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آخر نشاط: 11-26-2006 12:27 AM
| Sal Giandinoto, Ph.D. |
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| This site is dedicated to a purely mathematical description of Phi recursion and Phi recursive based forces of nature including those of Quantum Gravity and the Unified Field. The mathematical formulations contained on this site were derived by Sal Giandinoto, Ph.D. and were conceptualized by myself on 12/18/05. I have included other links to many valuable theories and information that is not only astounding but also cutting edge. Please take the time to explore the many interesting links on this website. |
| Please take a look at the following links containing some of the equations I have derived with regards to infinite Phi-recursion and the gFactor of the electron. I will give a much more complete and in- depth mathematical and conceptual formalism of these ideas as the website progresses towards its ultimate destiny, A Grand Unified Field Theory (GUFT) based on Phi-recursion and Quantum gravity. |
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| The above picture represents the quarks contained in a positively charged pi-meson. It is composed of an up quark and an anti-down quark. The antiparticle of the positively charged pi-meson is the negatively charged pi-meson and is composed of a down quark and an anti-up quark. I will create a new link shortly explaining the current Standard Model, Quantum Electrodynamics (QED), Quantum Chromodynamics (QCD) and Quantum Gravity. In the new link I will also explain why certain mesons composed of up and anti-up quarks and down and anti-down quarks are able to exist in terms of QCD. |
| There are 11 basic quantum numbers (flavors) for Quarks. These are the following: 1. Lepton Number (L) 2. Baryon Number (B) 3. Electric Charge (Q) 4. Weak Hypercharge (Yw) 5. Weak Isospin (Tz) 6. Isospin (Iz) 7. Hypercharge (Y) 8. Strangeness (S) 9. Charm (C) 10. Bottomness (B') 11. Topness (T) |
| The Following Relationships Exist Between the Quantum Numbers |
| Y= B + S + C + B' + T Q = Iz + Y/2 Q = Tz + Yw/2 B - L = Charge of Global Gauge U(1) Symmetry known as U(1)B-L Unlike Baryon and Lepton Number, this symmetry is NOT broken by Chiral or Gravitational Anomalies |
| The Eight Fold Way |
| The Beauty of this model is that each diagonal has its own particle/anti-particle pair with the neutral Pi-Meson, Eta and Eta' (Eta-prime) particles in the middle of the diagram. The neutral Pi-Meson, Eta and Eta' are each their own anti-particles. The Eta' is the Purple concentric circle and the neutral Pi-Meson and Eta particles are in the central Green region of the diagram. |
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| Picture of Lorenz Attractor |
| CP Violation |
| CP Violation provides an extremely important role in the explaination of Cosmology including that of Quantum Cosmology. C stands for Charge Conjugation symmetry and P for Parity symmetry. The violation of CP symmetry in particle physics is absolutely crucial for the explaination of the abundance of matter over anti-matter in the universe. CP violation was discovered in 1964 by James Cronin and Val Fitch who both shared the Nobel Prize in Physics for their discovery in 1980. CP is simply the product of two symmetries C (charge conjugation which changes particles into their anti-particles) and P (parity which creates the mirror image of a physical system). The Strong nuclear force and the Electromagnetic force are completely invariant under CP transformations, but the Weak nuclear force is sometimes slightly violated during CP transformations. CP symmetry was proposed to restore order after the discovery of Parity violations in the 1950's. In particle physics, the idea of Parity is that it is supposed to be invariant under mirror reflection. For example, this would mean that chemical and radiochemical reactions would occur at the same rate as the original reaction (i.e., before the mirror transformation). However, during the 1950's Parity violations were discovered for some examples of radioactive decay processes (processes known to involve the weak nuclear force). The symmetry of an overall quantum process or mechanical system can be restored if another symmetry S can be found such that the combined symmetry PS remains unbroken. In the case of the rather subtle structure of the Hilbert Space, it was realized shortly after the discovery of P violation, that C conjugation was the desired and correct symmetry to restore order in that space. The discovery of James Cronin and Val Fitch in 1964 that CP violation could be broken showed that both C conjugation between particles and anti-particles in weak interactions also violated P symmetry in many cases. Later it was discovered in a Kaon decay experiment that CP symmetry was violated and ownly a weaker version of the symmetry could be preserved by invoking CPT symmetry. Therefore, besides C and P symmetry, there is a third operation T (Time Reversal) which corresponds to reversal of motion. Invariance under time implies that whenever a motion is allowed by the laws of physics, the reversed motion is also allowed. Therefore, the combination of CPT symmetry is beleived to constitute an exact symmetry of all types of fundamental interactions. Because of the CPT symmetry, a violation of the CP symmetry is considered a violation of the T-symmetry. Therefore, CP violation implied violation of T-symmetry provided that the CPT symmetry theorem was valid. This theorem is therefore regarded as one of the basic principles of Quantum Field Theory. CP violation has not only been observed in Kaon decay processes, but also in B mesons. The CP violation of the Standard Model is incorporated by including a complex phase in the so called CKM Matrix. Please click here to see the mathematical representation of the CKM (Cabibbo Kobayashi Maskawa) Matrix On the left is the CKM Matrix along with a vector of strong force eigenstates of the quarks in the traditional quantum mechanical bra-ket notation, and on the right is the weak force eigenstates of the quarks. The CKM Matrix describes the probability of the transition from one quark q to another quark q'. Experimentally, the magnitudes of the matrix values have been determined to be CKM Values |
| References: G.C. Branco, L. Lavoura and J.P. Silva, CP Violation. Clarendon Press, Oxford (1999). I. Bigi and A. Sandra, CP Violation. Cambridge University Press (1999). I. Bigi, CP Violation, an essential mystery in Nature's Grand Design. Invited lecture given at the XXV ITEP Winter School of Physics, Feb. 18-27, 1997, Moscow Russia, at 'Frontiers of Contemporary Physics', May 11-16, 1997, Vanderbilt University, Nashville, USA, and at the International School of Physics 'Enrico Fermi', CXXXVII Course 'Heavy Flavour Physics: A Probe of Nature's Grand Design', Varenna, Italy, July 8-18, 1997. Davide Castelvecchi, What is Direct CP Violation?, Stanford Linear Accelerator (SLAC). |
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| Professor Emeritus, Dr. Lauri Vaska, Clarkson University |
| Here is a list of books that I have already read and suggest to those seriously interested in GUFT |
| 1.) The Tao of Physics, Fritjof Capra, Shambhala Publications, Inc., (1999). 2.) Group Theory and its Applications to Physical Problems, Morton Hamermesh, Dover Publications, (1962). 3.) The God Particle, Leon Lederman with Dick Teresi, Houghton Mifflin Company, Boston & New York, (1993). 4.) The Tenth Dimension, Jeremy Bernstein, McGrawHill, (1989). 5.) The Charm of Physics, Sheldon L. Glashow, Touchstone Simon & Schuster (1991). 6.) Superstrings and Other Things (A Guide to Physics), Carlos I. Calle, Institute of Physics Publishing (2001). 7.) In The Beginning (After COBE and Before the Big Bang), John Gribbin, Little, Brown and Company (1993). 8.) The Three Big Bangs, Philip M. Dauber and Richard A. Muller, Helix Books, Addison-Wesley Publishing Company, (1996). 9.) Hyperspace, Michio Kaku, Anchor Books, Doubleday 1995, Oxford University Press (1994). 10.) Black Holes & Time Warps, Kip Thorne (Einstein's Outrageous Legacy), W.W. Norton & Company (1994). 11.) The Big Bang (The Creation and Evolution of the Universe), Joseph Silk, Forward by Dennis Sciama, W.H. Freeman & Company (1980). 12) The End of Physics, David Lindley, BasicBooks, A Division of HarperCollins, Inc., (1993). 13.) Faster Than Light (Superluminal Loopholes In Physics), Nick Herbert, Ph.D., Penguin Books (1989). 14.) The First Three Minutes, Steven Weinberg, BasicBooks, A Division of HarperCollins, Inc. (1993). 15.) Quantum Reality (Beyond the New Physics), Nick Herbert, Doubleday, (1985). 16.) Einstein's Universe, Nigel Calder, Penguin Books, (1990). 17.) The Physical Principles of The Quantum Theory, Werner Heisenberg, Dover Publications, (1949). 18.) Beyond Einstein, Michio Kaku and Jennifer Thompson, Anchor Books Doubleday, (1995). 19.) Dreams of a Final Theory (The Scientist's Search for the Ultimate Laws of Nature), Steven Weinberg, Vintage Books, (1994). 20.) Theories of Everything (The Quest for Ultimate Explanation), John D. Barrow, Ballantine Books (1992). 21.) The Cosmic Code (Quantum Physics as the Language of Nature), Heinz R. Pagels, Bantum Books, (1990). 22.) The Golden Ratio (The Story of Phi, The World's Most Astonishing Number), Mario Livio, Broadway Books, a division of Random House, Inc. (2002). 23.) The Fabric of the Cosmos (Space, Time, and the Texture of Reality), Brian Greene, Vintage Books, a division of Random House, Inc., (2005). 24.) Coversations On the Dark Secrets of Physics, Edward Teller, Plenum Press, (1991). 25.) Wrinkles in Time, George Smoot and Keay Davidson, Avon Books, a division of The Hearst Corporation, (1993). 26.) Perfect Symmetry (The Search for the Beginning of Time), Heinz R. Pagels, Bantum Books (1991). 27.) The Great Design (Particles, Fields, and Creation), Robert K. Adair, Oxford University Press, Inc., (1987). 28.) Three Roads to Quantum Gravity, Lee Smolin, Basic Books, (2001). 29.) Introduction to Quantum Mechanics (With Applications to Chemistry), Linus Pauling and E. Bright Wilson, Jr., Dover Publications (1985). 30.) Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Rutherford Aris, Dover Publications (1989). 31.) The Quantum World, J.C. Polkinghorne, Princeton University Press, (1989). 32.) The Big Bang, Joseph Silk, W.H. Freeman & Company, (1989). 33.) The Meaning of Reality, Albert Einstein, Princeton University Press, (1953), Copyright Renewed (1984) by The Hebrew University of Jerusalem. 34.) Spaceship Neutrino, Christine Sutton, Cambridge University Press, (1992). 35.) Black Holes and Baby Universes, Stephen W. Hawking, Bantum Books, (1993). 36.) A Brief History of Time (From the Big Bang to Black Holes), Stephen W. Hawking, Bantum Books (1990). 37.) Theoretical Nuclear Physics, John M. Blatt and Victor F. Weisskopf, Dover Publications, (1979). 38.) The Big Bang Never Happened, Eric J. Lerner, Vintage Books (1992). 39.) The Arrow of Time (A Voyage Through Science to Solve Time's Greatest Mystery), Peter Coveney & Roger Highfield (Forward by Ilya Prigogine Nobel Laureate), Ballantine Books (1990). 40.) The Elegant Universe, (Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory), Brian Greene, Vintage Books (1999). 41.) The Dancing Wu Li Masters (An Overview of the New Physics), Gary Zukav, Bantum Books (1980). 42.) Stephen Hawkings Universe, John Boslough, Avon Books (1985). 43.) The Whole Shebang, Timothy Ferris, Touchstone, (1998). 44.) Before the Beginning (Our Universe and Others), Martin Rees, Helix Books, Perseus Books, (1997). 45.) From Quarks to the Cosmos, Leon M. Lederman & David N. Schramm, Scientific American Library, (1995). 46.) The New Physics, Edited by Paul Davies, Cambridge University Press, (1996). 47.) The Non-Local Universe (The New Physics and Matters of the Mind), Robert Nadeau & Menas Kafatos, Oxford University Press (1999). 48.) The Physics of Immortality (Modern Cosmology, God and the Resurrection of the Dead), Frank J. Tipler, Anchor Books (1994). 49.) Before the Big Bang (The Origins of the Universe), Ernest J. Sternglass, Four Walls Eight Windows, (1997). 50.) Alpha & Omega (The Search for the Beginning and the End of the Universe), Charles Seife, Viking Penguin (2003). 51.) The Quantum World, Kenneth W. Ford, Harvard University Press (2004). 52.) Quantum (A Guide for the Perplexed), Jim Al-Khalili, Weidenfeld & Nicolson (2004). 53.) Quantum Field Theory in a Nutshell, A. Zee, Princeton University Press (2003). 54.) Quantum Field Theory, Claude Itzykson and Jean-Bernard Zuber, Dover Publications (2005). (Replication of McGraw-Hill, Inc., New York (1980). 55.) The Field (The Quest for the Secret Force of the Universe), Lynne McTaggart, Harper Collins Publishing Company (2002). 56.) The Story of Spin, Sin-itiro Tomonaga, The University of Chicago Press (1997). 57.) Quest For Zero Point Energy, Moray B. King, Adventures Unlimited Press (2001). 58.) Science and the Akashic Field (An Integral Theory of Everything), Ervin Laszlo, Inner Traditions (2004). 59.) Parallel Worlds (A Journey Through Creation, Higher Dimensions and the Future of the Cosmos), Michio Kaku, Anchor Books (2005). 60.) Quantum Mechanics Demystified, David McMahon, McGraw-Hill (2005). 61.) Black Bodies and Quantum Cats, Jennifer Ouellette, Penguin Books (2005). |
| There is a strong possibility that the Many-Worlds Interpretation (MWI) of Quantum Mechanics (as opposed to the well known Copenhagen Interpretation or the collapse of the wavefunction upon observation) is the correct interpretation. A poll of the top 96 theoretical physicists shows that 60% of them are leaning towards the MWI of Quantum Mechanics. Below, I propose a Phi-based extension of the Georgi-Glashow GUT SU(5). |
| The compact GUT SU(5) developed by Georgi-Glashow can be extended ad infinitum using the various irreducible representations composed of the Fibonacci Numbers in Phi-Recursion. I propose the following possibility: Since SU(5) = SU(3) X SU(2) X U(1) where 1, 2, 3 and 5 are all Fibonacci numbers, then the possibility exists that the following is also true: SU(55) X SU(34) X SU(21) X SU(13) X SU(8) X SU(5) = SU(89) Likewise, SU(610) = SU(377) X SU(233) X SU(144) X SU(89) I will derive a more compact mathematical formalism of these Phi-Recursive Irreducible Representations soon. |
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| Levi-Civita antisymmetric Epsilon PermutationTensor |
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