1 Florentin Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J. Hutchison Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and Other Areas of Science 2006 F. Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J, Hutchison 2 Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics and other areas of Science Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro- physics, geophysics etc. It is of our hope that some of the problems dis- cussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation. The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plau- sible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage! The Authors Unfolding the Labyrinth: Open Problems in Physics, Mathematics,… 3 Unfolding the Labyrinth: Open Problems in Physics, Mathe- matics, Astrophysics, and Other Areas of Science F. Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J. Hutchison Contents Preface 5 Foreword 6 1 Unsolved Problems in Theoretical Physics 8 1.1. Problems related to elementary particles 8 1.2. Problems related to Unmatter 11 1.3 Some unresolved problems, questions and applications of the Brightsen nucleon cluster model 21 2 Unsolved Problems in Mathematics 24 2.1. Maximum number of circles 25 2.2. Consecutive sequence 25 2.3. Diophantine equation 25 2.4. Van Der Waerden Theorem 26 2.5. Differential equation with fractional power 26 2.6. Representation of odd number with prime 26 2.7. Magic square problem 27 2.8. Palindromic number and iteration 27 2.9. Non-Euclidean geometry by giving up its fifth postulate 28 2.10. Smarandache Geometry and Degree of Negation in Geometries 28 2.11. Non-Archimedean triangle theorem 33 2.12. The cubic Diophantine equation 33 2.13. Multispaces and applications in physics 34 3 Unsolved Problems in Astrophysics 35 3.1. Unsolved problems in Celestial Mechanics 35 3.2. Unsolved problems in Astrophysics 37 4 Unsolved Problems in Geophysics 45 4.1. Introduction 45 4.2. Some new questions 45 5 Unsolved Problems in Sorites Quantum Paradox and Smarandache F. Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J, Hutchison 4 Class of Paradoxes 52 5.1.Introduction 52 5.2.Quantum Paradox and Quantum SoritesParadox 53 5.3. Smarandache’s class of Paradoxes 54 5.4. Paradox 54 5.5. Generalization 55 6 Origin of Spin: Paradox of Classical Beth experiment 57 6.1. Angular momentum of circularly polarized light 57 6.2. Beth experiment is a puzzle 64 6.3. An explanation of Beth experiment 66 6.4. Electrodynamics spin tensor 68 7 Other unsolved problems in various areas of science 72 7.1. Relativity theory 72 7.2. Questions related to Modified Bell’s theorem 73 7.3. Mind-matter interaction, hidden mystery of water 77 7.4. Quaternion wave interpretation of superconductor 80 7.5. Solar dynamics 83 7.6. Science of Energy Conservation and Modified Coulomb-Newton Law 85 7.7. Do fundamental constants in Nature vary with time? 96 7.8. Scale invariance principle and coherent picture between microscale and macroscale phenomena 99 7.9. Does coral reef data support Earth slowing-day hypothesis? 99 7.10. Link between Planckian quantization and quantized information 100 8. Postscript: A description of anomalous electromagnetic phenomena known as the Hutchison Effect 103 Epilogue 111 Acknowledgment 112 References 113 Appendix A: Observation of anomalous potential electric energy of Distilled water under solar heating 121 Appendix B: On the origin of macroquantization in astrophysics 131 Unfolding the Labyrinth: Open Problems in Physics, Mathematics,… 5 Preface The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and func- tion of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind com- bined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. Revealing the secrets of Nature, so that we truly see ‘the sunlit plains ex- tended, and at night the wondrous glory of the everlasting stars’*, requires far more than mere technical ability and mechanical dexterity learnt form books and consensus. The dustbin of scientific history is replete with dis- credited consensus and the grand reputations of erudite reactionaries. Only by boldly asking questions, fearlessly, despite opposition, and searching for answers where most have not looked for want of courage and independence of thought, can one hope to discover for one’s self. From nothing else can creativity blossom and grow, and without which the garden of science can only aspire to an overpopulation of weeds. Stephen J. Crothers Queensland, Australia Progress in Physics Journal, http://www.ptep-online.com 14th July 2006. * A. B. (Banjo) Patterson’s ‘Clancy of the Overflow’. F. Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J, Hutchison 6 Foreword “…The central problem is unsolvable: the enumeration, even if only partial… I saw the Aleph from all points; I saw the earth in the Aleph and in the earth the Aleph once more and the earth in the Aleph; I saw my face and my viscera;... because my eyes had seen that conjectural and secret object whose name men usurp but which no man has gazed on: the inconceivable universe.”---Aleph, J.L. Borges Partly inspired by a well-known paper by Ginzburg [1], the present book discusses various open problems in different areas of Science, including Physics, Mathemathics, Geophysics, Astrophysics etc. Therefore this book could be viewed as an extended form of the aforementioned paper of Prof. V. Ginzburg [1]. Nonetheless the writers attempt herein to look deeper into what appear to us as open problems. Throughout the book the writers describe unsolved problems in various fields of science, with the hope that these problems might perhaps inspire other researchers in their quest of finding new answers. The writers have made their best effort to write the problems here in a refreshing style. This is why the present book is recommended for researchers and graduate students who are looking for potentially new, breakthrough ideas in physics or ap- plied mathematics. Needless to say, some of the questions posed here will sound a bit weird, if not completely incomprehensible. Some of them also contain things that the reader may not think easy to follow. For instance, a reader might find the extension of ‘quark’ ideas incomprehensible, because the quarks themselves may not pop-out easily in our daily dose of reality (because of the confine- ment problem). As Heisenberg once said, more or less: “If quarks exist then we have redefined the word 'exist'.” These belong to ideas that perhaps may have a chance to stimulate the neurons inside our brains. We would like to thank the reviewers of this book, Profs. T. Love and A. Kaivarainen, and also S. Crothers, for their patience in reading the draft version of this book, and for their comments. We are also grateful for valu- Unfolding the Labyrinth: Open Problems in Physics, Mathematics,… 7 able discussions with numerous colleagues from all over the world, for some of the questions in this book were inspired by their comments, in par- ticular Profs. C. Castro, M. Pitkanen, E. Scholz, E. Bakhoum, R.M. Kiehn, Dong Choi, Chen I-wan, D. Rabounski and numerous others. And also spe- cial thanks to peer-reviewers for critically reading our papers and suggesting improvements. We also thank Robert Davic for his comments on the Bright- sen model. All in all, hopefully, these unsolved problems could motivate other young researchers in their journey for unfolding the Labyrinth of Nature. FS, VC, FY, RK, JH August 28th 2006 F. Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J, Hutchison 8 1 Unsolved Problems in Theoretical Physics The only way of discovering the limits of the possible is to venture a little way past them into the impossible.--Arthur C. Clarke 1.1 Problems in elementary particles etc. It is known that Quantum Mechanics is the cornerstone of more recent theories intended to describe the nature of elementary particles, including Quantum Field Theory, Quantum Electrodynamics, Quantum Chromody- namics, and so forth. But Quantum Mechanics in its present form also suffers from the same limitations as the foundations of logic; therefore it is not surprising that there are difficult paradoxes that astonished physicists for almost eight decades. Some of these paradoxes are: - Wigner’s friend; - Einstein-Podolski-Rosen paradox; - Schrödinger’s cat paradox. While numerous attempts have been made throughout the past eight dec- ades to solve all these paradoxes, it seems that only a few of the present theories can solve these paradoxes completely. As a result, it is therefore not so surprising to find that both Quantum Electrodynamics (QED) and also Quantum Chromodynamics have their own problems. For instance Dirac and Feynman never accepted QED as a com- plete theory on its own (as Feynman put it: “It’s like sweeping under the rug.”). This is why Dirac attempted to propose a new theory to replace QED, albeit the result has not been so successful. Recently, there have been some attempts to reconsider Dirac’s new theory (1951) in the light of the biquater- nions.[2] Similarly, other big questions in theoretical / particle physics can be de- scribed as follows: (i) Is there a Dirac æther fluid? [2] (ii) Can Dirac’s recent theory 1951 solve the infinity problem? Unfolding the Labyrinth: Open Problems in Physics, Mathematics,… 9 (iii) Does Dirac’s new electron theory 1951 reconcile the quantum mechanical view with the electrodynamical view of the electron? [2] (iv) What is the dynamical mechanism behind the Koide mixing ma- trix of the lepton mass formula? [3][4][5] (v) Does the neutrino have mass? [6][7] [8][9] (vi) Does the rishon or preon model of elementary particles give bet- ter prediction than conventional Quantum Chromodynamics Theory? [10][11][12] (vii) Is there a physical explanation of quark confinement? (viii) Is there a theoretical link between Quantum Chromodynamics and quantum fluid dynamics? Harari is a physicist who made one of the earliest attempts to develop a preon [11] model to explain the phenomena appearing in hadrons. Harari proposed the rishon model in order to simplify the quark model of Gell- Mann. The model has two kinds of fundamental particles called "rishon" (which means "primary" in Hebrew).[11] They are T (Third for charge 1/3e or Tohu from "unformed" in Hebrew in Genesis) and V (Vanishes for charge 0 or va-Vohu which means "void" in Hebrew in Genesis). All leptons and all flavours of quarks are combinations of three rishons. They are as follows: These groups of three rishons have spin ½. They are as follows: TTT=positron; VVV=electron neutrino; TTV, TVT and VTT=three colors of u quarks; TVV, VTV and VVT=three colors of d antiquarks. Each rishon has its antiparticle, therefore: ttt=electron; vvv=anti-electron neutrino; ttv, tvt, vtt=three colors of anti-u quarks; vvt, vtv, tvv=three colors of d quarks. Furthermore, the search for a neutrino mass has recently become a big in- dustry in recent years. “Today's neutrino detectors, kept deep underground to avoid stray particles on Earth's surface, may contain thousands of tons of fluid. While trillions of neutrinos pass through the fluid every day, only a few dozen are likely to be detected. Scientists have discovered that there are three types of neutrinos, each associated with a different charged particle for which it is named. Thus they are called the electron neutrino, muon neutrino, and tau neutrino. The first type of neutrino to be discovered was the electron neutrino, in 1959. The muon neutrino was discovered in 1962. The tau neu- trino has yet to be directly observed. It was inferred from the existence of the tau particle itself, which was discovered in 1978. The tau particle is involved in decay reactions with the same imbalance that Pauli solved for beta decay by postulating the electron neutrino.”[14] F. Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J, Hutchison 10 As we see, some of these questions are very tough, and it is likely they will trigger new kinds of experiments. Now from these ‘known’ questions, we can also ask some new questions for further development of theoretical physics: (i) Is it possible to come up with a quantum liquid model of elemen- tary particles? How can it predict the elementary particle masses? (ii) Could we find isolated quarks or rishons in Nature? (iii) Could we find isolated quarks or rishons in a strong electromag- netic field environment? (iv) If Koide’s concept of the democratic mixing matrix is proved true, then how could we find fluid a dynamical interpretation of this mixing matrix? (v) Could we find a theoretical explanation of quarks / rishons from the viewpoint of multivalued-logic Quantum Mechanics? (vi) Could we find a theoretical explanation of quarks / rishons from the viewpoint of Quaternion Quantum Mechanics? If yes, then how could we ascribe physical meaning to a scalar in the qua- ternion field? (vii) Is there also quaternion-type symmetry (see Adler’s QQM the- ory, for instance) in neutrino mass? (viii) Could we find a theoretical explanation of quarks / rishons from the viewpoint of the Gross-Pitaevskii equation for a rotating Bose-Einstein Condensate? If yes, then how does the Magnus ef- fect affect the rotational dynamics of the quarks? (ix) What is the effect of gravitational field on the charges of quarks and rishons? (x) Could we alter the charges or masses of quarks? If yes, then how could it be done?