Commentary on Frank Tipler and Lawrence Krauss's 2007 Debate at Caltech
updated December 13, 2018; originally published April 3, 2013
Below is my commentary on the following video:
* Frank Tipler and Lawrence Krauss, Michael Shermer (Producer), A Great Debate: Can Physics Prove God and Christianity? (prod. co.: Skeptics Society [Altadena, Cal.]), run time: 2:13 h:min. Video of a debate held at the California Institute of Technology (Caltech; Pasadena, Cal.) on June 3, 2007.
Prof. Michael Shermer (founder of the Skeptics Society) is the moderator of the debate. Bill Nye (of the television show Bill Nye the Science Guy) is among the audience members.
Physicist and mathematician Prof. Frank J. Tipler starts his presentation at 15:57 min:sec. Tipler points out that we have had a Theory of Everything (TOE) in physics for some 30 years with the arrival of the Standard Model of particle physics, since the Standard Model describes all forces in nature except for gravity. The Standard Model is a quantum field theory, i.e., it involves Quantum Mechanics combined with special-relativistic particle physics. And gravity is described by General Relativity. The problem has been to make General Relativity and Quantum Mechanics consistent with each other, which Tipler points out is done with the Feynman-DeWitt-Weinberg theory of quantum gravity when the appropriate boundary conditions on the universe are used, which includes the initial Big Bang, and the final Omega Point, cosmological singularities.
Tipler shows a presentation slide listing General Relativity as having the general linear group of GL(4, R) symmetry group; and the Standard Model of particle physics as having the Lie group of 3 Lie symmetry group.
19:33 min:sec ff.: In the 1960s Richard Feynman at Caltech quantized a spin-2 field using his path integral method. Quantizing a spin-2 field requires it to be a spacetime metric and imposes the full GL(4, R) symmetry group.
At 19:54 min:sec ff., Tipler points out that the Feynman quantum gravity theory is unique, i.e., it is the only quantum gravity theory possible if General Relativity and Quantum Mechanics are correct (cf. 32:11 min:sec ff.), since General Relativity requires gravity to be a spin-2 field, and the Hulse and Taylor pulsar confirmation of Einstein's quadrupole formula verified that gravity is a spin-2 field. General Relativity also states that gravity is a phenomenon of the curvature of the spacetime metric with observer independence, i.e., physics cannot depend locally on the observer, which gives the GL(4, R) symmetry group of General Relativity.
20:44 min:sec ff.: Steven Weinberg later showed that the Feynman theory of quantum gravity is renormalizable, which means that the term-by-term infinities in the Feynman diagrams can be absorbed into constants, so it is no worse than other quantum field theories. However, there are actually two sources of infinity in quantum field theory: the ones that are renormalized away, as previously mentioned; and the ones that generate the divergence of the power series of the S-matrix (i.e., scattering matrix).
21:21 min:sec ff.: It has been known for 50 years what the cause of this series divergence is: it's a bad choice of the vacuum state, which Freeman Dyson showed in a paper in Physical Review in 1952 (see F. J. Dyson, "Divergence of Perturbation Theory in Quantum Electrodynamics", Physical Review, Vol. 85, No. 4 [Feb. 1952], pp. 631-632). Geroch showed that perturbation theory in String Theory also has a series divergence for essentially the same reason.
22:18 min:sec ff.: Tipler mentions Liouville's Theorem in complex analysis. One way of stating said Theorem is that all analytic functions (i.e., holomorphic functions) other than constants have singularities either a finite distance from the origin of coordinates or at infinity, which is analogous to what occurs with the universe: the only way to avoid infinities in spacetime (consequently causing the instantaneous collapse of the entire universe) is for the universe to begin and end at singularities. Moreover, it doesn't matter what form of physics one resorts to, as any physically-realistic cosmology (e.g., one capable of incorporating Quantum Mechanics, since the complex number field is intrinsic to the mathematical formulations of Quantum Mechanics) must begin at an initial singularity and end at a final singularity. (As Barrow and Tipler wrote, "Initial and final cosmological curvature singularities are required to avoid a universal action singularity." See John D. Barrow and Frank J. Tipler, "Action principles in nature", Nature, Vol. 331, No. 6151 [Jan. 7, 1988], pp. 31-34; see also Frank J. Tipler, "The Structure of the Classical Cosmological Singularity", in Origin and Early History of the Universe: Proceedings of the 26th Liège International Astrophyscial Colloquium, July 1-4, 1986 [Cointe-Ougree, Belgium: Universite de Liege, Institut d'Astrophysique, 1987], pp. 339-359; "Discussion", pp. 360-361.)
23:23 min:sec ff.: Feynman quantum gravity makes a singularity even more inevitable than the Penrose-Hawking-Geroch Singularity Theorems, since the Singularity Theorems assume attractive gravity, whereas with Feynman quantum gravity the sum-over-histories (i.e., sum-over-paths; path integral formulation) get arbitrarily close to infinite curvature. In other words, the multiverse has its own singularity.
24:04 min:sec ff.: 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. 25:12 min:sec ff.: This energy cut-off mechanism also means that some misnomered "constants" increase with cosmic time. 26:21 min:sec ff.: This mechanism to stabilize quantum field theory only works if there is an initial singularity and a final singularity and if there are no event horizons, which also solves the black hole information problem. 26:55 min:sec ff.: The absence of event horizons is only possible if the universe is spatially closed, and in particular has the spatial topology of a three-sphere (i.e., 3-sphere; S^3); also, only if the final singularity is a single point in the Penrose c-boundary construction, called the Omega Point.
27:18 min:sec ff.: This picks out a global vacuum state which must define a classical universe now; this means that the wave function of the universe must have initially been a Dirac delta function, which explains the observed flatness of the universe without resorting to nonempirical new physics such as Inflation Theory (requiring the unobserved inflation field, i.e., inflaton particles), but rather is simply quantum kinematics: a result of wave-packet spreading (as an analogy, Tipler gives a version of wave-packet spreading as sound waves heard around the corner of a building, which is an example of wave diffraction).
28:05 min:sec ff.: In such a universe, quantum field theory in the form of the Bekenstein Bound forces the initial state of the universe to be homogeneous and isotropic; and it also picks out a unique field of the Standard Model, the SU(2)_L field which gives the observed excess of matter over antimatter, whereas the usual boundary condition used by physicists--which is inconsistent with quantum field theory--gives a baryon-generating mechanism that produces far too many photons to baryons. Also, the perturbation spectrum is necessarily scale-invariant since the universe is necessarily flat (as was basically shown by Edward Robert Harrison long before Inflation Theory was even thought of).
29 min ff.: What the above all means is that reality consists of a multiverse, with each universe in the multiverse starting at an initial singularity and eventually collapsing into a final singularity. Said Big Bang initial singularity and Omega Point final singularity are actually connected by a third singularity: the All-Presents singularity, which exists at each time for each universe in the multiverse. That is, there exists three connected hypostases to existence: the First Cause, the Sustaining Cause, and the Final Cause, which are not in spacetime but instead are the boundary of space and time, and which are not themselves subject to any possible form of physics, i.e., they are quite literally supernatural.
32:11 min:sec ff.: Feynman-Weinberg quantum gravity is the unique quantization of General Relativity, i.e., it's the only way to quantize General Relativity, since gravity in General Relativity is a spin-2 field, and General Relativity is a spacetime metric and possesses the full GL(4, R) symmetry group. (Herein "unique" means the only one mathematically possible within the context of parsimony, as one can always add arbitrary yet small terms which change the output so insignificantly that no current instruments can measure the difference, and hence it would presently still conform to experiment, but such arbitrary terms would not then be parsimonious, since they are not justified by mathematical necessity [i.e., in order to obtain a mathematically-consistent theory] nor are they experimentally justified.) General Relativity is the unique specialization (i.e., subset; special case) of Newtonian mechanics with the specification imposed that Newtonian mechanics be consistent with Maxwell's Equations, i.e., that the speed of light is the same for all observers. Elie Cartan showed that in Newtonian mechanics, gravity is curvature of time only; whereas in General Relativity, gravity is curvature of space and time, i.e., spacetime (cf. Frank J. Tipler, The Physics of Christianity [New York: Doubleday, 2007], p. 33; and pp. 79-80 of Frank J. Tipler, "Albert Einstein: A Scientific Reactionary", pp. 73-83, in John Brockman [Ed.], My Einstein [New York: Vintage Books, 2007; orig. pub. 2006]). 33 min ff.: Similarly, Quantum Mechanics is the unique specialization of Newtonian mechanics in its most powerful formulation, the Hamilton-Jacobi Equation, with the specification imposed that determinism is maintained: since the Hamilton-Jacobi Equation is indeterministic, because when particle trajectories cross paths a singularity is produced (i.e., the values in the equations become infinite) and so it is not possible to predict (even in principle) what happens after that (cf. id., The Physics of Christianity, pp. 48-49; and 7:17 min:sec ff. of Casey Luskin, interview of Frank Tipler, "Part 1: Einstein Vs. Darwin", Intelligent Design the Future, Feb. 13, 2013, audio run time: 17:25 min:sec).
33:17 min:sec ff.: For these reasons--the fact that the history of physics since Newton has been a series of specializations, rather than generalizations, of fundamental physics--we can be confident that we have the correct Theory of Everything (TOE) in physics and that there is not going to be any new physics that comes along to displace the current known laws of physics. That is, since after Newton's physics, there has been no "revolution" in physics (e.g., such as with General Relativity and Quantum Mechanics, etc.), but instead an evolution of physics: 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. So in over 300 years 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 Feynman-DeWitt-Weinberg quantum gravity theory and the Standard Model of particle physics.
Prof. Tipler then goes on to show how, using only the known laws of physics, the miracles of Jesus Christ are physically possible. This process uses baryon annihilation (which is allowed in the Standard Model, as baryon number minus lepton number, B - L, is conserved), and its inverse, by way of electroweak quantum tunneling caused via the Principle of Least Action by the physical requirement that the Omega Point final cosmological singularity exists. Tipler also proposes that the virgin birth of Jesus by Mary could be possible via Jesus being a special type of XX male who obtained all of his genetic material from Mary (i.e., an instance of parthenogenesis). Tipler concludes that the Star of Bethlehem was either a Type Ic hypernova located in the Andromeda Galaxy, or a Type Ia supernova located in a globular cluster of our own Milky Way Galaxy.
If the Incarnation of Jesus Christ and the miracles attributed to him in the New Testament were necessary in order to lead to the formation of the Omega Point--and if the known laws of physics are correct--then the probability of these events occurring is certain. Furthermore, Tipler proposes tests on particular relics associated with Jesus which, if the relics are genuine, could verify whether in fact said miracles took place via the aforementioned mechanisms.
Physicist Prof. Lawrence M. Krauss starts his presentation at 49:36 min:sec. 52:54 min:sec ff.: Krauss begins by engaging in the logical fallacy of bare assertion. Krauss asserts that (1) the Standard Model of particle physics isn't complete; (2) we don't have a consistent theory of quantum gravity; (3) the universe doesn't have to collapse; (4) we don't understand the nature of dark energy; and (5) we don't know why there is more matter than antimatter in the universe.
In answer to Krauss: (1) The Standard Model describes all forces in nature except for gravity. And gravity is described by General Relativity. (2) The problem has been to make General Relativity and Quantum Mechanics consistent with each other, which is done with the Omega Point/Feynman-DeWitt-Weinberg quantum gravity theory. (3) The universe must collapse in finite proper time or otherwise unitarity will be violated (see p. 925 [cf. pp. 904-905] of 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). (4) The dark energy is the positive cosmological constant. As required by the Standard Model of particle physics, the net baryon number was created in the early universe by baryogenesis via electroweak quantum tunneling. This necessarily forces the Higgs field to be in a vacuum state that is not its absolute vacuum, which is the cause of the observed cosmological constant. (5) The universe's initial SU(2)_L field of the Standard Model--which is required by quantum field theory--gives the observed excess of matter over antimatter. See op. cit. for details on the foregoing matters.
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, https://www.youtube.com/playlist?list=PLA843654F0F6D4DA8 . Mirror: "Veritas Forum: Shattering the Christ Myth", Bethel Christian Fellowship, 26:39 min:sec, https://www.bitchute.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 , https://webcitation.org/6GiCQuDCk . 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, https://arxiv.org/abs/0704.3276 .
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, https://arxiv.org/abs/astro-ph/0111520 . For images that go with the article, see "Frank J. Tipler, Diagrams", Theophysics: God Is the Ultimate Physicist, https://webcitation.org/61sKVnDDA .
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 .