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==History==
==History==
Tipler has published his Omega Point Theory in a number of peer-reviewed scientific journals since 1986.<ref name="Tipler1986">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Cosmological-Limits-on-Computation.pdf "Cosmological Limits on Computation"], ''International Journal of Theoretical Physics'', Vol. 25, No. 6 (June 1986), pp. 617-661, {{doi|10.1007/BF00670475}}, {{bibcode|1986IJTP...25..617T}}. [http://www.webcitation.org/64KHgOccs Mirror link]. (First paper on the Omega Point Theory.)</ref><ref name="Tipler1987">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Achieved-spacetime-infinity.pdf "Achieved spacetime infinity"], ''Nature'', Vol. 325, No. 6101 (January 15, 1987), pp. 201-202, {{doi|10.1038/325201c0}}, {{bibcode|1987Natur.325..201T}}. [http://www.webcitation.org/64Upnqvnw Mirror link].</ref><ref name="Tipler1988">Frank J. Tipler, [http://www.jstor.org/stable/192869 "The Anthropic Principle: A Primer for Philosophers"], ''PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association'', Vol. 1988, Volume Two: Symposia and Invited Papers (1988), pp. 27-48; published by University of Chicago Press on behalf of the Philosophy of Science Association.</ref><ref name="Tipler1989">Frank J. Tipler, [http://theophysics.host56.com/pdf/tipler-omega-point-as-eschaton.pdf "The Omega Point as ''Eschaton'': Answers to Pannenberg's Questions for Scientists"], ''Zygon: Journal of Religion & Science'', Vol. 24, Issue 2 (June 1989), pp. 217-253, {{doi|10.1111/j.1467-9744.1989.tb01112.x}}. [http://www.webcitation.org/5nY0aytpz Mirror link]. Republished as Chapter 7: "The Omega Point as ''Eschaton'': Answers to Pannenberg's Questions to Scientists" in Carol Rausch Albright and Joel Haugen (editors), ''Beginning with the End: God, Science, and Wolfhart Pannenberg'' (Chicago, Ill.: Open Court Publishing Company, 1997), pp. 156-194, ISBN 0812693256, {{lccn|97000114}}.</ref><ref name="Tipler1992">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Life-in-universes-which-undergo-inflation.pdf "The ultimate fate of life in universes which undergo inflation"], ''Physics Letters B'', Vol. 286, Issues 1-2 (July 23, 1992), pp. 36-43, {{doi|10.1016/0370-2693(92)90155-W}}, {{bibcode|1992PhLB..286...36T}}. [http://www.webcitation.org/64Uskd785 Mirror link].</ref><ref name="Tipler1993">Frank J. Tipler, [http://theophysics.host56.com/pdf/tipler-constant-mean-curvature-foliation.pdf "A New Condition Implying the Existence of a Constant Mean Curvature Foliation"], {{bibcode|1993dgr2.conf..306T}}, in B. L. Hu and T. A. Jacobson (editors), ''Directions in General Relativity: Proceedings of the 1993 International Symposium, Maryland, Volume 2: Papers in Honor of Dieter Brill'' (Cambridge: [[Cambridge University Press]], 1993), pp. 306-315, ISBN 0521452678, {{bibcode|1993dgr2.conf.....H}}. [http://www.webcitation.org/5qbXJZiX5 Mirror link].</ref><ref name="Tipler1998">Frank J. Tipler, [http://theophysics.host56.com/pdf/tipler-ultrarelativistic-rockets.pdf "Ultrarelativistic Rockets and the Ultimate Future of the Universe"], [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990023204_1999021520.pdf ''NASA Breakthrough Propulsion Physics Workshop Proceedings''], [[NASA|National Aeronautics and Space Administration]], January 1999, pp. 111-119 ([http://www.webcitation.org/5nY13xRip mirror link]); an invited paper in the proceedings of a conference held at and sponsored by NASA Lewis Research Center, Cleveland, Ohio, August 12–14, 1998; {{doi|2060/19990023204}}. [http://ntrs.nasa.gov/search.jsp?Ntk=DocumentID&Ntt=19990023204 Document ID: 19990023204]. Report Number: E-11429; NAS 1.55:208694; NASA/CP-1999-208694. [http://www.webcitation.org/5nwu4fT31 Mirror link].</ref><ref name="Tipler2001">Frank J. Tipler, [http://arxiv.org/abs/astro-ph/0104011 "The Ultimate Future of the Universe, Black Hole Event Horizon Topologies, Holography, and the Value of the Cosmological Constant"], {{arxiv|astro-ph/0104011}}, April 1, 2001. Published in J. Craig Wheeler and Hugo Martel (editors), [http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=586&Issue=1 ''Relativistic Astrophysics: 20th Texas Symposium, Austin, TX, 10-15 December 2000''] (Melville, N.Y.: American Institute of Physics, 2001), pp. 769-772, ISBN 0735400261, {{lccn|2001094694}}, which is [http://link.aip.org/link/?APCPCS/586/769/1 ''AIP Conference Proceedings'', Vol. 586 (October 15, 2001)], {{doi|10.1063/1.1419654}}, {{bibcode|2001AIPC..586.....W}}.</ref><ref name="Tipler2003"/><ref name="Tipler2005"/><ref name="Tipler2007">Frank J. Tipler, Jessica Graber, Matthew McGinley, Joshua Nichols-Barrer and Christopher Staecker, [http://arxiv.org/abs/gr-qc/0003082 "Closed Universes With Black Holes But No Event Horizons As a Solution to the Black Hole Information Problem"], {{arxiv|gr-qc/0003082}}, March 20, 2000. Published in ''Monthly Notices of the Royal Astronomical Society'', Vol. 379, Issue 2 (August 2007), pp. 629-640, {{doi|10.1111/j.1365-2966.2007.11895.x}}, {{bibcode|2007MNRAS.379..629T}}.</ref> The first book wherein the Omega Point Theory was described was 1986's ''The Anthropic Cosmological Principle'', written by astrophysicist John D. Barrow and Tipler, wherein they concluded the book by writing that<ref name="BarrowTipler1986a">John D. Barrow and Frank J. Tipler, "Foreword" by John A. Wheeler, ''The Anthropic Cosmological Principle'' (Oxford: Oxford University Press, 1986), pp. 676-677, ISBN 0198519494, {{lccn|85004824}}, {{bibcode|1986acp..book.....B}}. [http://www.dhushara.com/book/quantcos/anth/anth.htm Excerpt from Chapter 1].</ref>
Tipler has published his Omega Point Theory in a number of peer-reviewed scientific journals and proceedings since 1986.<ref name="Tipler1986">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Cosmological-Limits-on-Computation.pdf "Cosmological Limits on Computation"], ''International Journal of Theoretical Physics'', Vol. 25, No. 6 (June 1986), pp. 617-661, {{doi|10.1007/BF00670475}}, {{bibcode|1986IJTP...25..617T}}. [http://www.webcitation.org/64KHgOccs Mirror link]. (First paper on the Omega Point Theory.)</ref><ref name="Tipler1986-6">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Sensorium-of-God.pdf "The Sensorium of God: Newton and Absolute Space"], {{bibcode|1988nnds.conf..215T}}, in G[eorge]. V. Coyne, M[ichał]. Heller and J[ozef]. Źyciński (Eds.), "Message" by Franciszek Macharski, ''Newton and the New Direction in Science: Proceedings of the Cracow Conference, 25 to 28 May 1987'' (Vatican City: Specola Vaticana, 1988), pp. 215-228, {{lccn|88162460}}, {{bibcode|1988nnds.conf.....C}}. [http://www.webcitation.org/69Vb0JF1W Mirror link].</ref><ref name="Tipler1987">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Achieved-spacetime-infinity.pdf "Achieved spacetime infinity"], ''Nature'', Vol. 325, No. 6101 (January 15, 1987), pp. 201-202, {{doi|10.1038/325201c0}}, {{bibcode|1987Natur.325..201T}}. [http://www.webcitation.org/64Upnqvnw Mirror link].</ref><ref name="Tipler1988a">Frank J. Tipler, [http://theophysics.freevar.com/pdf/Tipler-Omega-Point-Theory.pdf "The Omega Point Theory: A Model of an Evolving God"], in Robert J. Russell, William R. Stoeger and George V. Coyne (Eds.), message by John Paul II, ''Physics, Philosophy, and Theology: A Common Quest for Understanding'' (Vatican City: Vatican Observatory, 2nd ed., 2005; orig. pub. 1988), pp. 313-331, ISBN 0268015775, {{lccn|89203331}}, {{bibcode|1988pptc.book.....R}}. [http://www.webcitation.org/69VaKG2nd Mirror link].</ref><ref name="Tipler1988b">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Anthropic-Principle.pdf "The Anthropic Principle: A Primer for Philosophers"], in Arthur Fine and Jarrett Leplin (Eds.), ''PSA 1988: Proceedings of the 1988 Biennial Meeting of the Philosophy of Science Association, Volume Two: Symposia and Invited Papers'' (East Lansing, Mich.: Philosophy of Science Association, 1989), pp. 27-48, ISBN 091758628X. [http://www.webcitation.org/69VarCM3I Mirror link]. [http://www.jstor.org/stable/192869 Published by University of Chicago Press on behalf of the Philosophy of Science Association].</ref><ref name="Tipler1989">Frank J. Tipler, [http://theophysics.host56.com/pdf/tipler-omega-point-as-eschaton.pdf "The Omega Point as ''Eschaton'': Answers to Pannenberg's Questions for Scientists"], ''Zygon: Journal of Religion & Science'', Vol. 24, Issue 2 (June 1989), pp. 217-253, {{doi|10.1111/j.1467-9744.1989.tb01112.x}}. [http://www.webcitation.org/5nY0aytpz Mirror link]. Republished as Chapter 7: "The Omega Point as ''Eschaton'': Answers to Pannenberg's Questions to Scientists" in Carol Rausch Albright and Joel Haugen (editors), ''Beginning with the End: God, Science, and Wolfhart Pannenberg'' (Chicago, Ill.: Open Court Publishing Company, 1997), pp. 156-194, ISBN 0812693256, {{lccn|97000114}}.</ref><ref name="Tipler1992">Frank J. Tipler, [http://theophysics.host56.com/pdf/Tipler-Life-in-universes-which-undergo-inflation.pdf "The ultimate fate of life in universes which undergo inflation"], ''Physics Letters B'', Vol. 286, Issues 1-2 (July 23, 1992), pp. 36-43, {{doi|10.1016/0370-2693(92)90155-W}}, {{bibcode|1992PhLB..286...36T}}. [http://www.webcitation.org/64Uskd785 Mirror link].</ref><ref name="Tipler1993">Frank J. Tipler, [http://theophysics.host56.com/pdf/tipler-constant-mean-curvature-foliation.pdf "A New Condition Implying the Existence of a Constant Mean Curvature Foliation"], {{bibcode|1993dgr2.conf..306T}}, in B. L. Hu and T. A. Jacobson (editors), ''Directions in General Relativity: Proceedings of the 1993 International Symposium, Maryland, Volume 2: Papers in Honor of Dieter Brill'' (Cambridge: [[Cambridge University Press]], 1993), pp. 306-315, ISBN 0521452678, {{bibcode|1993dgr2.conf.....H}}. [http://www.webcitation.org/5qbXJZiX5 Mirror link].</ref><ref name="Tipler1998">Frank J. Tipler, [http://theophysics.host56.com/pdf/tipler-ultrarelativistic-rockets.pdf "Ultrarelativistic Rockets and the Ultimate Future of the Universe"], [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990023204_1999021520.pdf ''NASA Breakthrough Propulsion Physics Workshop Proceedings''], [[NASA|National Aeronautics and Space Administration]], January 1999, pp. 111-119 ([http://www.webcitation.org/5nY13xRip mirror link]); an invited paper in the proceedings of a conference held at and sponsored by NASA Lewis Research Center, Cleveland, Ohio, August 12–14, 1998; {{doi|2060/19990023204}}. [http://ntrs.nasa.gov/search.jsp?Ntk=DocumentID&Ntt=19990023204 Document ID: 19990023204]. Report Number: E-11429; NAS 1.55:208694; NASA/CP-1999-208694. [http://www.webcitation.org/5nwu4fT31 Mirror link].</ref><ref name="Tipler2001">Frank J. Tipler, [http://arxiv.org/abs/astro-ph/0104011 "The Ultimate Future of the Universe, Black Hole Event Horizon Topologies, Holography, and the Value of the Cosmological Constant"], {{arxiv|astro-ph/0104011}}, April 1, 2001. Published in J. Craig Wheeler and Hugo Martel (editors), [http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=586&Issue=1 ''Relativistic Astrophysics: 20th Texas Symposium, Austin, TX, 10-15 December 2000''] (Melville, N.Y.: American Institute of Physics, 2001), pp. 769-772, ISBN 0735400261, {{lccn|2001094694}}, which is [http://link.aip.org/link/?APCPCS/586/769/1 ''AIP Conference Proceedings'', Vol. 586 (October 15, 2001)], {{doi|10.1063/1.1419654}}, {{bibcode|2001AIPC..586.....W}}.</ref><ref name="Tipler2003"/><ref name="Tipler2005"/><ref name="Tipler2007">Frank J. Tipler, Jessica Graber, Matthew McGinley, Joshua Nichols-Barrer and Christopher Staecker, [http://arxiv.org/abs/gr-qc/0003082 "Closed Universes With Black Holes But No Event Horizons As a Solution to the Black Hole Information Problem"], {{arxiv|gr-qc/0003082}}, March 20, 2000. Published in ''Monthly Notices of the Royal Astronomical Society'', Vol. 379, Issue 2 (August 2007), pp. 629-640, {{doi|10.1111/j.1365-2966.2007.11895.x}}, {{bibcode|2007MNRAS.379..629T}}.</ref> The first book wherein the Omega Point Theory was described was 1986's ''The Anthropic Cosmological Principle'', written by astrophysicist John D. Barrow and Tipler, wherein they concluded the book by writing that<ref name="BarrowTipler1986a">John D. Barrow and Frank J. Tipler, "Foreword" by John A. Wheeler, ''The Anthropic Cosmological Principle'' (Oxford: Oxford University Press, 1986), pp. 676-677, ISBN 0198519494, {{lccn|85004824}}, {{bibcode|1986acp..book.....B}}. [http://www.dhushara.com/book/quantcos/anth/anth.htm Excerpt from Chapter 1].</ref>
<blockquote>if life evolves in all of the many universes in a quantum cosmology, and if life continues to exist in all of these universes, then ''all'' of these universes, which include ''all'' possible histories among them, will approach the Omega Point. At the instant the Omega Point is reached, life will have gained control of ''all'' matter and forces not only in a single universe, but in all universes whose existence is logically possible; life will have spread into ''all'' spatial regions in all universes which could logically exist, and will have stored an infinite amount of information, including ''all'' bits of knowledge which it is logically possible to know. And this is the end.</blockquote>
<blockquote>if life evolves in all of the many universes in a quantum cosmology, and if life continues to exist in all of these universes, then ''all'' of these universes, which include ''all'' possible histories among them, will approach the Omega Point. At the instant the Omega Point is reached, life will have gained control of ''all'' matter and forces not only in a single universe, but in all universes whose existence is logically possible; life will have spread into ''all'' spatial regions in all universes which could logically exist, and will have stored an infinite amount of information, including ''all'' bits of knowledge which it is logically possible to know. And this is the end.</blockquote>
According to Tipler from a 2005 paper<ref name="Tipler2005">F. J. Tipler, [http://math.tulane.edu/~tipler/theoryofeverything.pdf "The structure of the world from pure numbers"], ''Reports on Progress in Physics'', Vol. 68, No. 4 (April 2005), pp. 897-964, {{doi|10.1088/0034-4885/68/4/R04}}, {{bibcode|2005RPPh...68..897T}}. [http://www.webcitation.org/5nx3CxKm0 Mirror link]. (Note: citation formatting in the above-quoted passages have been modified for clarity. Typographical errors in the third quoted passage have been corrected, again for clarity.) Also released as [http://arxiv.org/abs/0704.3276 "Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything"], {{arxiv|0704.3276}}, April 24, 2007.</ref> in the journal ''Reports on Progress in Physics'', he outlines the following reasons why he maintains the universe must end in the Omega Point in order for the known laws of physics (i.e., the [[second law of thermodynamics]], [[general relativity]], and [[quantum mechanics]]) to be mutually consistent at all times:
According to Tipler from a 2005 paper<ref name="Tipler2005">F. J. Tipler, [http://math.tulane.edu/~tipler/theoryofeverything.pdf "The structure of the world from pure numbers"], ''Reports on Progress in Physics'', Vol. 68, No. 4 (April 2005), pp. 897-964, {{doi|10.1088/0034-4885/68/4/R04}}, {{bibcode|2005RPPh...68..897T}}. [http://www.webcitation.org/5nx3CxKm0 Mirror link]. (Note: citation formatting in the above-quoted passages have been modified for clarity. Typographical errors in the third quoted passage have been corrected, again for clarity.) Also released as [http://arxiv.org/abs/0704.3276 "Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything"], {{arxiv|0704.3276}}, April 24, 2007.</ref> in the journal ''Reports on Progress in Physics'', he outlines the following reasons why he maintains the universe must end in the Omega Point in order for the known laws of physics (i.e., the [[second law of thermodynamics]], [[general relativity]], and [[quantum mechanics]]) to be mutually consistent at all times:
<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.ifastnet.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:
<p>Now twice zero is also zero. Thus the universe can double the amount of positive matter energy and also double the negative gravitational energy without violation of the conservation of energy. ... As [physicist Alan] Guth has remarked, "It is said that there's no such thing as a free lunch. But the universe is the ultimate free lunch."</p></blockquote></ref>
<p>Now twice zero is also zero. Thus the universe can double the amount of positive matter energy and also double the negative gravitational energy without violation of the conservation of energy. ... As [physicist Alan] Guth has remarked, "It is said that there's no such thing as a free lunch. But the universe is the ultimate free lunch."</p></blockquote></ref>
Some have pointed out that the current acceleration of the universe's expansion due to the positive cosmological constant would appear to obviate the Omega Point. Although physicists Lawrence M. Krauss and Michael S. Turner state that "there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be."<ref name="Krauss1999">Lawrence M. Krauss and Michael S. Turner, [http://www.springerlink.com/content/h925275822n54121/ "Geometry and Destiny"], ''General Relativity and Gravitation'', Vol. 31, No. 10 (October 1999), pp. 1453-1459, {{doi|10.1023/A:1026757718530}}, {{bibcode|1999GReGr..31.1453K}}. Also at {{arxiv|astro-ph/9904020}}, April 1, 1999.</ref> On this matter Tipler maintains<ref name="Tipler2003b">Frank Tipler, [http://theophysics.host56.com/tipler-omega-point-and-christianity.html "The Omega Point and Christianity"], ''Gamma'', Vol. 10, No. 2 (April 2003), pp. 14-23 ([http://www.webcitation.org/5nx1sZDVR mirror link]); note that the foregoing version corrects character formatting errors of the versions available [http://web.archive.org/web/20031113125255/http://home.worldonline.nl/~sttdc/tipler.htm here], [http://web.archive.org/web/20030609141230/http://home.tiscali.nl/~sttdc/tipler.htm here] and [http://www.teilharddechardin.nl/tipler.htm here]. (Note: citation formatting in the above-quoted passage has been modified for clarity.) For the version in Dutch, see [http://web.archive.org/web/20050312194029/http://home.worldonline.nl/~sttdc/jrg10_nr2_p1423.htm "Het Punt Omega en het christendom"], ''Gamma'', Jrg. 10, Nr. 2 (April 2003), pp. 14-23; also available [http://web.archive.org/web/20031217154256/http://home.tiscali.nl/~sttdc/jrg10_nr2_p1423.htm here] and [http://www.teilharddechardin.nl/jrg10_nr2_p1423.htm here].</ref> (see also references <ref name="Tipler2005"/> and <ref name="Tipler2003">Frank J. Tipler, [http://theophysics.host56.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>) that [[baryon]] annihilation—which he says would be the ideal form of energy resource and rocket propulsion during the colonization of the universe—will force the Higgs field to its absolute vacuum state, resulting in the universe's collapse:
Some have pointed out that the current acceleration of the universe's expansion due to the positive cosmological constant would appear to obviate the Omega Point. Although physicists Lawrence M. Krauss and Michael S. Turner state that "there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be."<ref name="Krauss1999">Lawrence M. Krauss and Michael S. Turner, [http://www.springerlink.com/content/h925275822n54121/ "Geometry and Destiny"], ''General Relativity and Gravitation'', Vol. 31, No. 10 (October 1999), pp. 1453-1459, {{doi|10.1023/A:1026757718530}}, {{bibcode|1999GReGr..31.1453K}}. Also at {{arxiv|astro-ph/9904020}}, April 1, 1999.</ref> On this matter Tipler maintains<ref name="Tipler2003b">Frank Tipler, [http://theophysics.host56.com/tipler-omega-point-and-christianity.html "The Omega Point and Christianity"], ''Gamma'', Vol. 10, No. 2 (April 2003), pp. 14-23 ([http://www.webcitation.org/5nx1sZDVR mirror link]); note that the foregoing version corrects character formatting errors of the versions available [http://web.archive.org/web/20031113125255/http://home.worldonline.nl/~sttdc/tipler.htm here], [http://web.archive.org/web/20030609141230/http://home.tiscali.nl/~sttdc/tipler.htm here] and [http://www.teilharddechardin.nl/tipler.htm here]. (Note: citation formatting in the above-quoted passage has been modified for clarity.) For the version in Dutch, see [http://web.archive.org/web/20050312194029/http://home.worldonline.nl/~sttdc/jrg10_nr2_p1423.htm "Het Punt Omega en het christendom"], ''Gamma'', Jrg. 10, Nr. 2 (April 2003), pp. 14-23; also available [http://web.archive.org/web/20031217154256/http://home.tiscali.nl/~sttdc/jrg10_nr2_p1423.htm here] and [http://www.teilharddechardin.nl/jrg10_nr2_p1423.htm here].</ref> (see also references <ref name="Tipler2005"/> and <ref name="Tipler2003">Frank J. Tipler, [http://theophysics.host56.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.freevar.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>) that [[baryon]] annihilation—which he says would be the ideal form of energy resource and rocket propulsion during the colonization of the universe—will force the Higgs field to its absolute vacuum state, resulting in the universe's collapse:
<blockquote>The [[Standard Model|SM]] provides such a mechanism, which I actually discussed in the last section of the Appendix for Scientists in (<ref name="Tipler1994b" 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}}.</ref>, p. 515). This mechanism is the creation/destruction of baryon number by electroweak quantum tunneling. (Baryons are the heavy particles made up of quarks. Examples are neutrons and protons.) In my book, I pointed out that this mechanism would be ideal for propelling interstellar spacecraft, but I did not discuss its implications for the Higgs vacuum, a serious oversight on my part. (An oversight which invalidates the second part of my Fifth Prediction on page 149 of <ref name="Tipler1994b" group="q"/>.) If the SM is true—ALL experiments conducted to date indicate that it is (e.g.<ref name="Wilczek2002" group="q">Frank Wilczek, [http://xserver2.lns.mit.edu/~csuggs/physics_today/phystoday/SMPIII.pdf "Scaling Mount Planck III: Is That All There Is?"], ''Physics Today'', Vol. 55, Issue 8 (August 2002), pp. 10-11, {{doi|10.1063/1.1510264}}, {{bibcode|2002PhT....55h..10W}}. [http://www.webcitation.org/5o9RAgfxB Mirror link]; also available [http://web.archive.org/web/20020901123632/http://www.if.ufrgs.br/~jgallas/wilczek.html here].</ref> and <ref name="Quinn2003" group="q">Helen R. Quinn, [http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-9258.pdf "The Asymmetry Between Matter and Antimatter"], ''Physics Today'', Vol. 56, Issue 2 (February 2003), pp. 30-35, {{doi|10.1063/1.1564346}}, {{bibcode|2003PhT....56b..30Q}}. [http://www.webcitation.org/5o9RlbRcl Mirror link]; also available [http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-9258.ps.gz here].</ref>, last full paragraph on p. 35)—then the net baryon number observed in the universe must have been created in the early universe by this mechanism of electroweak quantum tunneling. If the baryons were so created, then this process necessarily forces the Higgs field to be in a vacuum state that is not its absolute vacuum. But if the baryons in the universe were to be annihilated by this process, say by the action of intelligent life, then this would force the Higgs field toward its absolute vacuum, canceling the positive cosmological constant, stopping the acceleration, and allowing the universe to collapse into the Omega Point. Conversely, if enough baryons are not annihilated by this process, the positive cosmological constant will never be canceled, the universe will expand forever, unitarity will be violated, and the Omega Point will never come into existence. Only if life makes use of this process to annihilate baryons will the Omega Point come into existence.</blockquote>
<blockquote>The [[Standard Model|SM]] provides such a mechanism, which I actually discussed in the last section of the Appendix for Scientists in (<ref name="Tipler1994b" 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}}.</ref>, p. 515). This mechanism is the creation/destruction of baryon number by electroweak quantum tunneling. (Baryons are the heavy particles made up of quarks. Examples are neutrons and protons.) In my book, I pointed out that this mechanism would be ideal for propelling interstellar spacecraft, but I did not discuss its implications for the Higgs vacuum, a serious oversight on my part. (An oversight which invalidates the second part of my Fifth Prediction on page 149 of <ref name="Tipler1994b" group="q"/>.) If the SM is true—ALL experiments conducted to date indicate that it is (e.g.<ref name="Wilczek2002" group="q">Frank Wilczek, [http://xserver2.lns.mit.edu/~csuggs/physics_today/phystoday/SMPIII.pdf "Scaling Mount Planck III: Is That All There Is?"], ''Physics Today'', Vol. 55, Issue 8 (August 2002), pp. 10-11, {{doi|10.1063/1.1510264}}, {{bibcode|2002PhT....55h..10W}}. [http://www.webcitation.org/5o9RAgfxB Mirror link]; also available [http://web.archive.org/web/20020901123632/http://www.if.ufrgs.br/~jgallas/wilczek.html here].</ref> and <ref name="Quinn2003" group="q">Helen R. Quinn, [http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-9258.pdf "The Asymmetry Between Matter and Antimatter"], ''Physics Today'', Vol. 56, Issue 2 (February 2003), pp. 30-35, {{doi|10.1063/1.1564346}}, {{bibcode|2003PhT....56b..30Q}}. [http://www.webcitation.org/5o9RlbRcl Mirror link]; also available [http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-9258.ps.gz here].</ref>, last full paragraph on p. 35)—then the net baryon number observed in the universe must have been created in the early universe by this mechanism of electroweak quantum tunneling. If the baryons were so created, then this process necessarily forces the Higgs field to be in a vacuum state that is not its absolute vacuum. But if the baryons in the universe were to be annihilated by this process, say by the action of intelligent life, then this would force the Higgs field toward its absolute vacuum, canceling the positive cosmological constant, stopping the acceleration, and allowing the universe to collapse into the Omega Point. Conversely, if enough baryons are not annihilated by this process, the positive cosmological constant will never be canceled, the universe will expand forever, unitarity will be violated, and the Omega Point will never come into existence. Only if life makes use of this process to annihilate baryons will the Omega Point come into existence.</blockquote>
==External links==
==External links==
* [http://www.math.tulane.edu/~tipler/ Tipler's Tulane University website]. Also available [http://129.81.170.14/~tipler/ here].
* [http://www.math.tulane.edu/~tipler/ Tipler's Tulane University website]. Also available [http://129.81.170.14/~tipler/ here].
* [http://www.math.tulane.edu/~tipler/summary.html "The Omega Point Theory"], at Tipler's website. Also available [http://129.81.170.14/~tipler/summary.html here].
* [http://www.math.tulane.edu/~tipler/summary.html "The Omega Point Theory"], at Tipler's website. Also available [http://129.81.170.14/~tipler/summary.html here].
* [http://theophysics.host56.com ''Theophysics'']. A website with information on Tipler's Omega Point Theory. [http://theophysics.ifastnet.com Mirror site].
* [http://theophysics.host56.com ''Theophysics'']. A website with information on Tipler's Omega Point Theory. [http://theophysics.ifastnet.com Mirror site].
* James Redford, [http://ssrn.com/abstract=1974708 "The Physics of God and the Quantum Gravity Theory of Everything"], ''Social Science Research Network'' (''SSRN''), August 6, 2012 (orig. pub. December 19, 2011), {{doi|10.2139/ssrn.1974708}}. Also available [http://www.webcitation.org/69kSvuziV here].
* James Redford, [http://ssrn.com/abstract=1974708 "The Physics of God and the Quantum Gravity Theory of Everything"], ''Social Science Research Network'' (''SSRN''), September 10, 2012 (orig. pub. December 19, 2011), {{doi|10.2139/ssrn.1974708}}. Also available [http://archive.org/download/ThePhysicsOfGodAndTheQuantumGravityTheoryOfEverything/Redford-Physics-of-God.pdf here] and [http://www.webcitation.org/6Abfap2bp here].
* [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].