Draft dated January 19, 2008 HADRONIC MATHEMATICS, MECHANICS AND CHEMISTRY Volume II: Isodual Theory of Antimatter Antigravity and Spacetime Machines Ruggero Maria Santilli CV: http://www.i-b-r.org/Ruggero-Maria-Santilli.htm President Institute for Basic Research P. O. Box 1577, Palm Harbor, FL 34682, U.S.A. [email protected], http://www.i-b-r.org http://www.neutronstructure.org http://www.magnegas.com International Academic Press Copyright (cid:13)c 2007 owned by Ruggero Maria Santilli P. O. Box 1577, Palm Harbor, FL 34682, U.S.A. All rights reserved. This book can be reproduced in its entirely or in part, or stored in a retrieval system or transmitted in any form, provided that the source and its paternity are identified fully and clearly. Violators will be prosecuted in the U. S. Federal Court and lawsuits will be listed in the web site http://www.scientificethics.org U. S. Library of Congress Cataloguing in publication data: Santilli, Ruggero Maria, 1935 – Foundations of Hadronic Mathematics Mechanics and Chemistry Volume II: Isodual Theory of Antimatter Antigravity and Spacetime Machines with Bibliography and Index Additional data sup-plied on request INTERNATIONAL ACADEMIC PRESS This volume is dedicated to the memory of Professor Grigorios Tsagas in recognition of his pioneering work on the Lie-Santilli isotheory. Contents Foreword vii Preface x Legal Notice xiii Acknowledgments xv 2. ISODUAL THEORY OF POINT-LIKE ANTIPARTICLES 163 2.1 ELEMENTS OF ISODUAL MATHEMATICS 163 2.1.1 Isodual Unit, Isodual Numbers and Isodual Fields 163 2.1.2 Isodual Functional Analysis 167 2.1.3 Isodual Differential and Integral Calculus 168 2.1.4 Lie-Santilli Isodual Theory 169 2.1.5 Isodual Euclidean Geometry 170 2.1.6 Isodual Minkowskian Geometry 171 2.1.7 Isodual Riemannian Geometry 172 2.2 CLASSICAL ISODUAL THEORY OF POINT-LIKE ANTIPARTICLES 174 2.2.1 Basic Assumptions 174 2.2.2 Need for Isoduality to Represent All Time Directions 175 2.2.3 Experimental Verification of the Isodual Theory of Antimatter in Classical Physics 176 2.2.4 Isodual Newtonian Mechanics 177 2.2.5 Isodual Lagrangian Mechanics 180 2.2.6 Isodual Hamiltonian Mechanics 180 2.2.7 Isodual Galilean Relativity 182 2.2.8 Isodual Special Relativity 184 2.2.9 Inequivalence of Isodual and Spacetime Inversions 188 2.2.10 Dunning-Davies Isodual Thermodynamics of Antimatter 189 2.2.11 Isodual General Relativity 190 2.3 OPERATOR ISODUAL THEORY OF POINT-LIKE ANTIPARTICLES 191 2.3.1 Basic Assumptions 191 2.3.2 Isodual Quantization 192 2.3.3 Isodual Hilbert Spaces 193 2.3.4 Isoselfduality of Minkowski’s Line Elements and Hilbert’s Inner Products 195 2.3.5 Isodual Schr¨odinger and Heisenberg’s Equations 195 vi RUGGERO MARIA SANTILLI 2.3.6 Isoselfdual Re-Interpretation of Dirac’s Equation 196 2.3.7 Equivalence of Isoduality and charge conjugation 199 2.3.8 Experimental Verification of the Isodual Theory of Antimatter in Particle Physics 202 2.3.9 Elementary Particles and their Isoduals 202 2.3.10 Photons and their Isoduals 203 2.3.11 Electrons and their Isoduals 205 2.3.12 Protons and their Isoduals 205 2.3.13 The Hydrogen Atom and its Isodual 206 2.3.14 Isoselfdual Bound States 207 2.3.15 Resolution of the Inconsistencies of Negative Energies 209 2.4 THEORETICAL PREDICTIONS OF ANTIGRAVITY 210 2.4.1 The Problem for Studies on Antigravity: Ethical Decay in Physics 210 2.4.2 Outline of the Literature on Antigravity 212 2.4.3 Newtonian and Euclidean Prediction of Antigravity 213 2.4.4 Minkowskian and Riemannian Predictions of Antigravity 215 2.4.5 Prediction of Antigravity from Isodual Einstein’s Gravitation 216 2.4.6 Identification of Gravitation and Electromagnetism 218 2.4.7 Prediction of Antigravity from the Identification of Gravitation and Electromagnetism 222 2.4.8 Prediction of Gravitational Repulsion for Isodual Light Emitted by Antimatter 223 2.5 EXPERIMENTAL VERIFICATION OF ANTIGRAVITY 224 2.5.1 Santilli’s Proposed Test of Antigravity for Positrons in Horizontal Flight 224 2.5.2 Santilli’s Proposed Tests of Antigravity for Isodual Light 229 2.5.3 Mills’ Studies of Santilli’s Proposed Tests of Antigravity 230 2.6 SPACETIME LOCOMOTIONS 235 2.6.1 Introduction 235 2.6.2 Causal Time Machine 236 2.6.3 Isogeometric Propulsion 238 References 243 Postscript 246 Index 251 Index 255 Foreword Mathematics is a subject which possibly finds itself in a unique position in academia in that it is viewed as both an Art and a Science. Indeed, in different universities, graduates in mathematics may receive Bachelor Degrees in Arts or Sciences. This probably reflects the dual nature of the subject. On the one hand, it may be studied as a subject in its own right. In this sense, its own beauty is there for all to behold; some as serene as da Vinci’s “Madonna of the Rocks”, other as powerful and majestic as Michelangelo’s glorious ceiling of the Sistine Chapel, yet more bringing to mind the impressionist brilliance of Monet’s Water Lily series. It is this latter example, with the impressionists interest in light, that links up with the alternative view of mathematics; that view which sees mathematics as the language of science, of physics in particular since physics is that area of science at the very hub of all scientific endeavour, all other branches being dependent on it to some degree. In this guise, however, mathematics is really a tool and any results obtained are of interest only if they relate to what is found in the real world; if results predict some effect, that prediction must be verified by observation and/or experiment. Again, it may be remembered that physics is really a collection of related theories. These theories are all manmade and, as such, are incomplete and imperfect. This is where the work of Ruggero Santilli enters the scientific arena. Although “conventional wisdom” dictates otherwise, both the widely accepted theories of relativity and quantum mechanics, particularly quantum mechanics, areincomplete. Thequalmssurroundingbothhavebeenmutedbutpossiblymore has emerged concerning the inadequacies of quantum mechanics because of the people raising them. Notably, although it is not publicly stated too frequently, Einstein had grave doubts about various aspects of quantum mechanics. Much of the worry has revolved around the role of the observer and over the question of whether quantum mechanics is an objective theory or not. One notable contrib- utor to the debate has been that eminent philosopher of science, Karl Popper. As discussed in my book, “Exploding a Myth”, Popper preferred to refer to the experimentalist rather than observer, and expressed the view that that person played the same role in quantum mechanics as in classical mechanics. He felt, therefore, that such a person was there to test the theory. This is totally opposed to the Copenhagen Interpretation which claims that “objective reality has evap- orated” and “quantum mechanics does not represent particles, but rather our knowledge, our observations, or our consciousness, of particles”. Popper points viii RUGGERO MARIA SANTILLI out that, over the years, many eminent physicists have switched allegiance from the pro-Copenhagen view. In some ways, the most important of these people was David Bohm, a greatly respected thinker on scientific matters who wrote a book presenting the Copenhagen view of quantum mechanics in minute detail. However, later, apparently under Einstein’s influence, he reached the conclusion that his previous view had been in error and also declared the total falsity of the constantly repeated dogma that the quantum theory is complete. It was, of course, this very question of whether or not quantum mechanics is complete which formed the basis of the disagreement between Einstein and Bohr; Einstein stating “No”, Bohr “Yes”. However, where does Popper fit into anything to do with Hadronic Mechanics? Quite simply, it was Karl Popper who first drew public attention to the thoughts and ideas of Ruggero Santilli. Popper reflected on, amongst other things, Chad- wick’s neutron. He noted that it could be viewed, and indeed was interpreted originally, as being composed of a proton and an electron. However, again as he notes, orthodox quantum mechanics offered no viable explanation for such a structure. Hence, in time, it became accepted as a new particle. Popper then noted that, around his (Popper’s) time of writing, Santilli had produced an arti- cle in which the “first structure model of the neutron” was revived by “resolving the technical difficulties which had led, historically, to the abandonment of the model”. It is noted that Santilli felt the difficulties were all associated with the assumptionthatquantummechanicsappliedwithintheneutronanddisappeared when a generalised mechanics is used. Later, Popper goes on to claim Santilli to belong to a new generation of scientists which seemed to him to move on a different path. Popper identifies quite clearly how, in his approach, Santilli dis- tinguishes the region of the arena of incontrovertible applicability of quantum mechanics from nuclear mechanics and hadronics. He notes also his most fas- cinating arguments in support of the view that quantum mechanics should not, without new tests, be regarded as valid in nuclear and hadronic mechanics. Ruggero Santilli has devoted his life to examining the possibility of extending the theories of quantum mechanics and relativity so that the new more general theories will apply in situations previously excluded from them. To do this, he has had to go back to the very foundations and develop new mathematics and new mathematical techniques. Only after these new tools were developed was he able to realistically examine the physical situations which originally provoked this lifetime’s work. The actual science is his, and his alone, but, as with the realization of all great endeavours, he has not been alone. The support and encouragement he has received from his wife Carla cannot be exaggerated. In truth, the scientific achievements of Ruggero Santiili may be seen, in one light, as the results of a team effort; a team composed of Ruggero himself and Carla GandiglioinSantilli. Thetheoreticalfoundationsoftheentireworkarecontained HADRONIC MATHEMATICS, MECHANICS AND CHEMISTRY ix in this volume; a volume which should be studied rigorously and with a truly open mind by the scientific community at large. This volume contains work which might be thought almost artistic in nature and is that part of the whole possessing the beauty so beloved of mathematicians and great artists. However, the scientific community should reserve its final judgement until it has had a chance to view the experimental and practical evidence which may be produced later in support of this elegant new theoretical framework. Jeremy Dunning-Davies, Physics Department, University of Hull, England. September 8, 2007 Preface The author has indicated various times in his works that Albert Einstein has beenthebiggestscientistofthe20-thcentury,butalsothemostexploitedscientist in history, because organized academic, financial and ethnic interests on Einstein have pushed the validity of his views way beyond the conditions of his original conception,bythereforeturningwhatissupposedtobeaseriousscientificprocess into a pool of often ascientific conduits generally manipulated for personal gains. This volume presents a solution of one of the several scientific imbalances of historical proportions caused by said ascientific interests in science, the abuse of academic authority and public funds to impose Einstein ’s special and general relativityforthetreatmentofantimatter,whileinthescientificrealityEinsteinian theorieshavenomeansforaquantitativeclassicaldifferentiationbetweenneutral matter and antimatter, and even when assumed for charged classical particles, their operator image is a particle (rather than the correct charge conjugated antiparticle) with the wrong sign of the charge. To defend the name of Albert Einstein, it must be noted that antimatter had yet to be discovered at the time of the formulation of his theories. Hence, the entire responsibility of this large scientific imbalance, and the expected severe judgment by posterity, must solely rest with said organized academic, financial and ethnic interests that extended for personal gains Einstein’s views beyond the conditions of their original conception without a serious scrutiny. Thesolutionpresentedinthisvolumeofthehistoricalimbalancebetweenmat- ter and antimatter is based on the necessary development of a new mathematics, today called Santilli isodual mathematics, allowing for the first time the classical representation of antimatter as an anti-isomorphic image of that for matter. The isodual conjugation then persists under quantization, where it turns out to be equivalent to charge conjugation, thus restoring a full equivalence and scientific democracy in the treatment of matter and antimatter at all levels, from Newto- nianmechanicstosecondquantization. Theresultingisodualtheoryofantimatter then verifies, by conception and construction, all available experimental data on antimatter at the classical and operator level. It should be stressed that, by no mans, the isodual theory of antimatter is presented as final, or complete or unique, because so many intriguing problems remain open. However, its dismissal in the absence of an alternative broadening of Einsteinian doctrines must be denounced as scientific corruption for personal