James Redford
Lux et veritas et libertas
[Continued from a previous post.]
Prof. Krauss attempts to rebut Prof. Tipler's proposed mechanism for the miracles of Jesus Christ by relating how statistically improbable such events are, yet this doesn't actually address Tipler's arguments since Tipler's point is that such seemingly improbable events would be forced to occur by the known laws of physics via the Principle of Least Action if said events are required in order for the universe to evolve into the Omega Point final singularity. Krauss himself in his review of Tipler's book The Physics of Christianity admits that this mechanism which Tipler proposes for Jesus Christ's miracles is physically sound if said miracles were necessary in order to lead to the formation of the Omega Point and if the Omega Point is required in order for existence to exist (see Lawrence Krauss, "More dangerous than nonsense", New Scientist, Vol. 194, No. 2603 [May 12, 2007], p. 53).
1:00:52 h:min:sec ff.: Krauss provides a quote from Gerardus 't Hooft, but as with Krauss's discussion of probabilities, 't Hooft's remarks are irrelevant to Tipler's actual argument, since 't Hooft is assuming boundary conditions on the universe which are inconsistent with quantum field theory rather than the Omega Point/Feynman-DeWitt-Weinberg quantum gravity/Standard Model TOE boundary conditions which make all the laws of physics mutually mathematically consistent with each other.
1:02:01 h:min:sec ff.: Krauss provides a quote from Steven Weinberg, of which again is irrelevant to Tipler's actual argument, since as with 't Hooft, Weinberg is assuming inconsistent boundary conditions.
Krauss, 't Hooft, and Weinberg are all particle physicists. Whereas Tipler is not only an expert in quantum field theory (i.e., Quantum Mechanics combined with special-relativistic particle physics) but also an expert in Global General Relativity and computer theory. Furthermore, neither Krauss, 't Hooft, nor Weinberg display any awareness of Tipler's 2005 Reports on Progress in Physics paper which presents the technical details of the Omega Point TOE.
1:03:15 h:min:sec ff.: Krauss claims that all the evidence in nature indicates that the universe will expand forever. Ironically, Krauss has actually published a paper that greatly helped to strengthen Tipler's Omega Point cosmology. Some have suggested that the current acceleration of the universe's expansion due to the positive cosmological constant would appear to obviate the Omega Point. However, Profs. Krauss and Turner point out 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." (See Lawrence M. Krauss and Michael S. Turner, "Geometry and Destiny", General Relativity and Gravitation, Vol. 31, No. 10 [Oct. 1999], pp. 1453-1459.) While cosmological observations cannot tell us what the ultimate fate of the universe will be, the known laws of physics themselves can, as the universe is forced to end in finite proper time in order for unitarity to remain unviolated (again, see p. 925 [cf. pp. 904-905] of id., "The structure of the world from pure numbers", op. cit.).
1:23:06 h:min:sec ff.: Tipler starts his response to Krauss, wherein Tipler addresses Krauss's claims.
1:29:22 h:min:sec ff.: Krauss starts his second response to Tipler.
1:30:34 h:min:sec ff.: Krauss claims that the laws of physics prevent sapient life from harnessing baryon annihilation. However, the laws of physics allow baryon annihilation using electroweak quantum tunneling via quantum coherence. As Tipler writes, "Atoms have energy levels that differ by a few electron volts. Quantum coherence among a trillion atoms would allow the atoms to concentrate the energy differences of the levels on a single atom, and this would be 10 TeV, the amount of energy needed for the baryon-annihilation process to go forward." (See Frank J. Tipler, The Physics of Christianity [New York: Doubleday, 2007], p. 73.)
1:31:09 h:min:sec ff.: Krauss talks about "the energy of empty space", by which he means the dark energy. See my above response to Krauss's previous comments on the dark energy.
1:32:29 h:min:sec ff.: Tipler and Krauss take questions from the audience.
1:35:57 h:min:sec ff.: Krauss claims that we don't understand physics well enough to know whether unitarity is violated if an astrophysical black hole were to evaporate.
Regarding proposed solutions to the black hole information issue, all except for Tipler's Omega Point cosmology share the common feature of using proposed new laws of physics that have never been experimentally confirmed--and indeed which violate the known laws of physics--such as with Prof. Stephen Hawking's paper on the black hole information issue which is dependent on the conjectured String Theory-based anti-de Sitter space/conformal field theory correspondence (AdS/CFT correspondence). (See S. W. Hawking, "Information loss in black holes", Physical Review D, Vol. 72, No. 8 [Oct. 15, 2005], Art. No. 084013, 4 pp.) Hence, the end of the universe in finite proper time via collapse before a black hole completely evaporates is required if unitarity is to remain unviolated, i.e., if General Relativity and Quantum Mechanics--which are what the proofs of Hawking radiation derive from--are true statements of how the world works.
1:42:13 h:min:sec ff.: Krauss invokes the Christ myth theory, including incorrectly claiming that nearly every religion has had virgin births.
Regarding the Christ myth theory, virtually all the items which the Christ myth theorists claim as facts which show the parallels of Christianity with earlier pagan religions are completely fabricated modern claims that can't be found in the historical record. For an excellent discussion on this, see the following video:
* "Shattering the Christ Myth", DrCraigJohnson (YouTube), Apr. 17, 2009, Shattering the Christ Myth - YouTube . Mirror: "Veritas Forum: Shattering the Christ Myth", Bethel Christian Fellowship, 26:39 min:sec, https://www.[bless and do not curse... and do not curse]ute.com/video/Uo1HFlDMDhtS/ , http://bethelchristianfellowship.info/flash_media/jp3ChristMythCopyCat.m4v , https://bit.ly/2PzXxtV .
The above video is an interview of James Patrick Holding (editor of Shattering the Christ Myth: Did Jesus Not Exist? [Maitland, Fla.: Xulon Press, 2008], https://amazon.com/dp/1606472712 ) by Dr. Craig Johnson on the topic of the Christ myth theory. See also the below resources regarding the Christ myth theory on J. P. Holding's website:
* "Were Bible stories and characters stolen from pagan myths?", Tekton Education and Apologetics Ministry, http://www.tektonics.org/copycathub.html .
* "Did Jesus exist?", op. cit., http://www.tektonics.org/jesusexisthub.html .
1:47:06 h:min:sec ff.: Krauss agrees that the only hope for eternal life is in a collapsing universe.
1:48:06 h:min:sec ff.: An audience member asks Tipler about Matthew 10:23, Mark 9:1 and John 5:25 as being examples of where Jesus Christ incorrectly thought that the End Time was imminent, i.e., within Jesus's own generation.
Matthew 10:23, New King James Version (NKJV) states, "When they persecute you in this city, flee to another. For assuredly, I say to you, you will not have gone through the cities of Israel before the Son of Man comes." And indeed they did not go through all the cities of Israel before they died, and hence before Christ's Second Coming.
Mark 9:1, NKJV (cf. Matthew 16:28; Luke 9:27) states, "And He said to them, 'Assuredly, I say to you that there are some standing here who will not taste death till they see the kingdom of God present with power.'" And then the very next passages concern Christ's Transfiguration, whereby Heaven was also shown.
John 5:25, NKJV states, "Most assuredly, I say to you, the hour is coming, and now is, when the dead will hear the voice of the Son of God; and those who hear will live." But the next passages, John 5:26-29, go on to state, "For as the Father has life in Himself, so He has granted the Son to have life in Himself, and has given Him authority to execute judgment also, because He is the Son of Man. Do not marvel at this; for the hour is coming in which all who are in the graves will hear His voice and come forth--those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation." These passages relate to Jesus's statement that "I am the resurrection and the life." (John 11:25, NKJV. Cf. John 8:12 [cf. 1 John 1:5]; 14:6.) In other words, those raised from death are already existing within Jesus Christ in His transcendent Second Person aspect, since the Father and the Son are One (see Isaiah 9:6; John 10:30; 14:6-13). So when Jesus said this, it was a different way of saying that the Resurrection and the Life stood there before them right then in His human aspect.
So in each of these scripture passages which this audience member gave as examples of Christ getting some things wrong are all examples of Him being correct.
Sometimes people also give Matthew 24:32-35 as being an example of Christ making an incorrect prophecy. However, "this generation" referred to in Matthew 24:34 concerns the generation which witnesses the signs of the End Time which Jesus discusses.
2:02:13 h:min:sec ff.: Krauss talks about Newtonian mechanics being replaced by General Relativity and Quantum Mechanics, and hence that we shouldn't be surprised that the current known laws of physics might also be replaced. However, as Tipler pointed out in his presentation, the fundamental physics of today are simply more specific subsets of Newtonian mechanics, i.e., Newtonian mechanics with specific constrains put on it in order to make it consistent with observations and to make its resulting subsets mutually mathematically consistent with each other. Hence, we have never left the realm of Newton's physics. And all the forces in physics are now described and made mutually consistent with the Omega Point/Feynman-DeWitt-Weinberg quantum gravity/Standard Model TOE. (See above for more on that.) 2:03:26 h:min:sec ff.: Krauss states that the Standard Model of particle physics produces nonsense answers when pushed to high enough energies, as does Quantum Electrodynamics (QED). However, as Tipler previously pointed out in his presentation, imposing unitarity avoids the spacetime infinities of quantum field theory, since if there were not a cut-off to the energies of quantum field theory then miniature black holes would be created and quickly evaporate, thereby violating unitarity. Krauss also gives the infinities of quantum field theory as a reason for thinking that new forms of physics will be required at higher energy scales. However, this mechanism to the energy cut-off also allows the energies to gradually scale to infinity during the collapse phase of the universe (the energies only become actually infinite at the cosmological singularity), which means that there is no need for new physics at higher energy scales.
* * * * *
Since the Omega Point/Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (TOE) is mathematically required by the known laws of physics, of which said physical laws have been confirmed by every experiment to date, the only way Krauss could have actually argued against Tipler is to argue that the known laws of physics might be wrong. But because those physical laws have been confirmed by every experiment to date, there exists no rational reason to think that they are wrong. Hence, Krauss's irrelevant arguments (or bare assertions, as Krauss also engaged in) against Tipler were unavoidable, since Krauss set himself a logically-impossible task.
For details on the Omega Point TOE, see the following paper by Prof. Tipler:
* F. J. Tipler, "The structure of the world from pure numbers", Reports on Progress in Physics, Vol. 68, No. 4 (Apr. 2005), pp. 897-964, doi:10.1088/0034-4885/68/4/R04, bibcode: 2005RPPh...68..897T, http://dauns01.math.tulane.edu/~tipler/theoryofeverything.pdf , WebCite query result . Also released as Frank J. Tipler, "Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything", arXiv:0704.3276, Apr. 24, 2007, Feynman-Weinberg Quantum Gravity and the Extended Standard Model... .
The following is the first article on the Omega Point TOE:
* Frank J. Tipler, "Genesis: How the Universe Began According to Standard Model Particle Physics", arXiv:astro-ph/0111520, Nov. 28, 2001, Genesis: How the Universe Began According to Standard Model... . For images that go with the article, see "Frank J. Tipler, Diagrams", Theophysics: God Is the Ultimate Physicist, WebCite query result .
For the details regarding the point Prof. Tipler made in his presentation about how modern physics (i.e., General Relativity, Quantum Mechanics, and the Standard Model of particle physics) are simply special cases of classical mechanics (i.e., Newtonian mechanics, particularly in its most powerful formulation of the Hamilton-Jacobi Equation), see the following articles:
* Frank J. Tipler, "The Obama-Tribe 'Curvature of Constitutional Space' Paper is Crackpot Physics", Social Science Research Network (SSRN), Oct. 26, 2008, 45 pp., doi:10.2139/ssrn.1271310, http://ssrn.com/abstract=1271310 .
* Maurice J. Dupré and Frank J. Tipler, "General Relativity as an Æther Theory", International Journal of Modern Physics D, Vol. 21, No. 2 (Feb. 2012), Art. No. 1250011, 16 pp., doi:10.1142/S0218271812500113, bibcode: 2012IJMPD..2150011D, http://worldscientific.com/doi/abs/10.1142/S0218271812500113 . Also at arXiv:1007.4572, July 26, 2010, https://arxiv.org/abs/1007.4572 .
* Frank J. Tipler, "Hamilton-Jacobi Many-Worlds Theory and the Heisenberg Uncertainty Principle", arXiv:1007.4566, July 26, 2010, https://arxiv.org/abs/1007.4566 .
The foregoing articles, in addition to many other papers by Prof. Tipler on the Omega Point cosmology, are also available in the below archive:
* Frank-J-Tipler-Omega-Point-Papers.zip , 26712158 bytes, MD5: 6e5d29b994bc2f9aa4210d72ef37ab68, https://webcitation.org/6GjhT6t52 , https://amazon.com/clouddrive/share?s=bTI58F1dSAIjSrxJ26R7d8 , https://docs.google.com/file/d/0B7k4r80YepnxNjNOX2x0XzBOV00/edit .
Prof. Krauss attempts to rebut Prof. Tipler's proposed mechanism for the miracles of Jesus Christ by relating how statistically improbable such events are, yet this doesn't actually address Tipler's arguments since Tipler's point is that such seemingly improbable events would be forced to occur by the known laws of physics via the Principle of Least Action if said events are required in order for the universe to evolve into the Omega Point final singularity. Krauss himself in his review of Tipler's book The Physics of Christianity admits that this mechanism which Tipler proposes for Jesus Christ's miracles is physically sound if said miracles were necessary in order to lead to the formation of the Omega Point and if the Omega Point is required in order for existence to exist (see Lawrence Krauss, "More dangerous than nonsense", New Scientist, Vol. 194, No. 2603 [May 12, 2007], p. 53).
1:00:52 h:min:sec ff.: Krauss provides a quote from Gerardus 't Hooft, but as with Krauss's discussion of probabilities, 't Hooft's remarks are irrelevant to Tipler's actual argument, since 't Hooft is assuming boundary conditions on the universe which are inconsistent with quantum field theory rather than the Omega Point/Feynman-DeWitt-Weinberg quantum gravity/Standard Model TOE boundary conditions which make all the laws of physics mutually mathematically consistent with each other.
1:02:01 h:min:sec ff.: Krauss provides a quote from Steven Weinberg, of which again is irrelevant to Tipler's actual argument, since as with 't Hooft, Weinberg is assuming inconsistent boundary conditions.
Krauss, 't Hooft, and Weinberg are all particle physicists. Whereas Tipler is not only an expert in quantum field theory (i.e., Quantum Mechanics combined with special-relativistic particle physics) but also an expert in Global General Relativity and computer theory. Furthermore, neither Krauss, 't Hooft, nor Weinberg display any awareness of Tipler's 2005 Reports on Progress in Physics paper which presents the technical details of the Omega Point TOE.
1:03:15 h:min:sec ff.: Krauss claims that all the evidence in nature indicates that the universe will expand forever. Ironically, Krauss has actually published a paper that greatly helped to strengthen Tipler's Omega Point cosmology. Some have suggested that the current acceleration of the universe's expansion due to the positive cosmological constant would appear to obviate the Omega Point. However, Profs. Krauss and Turner point out 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." (See Lawrence M. Krauss and Michael S. Turner, "Geometry and Destiny", General Relativity and Gravitation, Vol. 31, No. 10 [Oct. 1999], pp. 1453-1459.) While cosmological observations cannot tell us what the ultimate fate of the universe will be, the known laws of physics themselves can, as the universe is forced to end in finite proper time in order for unitarity to remain unviolated (again, see p. 925 [cf. pp. 904-905] of id., "The structure of the world from pure numbers", op. cit.).
1:23:06 h:min:sec ff.: Tipler starts his response to Krauss, wherein Tipler addresses Krauss's claims.
1:29:22 h:min:sec ff.: Krauss starts his second response to Tipler.
1:30:34 h:min:sec ff.: Krauss claims that the laws of physics prevent sapient life from harnessing baryon annihilation. However, the laws of physics allow baryon annihilation using electroweak quantum tunneling via quantum coherence. As Tipler writes, "Atoms have energy levels that differ by a few electron volts. Quantum coherence among a trillion atoms would allow the atoms to concentrate the energy differences of the levels on a single atom, and this would be 10 TeV, the amount of energy needed for the baryon-annihilation process to go forward." (See Frank J. Tipler, The Physics of Christianity [New York: Doubleday, 2007], p. 73.)
1:31:09 h:min:sec ff.: Krauss talks about "the energy of empty space", by which he means the dark energy. See my above response to Krauss's previous comments on the dark energy.
1:32:29 h:min:sec ff.: Tipler and Krauss take questions from the audience.
1:35:57 h:min:sec ff.: Krauss claims that we don't understand physics well enough to know whether unitarity is violated if an astrophysical black hole were to evaporate.
Regarding proposed solutions to the black hole information issue, all except for Tipler's Omega Point cosmology share the common feature of using proposed new laws of physics that have never been experimentally confirmed--and indeed which violate the known laws of physics--such as with Prof. Stephen Hawking's paper on the black hole information issue which is dependent on the conjectured String Theory-based anti-de Sitter space/conformal field theory correspondence (AdS/CFT correspondence). (See S. W. Hawking, "Information loss in black holes", Physical Review D, Vol. 72, No. 8 [Oct. 15, 2005], Art. No. 084013, 4 pp.) Hence, the end of the universe in finite proper time via collapse before a black hole completely evaporates is required if unitarity is to remain unviolated, i.e., if General Relativity and Quantum Mechanics--which are what the proofs of Hawking radiation derive from--are true statements of how the world works.
1:42:13 h:min:sec ff.: Krauss invokes the Christ myth theory, including incorrectly claiming that nearly every religion has had virgin births.
Regarding the Christ myth theory, virtually all the items which the Christ myth theorists claim as facts which show the parallels of Christianity with earlier pagan religions are completely fabricated modern claims that can't be found in the historical record. For an excellent discussion on this, see the following video:
* "Shattering the Christ Myth", DrCraigJohnson (YouTube), Apr. 17, 2009, Shattering the Christ Myth - YouTube . Mirror: "Veritas Forum: Shattering the Christ Myth", Bethel Christian Fellowship, 26:39 min:sec, https://www.[bless and do not curse... and do not curse]ute.com/video/Uo1HFlDMDhtS/ , http://bethelchristianfellowship.info/flash_media/jp3ChristMythCopyCat.m4v , https://bit.ly/2PzXxtV .
The above video is an interview of James Patrick Holding (editor of Shattering the Christ Myth: Did Jesus Not Exist? [Maitland, Fla.: Xulon Press, 2008], https://amazon.com/dp/1606472712 ) by Dr. Craig Johnson on the topic of the Christ myth theory. See also the below resources regarding the Christ myth theory on J. P. Holding's website:
* "Were Bible stories and characters stolen from pagan myths?", Tekton Education and Apologetics Ministry, http://www.tektonics.org/copycathub.html .
* "Did Jesus exist?", op. cit., http://www.tektonics.org/jesusexisthub.html .
1:47:06 h:min:sec ff.: Krauss agrees that the only hope for eternal life is in a collapsing universe.
1:48:06 h:min:sec ff.: An audience member asks Tipler about Matthew 10:23, Mark 9:1 and John 5:25 as being examples of where Jesus Christ incorrectly thought that the End Time was imminent, i.e., within Jesus's own generation.
Matthew 10:23, New King James Version (NKJV) states, "When they persecute you in this city, flee to another. For assuredly, I say to you, you will not have gone through the cities of Israel before the Son of Man comes." And indeed they did not go through all the cities of Israel before they died, and hence before Christ's Second Coming.
Mark 9:1, NKJV (cf. Matthew 16:28; Luke 9:27) states, "And He said to them, 'Assuredly, I say to you that there are some standing here who will not taste death till they see the kingdom of God present with power.'" And then the very next passages concern Christ's Transfiguration, whereby Heaven was also shown.
John 5:25, NKJV states, "Most assuredly, I say to you, the hour is coming, and now is, when the dead will hear the voice of the Son of God; and those who hear will live." But the next passages, John 5:26-29, go on to state, "For as the Father has life in Himself, so He has granted the Son to have life in Himself, and has given Him authority to execute judgment also, because He is the Son of Man. Do not marvel at this; for the hour is coming in which all who are in the graves will hear His voice and come forth--those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation." These passages relate to Jesus's statement that "I am the resurrection and the life." (John 11:25, NKJV. Cf. John 8:12 [cf. 1 John 1:5]; 14:6.) In other words, those raised from death are already existing within Jesus Christ in His transcendent Second Person aspect, since the Father and the Son are One (see Isaiah 9:6; John 10:30; 14:6-13). So when Jesus said this, it was a different way of saying that the Resurrection and the Life stood there before them right then in His human aspect.
So in each of these scripture passages which this audience member gave as examples of Christ getting some things wrong are all examples of Him being correct.
Sometimes people also give Matthew 24:32-35 as being an example of Christ making an incorrect prophecy. However, "this generation" referred to in Matthew 24:34 concerns the generation which witnesses the signs of the End Time which Jesus discusses.
2:02:13 h:min:sec ff.: Krauss talks about Newtonian mechanics being replaced by General Relativity and Quantum Mechanics, and hence that we shouldn't be surprised that the current known laws of physics might also be replaced. However, as Tipler pointed out in his presentation, the fundamental physics of today are simply more specific subsets of Newtonian mechanics, i.e., Newtonian mechanics with specific constrains put on it in order to make it consistent with observations and to make its resulting subsets mutually mathematically consistent with each other. Hence, we have never left the realm of Newton's physics. And all the forces in physics are now described and made mutually consistent with the Omega Point/Feynman-DeWitt-Weinberg quantum gravity/Standard Model TOE. (See above for more on that.) 2:03:26 h:min:sec ff.: Krauss states that the Standard Model of particle physics produces nonsense answers when pushed to high enough energies, as does Quantum Electrodynamics (QED). However, as Tipler previously pointed out in his presentation, imposing unitarity avoids the spacetime infinities of quantum field theory, since if there were not a cut-off to the energies of quantum field theory then miniature black holes would be created and quickly evaporate, thereby violating unitarity. Krauss also gives the infinities of quantum field theory as a reason for thinking that new forms of physics will be required at higher energy scales. However, this mechanism to the energy cut-off also allows the energies to gradually scale to infinity during the collapse phase of the universe (the energies only become actually infinite at the cosmological singularity), which means that there is no need for new physics at higher energy scales.
* * * * *
Since the Omega Point/Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (TOE) is mathematically required by the known laws of physics, of which said physical laws have been confirmed by every experiment to date, the only way Krauss could have actually argued against Tipler is to argue that the known laws of physics might be wrong. But because those physical laws have been confirmed by every experiment to date, there exists no rational reason to think that they are wrong. Hence, Krauss's irrelevant arguments (or bare assertions, as Krauss also engaged in) against Tipler were unavoidable, since Krauss set himself a logically-impossible task.
For details on the Omega Point TOE, see the following paper by Prof. Tipler:
* F. J. Tipler, "The structure of the world from pure numbers", Reports on Progress in Physics, Vol. 68, No. 4 (Apr. 2005), pp. 897-964, doi:10.1088/0034-4885/68/4/R04, bibcode: 2005RPPh...68..897T, http://dauns01.math.tulane.edu/~tipler/theoryofeverything.pdf , WebCite query result . Also released as Frank J. Tipler, "Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything", arXiv:0704.3276, Apr. 24, 2007, Feynman-Weinberg Quantum Gravity and the Extended Standard Model... .
The following is the first article on the Omega Point TOE:
* Frank J. Tipler, "Genesis: How the Universe Began According to Standard Model Particle Physics", arXiv:astro-ph/0111520, Nov. 28, 2001, Genesis: How the Universe Began According to Standard Model... . For images that go with the article, see "Frank J. Tipler, Diagrams", Theophysics: God Is the Ultimate Physicist, WebCite query result .
For the details regarding the point Prof. Tipler made in his presentation about how modern physics (i.e., General Relativity, Quantum Mechanics, and the Standard Model of particle physics) are simply special cases of classical mechanics (i.e., Newtonian mechanics, particularly in its most powerful formulation of the Hamilton-Jacobi Equation), see the following articles:
* Frank J. Tipler, "The Obama-Tribe 'Curvature of Constitutional Space' Paper is Crackpot Physics", Social Science Research Network (SSRN), Oct. 26, 2008, 45 pp., doi:10.2139/ssrn.1271310, http://ssrn.com/abstract=1271310 .
* Maurice J. Dupré and Frank J. Tipler, "General Relativity as an Æther Theory", International Journal of Modern Physics D, Vol. 21, No. 2 (Feb. 2012), Art. No. 1250011, 16 pp., doi:10.1142/S0218271812500113, bibcode: 2012IJMPD..2150011D, http://worldscientific.com/doi/abs/10.1142/S0218271812500113 . Also at arXiv:1007.4572, July 26, 2010, https://arxiv.org/abs/1007.4572 .
* Frank J. Tipler, "Hamilton-Jacobi Many-Worlds Theory and the Heisenberg Uncertainty Principle", arXiv:1007.4566, July 26, 2010, https://arxiv.org/abs/1007.4566 .
The foregoing articles, in addition to many other papers by Prof. Tipler on the Omega Point cosmology, are also available in the below archive:
* Frank-J-Tipler-Omega-Point-Papers.zip , 26712158 bytes, MD5: 6e5d29b994bc2f9aa4210d72ef37ab68, https://webcitation.org/6GjhT6t52 , https://amazon.com/clouddrive/share?s=bTI58F1dSAIjSrxJ26R7d8 , https://docs.google.com/file/d/0B7k4r80YepnxNjNOX2x0XzBOV00/edit .
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