''. [http://www.webcitation.org/5o9VslFbX Mirror link].</ref> ''Reports on Progress in Physics'' is the leading journal of the Institute of Physics (based on its impact factor, according to ''Journal Citation Reports''<ref name="JCR">[http://stang.sc.mahidol.ac.th/internal/if2006/pdf_sci/PMu.pdf "Journal Citation Reports (JCR) Year 2006—Science Edition"], September 2007. [http://www.webcitation.org/5o9V0MpEl Mirror link].</ref><ref name="IOPPublishing">[http://ej.iop.org/pdf/pricing/catalogue2008row.pdf "Journals Catalogue 2008"], IOP Publishing (Institute of Physics), Section: "IOP Impact Factors", p. 37. [http://www.webcitation.org/5o9UtmzXx Mirror link].</ref>), Britain's main professional body for physicists.
Out of 50 articles, Tipler's said paper<ref name="Tipler2005"/> was selected as one of 12 for the "Highlights of 2005" accolade as "the very best articles published in ''Reports on Progress in Physics'' in 2005 [Vol. 68]. Articles were selected by the Editorial Board for their outstanding reviews of the field. They all received the highest praise from our international referees and a high number of downloads from the journal Website."<ref name="Palmer">Richard Palmer, Publisher, [http://www.iop.org/EJ/journal/-page=extra.highlights/0034-4885 "Highlights of 2005"], ''Reports on Progress in Physics''. [http://www.webcitation.org/5o9VkK3eE Mirror link]. See also [http://www.iop.org/EJ/journal/-page=board/0034-4885 "Editorial board"], ''Reports on Progress in Physics''. [http://www.webcitation.org/5o9VslFbX Mirror link].</ref> ''Reports on Progress in Physics'' is the leading journal of the Institute of Physics (based on its impact factor, according to ''Journal Citation Reports''<ref name="JCR">[http://stang.sc.mahidol.ac.th/internal/if2006/pdf_sci/PMu.pdf "Journal Citation Reports (JCR) Year 2006—Science Edition"], September 2007. [http://www.webcitation.org/5o9V0MpEl Mirror link].</ref><ref name="IOPPublishing">[http://ej.iop.org/pdf/pricing/catalogue2008row.pdf "Journals Catalogue 2008"], IOP Publishing (Institute of Physics), Section: "IOP Impact Factors", p. 37. [http://www.webcitation.org/5o9UtmzXx Mirror link].</ref>), Britain's main professional body for physicists.
If [[string theory]] is valid, it would seem to contradict the Omega Point Theory, since the Omega Point Theory requires the existence of a cosmological singularity at the end of time. Whereas, according to string theory, singularities do not actually exist because no material object can be compressed below the Planck length.<ref name=Greene>[[Brian Greene]], ''The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory'' (New York, N.Y.: W. W. Norton, 1999), ISBN 0393046885, {{lccn|98025695}}, {{bibcode|1999eush.conf.....G}}, pp. 252-253.</ref>
If [[string theory]] is valid, it would seem to contradict the Omega Point Theory, since the Omega Point Theory requires the existence of a cosmological singularity at the end of time. Whereas, according to string theory, singularities do not actually exist because no material object can be compressed below the Planck length.<ref name=Greene>[[Brian Greene]], ''The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory'' (New York, N.Y.: W. W. Norton, 1999), ISBN 0393046885, {{lccn|98025695}}, {{bibcode|1999eush.conf.....G}}, pp. 252-253.</ref>
Stephen Hawking has proposed a solution to the black hole information issue in order to preserve unitarity but without the universe collapsing which is dependent on the conjectured string theory-based anti-de Sitter space/conformal field theory correspondence (AdS/CFT correspondence).<ref name="Hawking2005">S. W. Hawking, [http://www.physics.princeton.edu/~mcdonald/examples/QM/hawking_prd_72_084013_05.pdf "Information loss in black holes"], ''Physical Review D'', Vol. 72, No. 8 (October 2005), Art. No. 084013, 4 pages, {{doi|10.1103/PhysRevD.72.084013}}, {{bibcode|2005PhRvD..72h4013H}}. [http://www.webcitation.org/5oCZDMztm Mirror link]. Also at {{arxiv|hep-th/0507171}}, July 18, 2005.</ref>
Tipler himself argues against the validity of string theory.<ref name="Tipler2005"/>
Tipler himself argues against the validity of string theory.<ref name="Tipler2005"/>
==See also==
==See also==
* [[computer science]]
* [[computer science]]
* [[eschatology]]
* [[eschatology]]
* [[first cause]]
* [[first cause]]
* [[physics]]
* [[physics]]
* [[quantum gravity]]
* [[quantum gravity]]
* [http://www.closertotruth.com/participant/Frank-Tipler/109 "Tipler, Frank"], ''Closer to Truth'' ([[PBS|Public Broadcasting Service]] [PBS]). Contains a number of video clips of Tipler interviewed by ''Closer to Truth'' host Robert Lawrence Kuhn on the Omega Point Theory.
* [http://www.closertotruth.com/participant/Frank-Tipler/109 "Tipler, Frank"], ''Closer to Truth'' ([[PBS|Public Broadcasting Service]] [PBS]). Contains a number of video clips of Tipler interviewed by ''Closer to Truth'' host Robert Lawrence Kuhn on the Omega Point Theory.
* Video of a lecture by Tipler on the Omega Point Theory, [http://www.terasemfoundation.org/program.htm "Program for 1st Annual Workshop on Geoethical Nanotechnology"], ''Terasem Movement'', July 20, 2005: [http://mfile3.akamai.com/12032/wmv/kurzweil.download.akamai.com/12032/terasem/Tipler56k.wmv 56 kbs WMV], [http://mfile3.akamai.com/12032/wmv/kurzweil.download.akamai.com/12032/terasem/Tiplerdsl.wmv Broadband WMV] and [http://mfile3.akamai.com/12032/mov/kurzweil.download.akamai.com/12032/terasem/Tiplerdsl.mov Broadband MOV]. Microsoft PowerPoint [http://www.terasemfoundation.org/webcast/ppt/Tipler.ppt file of the topics of discussion].
* Video of a lecture by Tipler on the Omega Point Theory, [http://www.terasemfoundation.org/program.htm "Program for 1st Annual Workshop on Geoethical Nanotechnology"], ''Terasem Movement'', July 20, 2005: [http://mfile3.akamai.com/12032/wmv/kurzweil.download.akamai.com/12032/terasem/Tipler56k.wmv 56 kbs WMV], [http://mfile3.akamai.com/12032/wmv/kurzweil.download.akamai.com/12032/terasem/Tiplerdsl.wmv Broadband WMV] and [http://mfile3.akamai.com/12032/mov/kurzweil.download.akamai.com/12032/terasem/Tiplerdsl.mov Broadband MOV]. Microsoft PowerPoint [http://www.terasemfoundation.org/webcast/ppt/Tipler.ppt file of the topics of discussion].
* Jennifer Mayerle, [http://www.cbsatlanta.com/news/17975543/detail.html "Does God Exist?"], ''CBS 46 News'' (WGCL-TV, Atlanta, Georgia), November 13, 2008. In additon to video of the television news report, also contains a 1:08:33 h:min:sec video of a lecture by Prof. Tipler on the Omega Point cosmology.
* Jennifer Mayerle, [http://www.cbsatlanta.com/news/17975543/detail.html "Does God Exist?"], ''CBS 46 News'' (WGCL-TV, Atlanta, Georgia), November 13, 2008. In addition to video of the television news report, also contains a 1:08:33 h:min:sec video of a lecture by Prof. Tipler on the Omega Point cosmology.
[[Category:Cosmology]]
[[Category:Cosmology]]