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Is an Outline of the E8 Lie Algebra PROLOGUE I was David Finkelsten's student from the 1980s until his death on 24 January 2016. Here is my view of the last 100 years or so of physics: 1910s - Einstein-Hilbert General Relativity 1920s - Cambridge - Clifford Algebra Dirac Equation 1930s - Fission Chain Reaction 1940s - Harvard-Princeton - Schwinger-Feynman QED 1950s - Princeton IAS - Bohm Quantum created and rejected ! David Finkelstein invented Black Hole SpaceTime Metric and (with Misner) Kink-! ! Solitons related to Pion Breathers 1960s - Harvard - Schwinger Sources created and rejected ! David Finkelstein (with Jauch, Schiminovich, and Speiser) showed that Quaternions produced Massive Weak Bosons (now called Higgs mechanism) 1970s - Harvard - Standard Model ! Armand Wyler used Complex Domain Geometry of Loo-Keng Hua (and implicitly used Schwinger Sources) to calculate Force Strengths and Particle Masses 1980s - Harvard-Princeton-Caltech et al - Superstrings dominate physics ! David Finkelstein used Clifford Algebra for Space-Time Code and proposed ! that Our Universe began with a VOID fluctuation in a parent universe and ! ! evolved according to a chain of iterations of Real Clifford Algebras !! VOID !! Cl(VOID) = Z = Integers = 0-dimensional !! Cl(0) = R = Real Numbers = 1-dimensional !! Cl(1) = C = Complex Numbers = 2-dimensional !! Cl(2) = H = Quaternions = 4-dimensional !! Cl(4) = M2(H) = 2x2x4 = 16-dimensional !! Cl(16) = M256(R) = 256x256 = 65,536-dimensional ! David saw that the next step of iteration would produce Cl(65,536) which ! at 2^65,536-dimensions is large enough to include a realistic description of ! the Physics of Our Universe. 1990s - Caltech - Clifford Algebra, Quantum Information, and Particle Physics 2000s - LHC refuted Superstrings but No Alternatives Investigated Now - I have tried to summarize my work of the past 35 years or so in this book which is based on Clifford Algebra (David Finkelstein’s Cl(16)) and uses Geometry of Loo-Keng Hua and Schwinger Sources and is 422 pages (plus Prologue-Epilogue cover pages) pdf file (free book) on the web at http://vixra.org/abs/1905.0568 This book shows how realistic Physics model emerges from Cl(16) structure: ! Cl(16) Vectors = Spacetime = Shilov Boundary of Lie Ball Complex Domain ! Cl(16) BiVectors and half-Spinors = E8 = Gauge Bosons and Fermions ! ClI(16) TriVectors = 10 copies of 56-dim Fr3(O) = complexification of 27-dim !! J3(O) for 26D String=World-Line Theory whose spin-2 part = Bohm !! Quantum Potential and whose Tachyons produce virtual clouds of !! particles and antiparticles so that elementary particles are not points but !! are Schwinger Sources whose Green's Function propagators are !! Bergman Kernels of Complex Domains. (for Epilogue see last page - back cover) Cl(16) Science, Art, Music Frank Dodd (Tony) Smith, Jr. - 2019 Abstract There is a realistic Physics model, based on Real Clifford Algebras including Cl(16) and Cl(1,25). Part I describes Real Clifford Algebras. Part II of this book describes Clifford Algebra Physics and its calculations of Force Strengths, Particle Masses, Dark Energy : Dark Matter : Ordinary Matter ratio, Kobayashi-Maskawa Parameters, and 3 mass states of Higgs-Truth Quark Nambu-Jona-Lasinio System as they appear in Fermilab and LHC data. Part III describes how Clifford Algebra Physics is related to Art (specifically to The Large Glass by Marcel Duchamp) and to Music (specifically to the Grosse Fugue by Ludwig van Beethoven) and to Archetypes of the Red Book by Carl Gustav Jung. Part IV describes History: Universe - Humanity - my family. Part V describes Deuterium fusion D+D+D+D to He+He + 47.6 MeV by Klein Paradox Quantum Tunnelling in Palladium Clusters. ! Terminology note - I use the term Spinor for Column Vectors ! of full Matrix Algebras (such as Real Clifford Algebras) ! instead of their Even Subalgebras so what I call Spinors ! are what most people call Pinors. I hope that my usage ! will be clear from context. 1 Table of Contents Part I - Real Clifford Algebras ! Cl(VOID) -> Cl(16) Finkelstein Clifford Iteration Universe Origin ... page 4 ! Cl(n) for n = VOID,0,1,2,3 ... page 6 Cl(4) ... page 8 Cl(8) ... page 9 !! TriVectors = Fr3(O) !!! 26D String=World-Line Theory, Tachyons, Bohmions ... page 10 !! Vectors + BiVectors + Spinors = F4 !!! Spacetime, Gauge Bosons, Fermions ... page 14 !!!! Primes and Powers of 2 ... page 19 ! Cl(16) ... page 22 !! Cl(8) ✇ Cl(8) = Cl(16) ... page 23 !! H4 + H4 = E8 ... page 24 !! E8 Root Vectors ... page 25 !!! Fermion Particles ... page 26 !!! Fermion AntiParticles ... page 27 !!! Spacetime Creation/Annihilation ... page 28 !!! Standard Model Gauge Bosons ... page 30 !!! Gravity+Dark Energy Gauge Boson ... page 32 !! Overview Graphic for Cl(16) ... page 33 Part II - Cl(16) Physics ! Basic Structure of Cl(16) and Cl(1,25) Physics ... page 34 ! Cl(16) Vectors = Spacetime ... page 35 ! Cl(16) BiVectors and half-Spinors = Gauge Bosons and Fermions ... page 37 !! Octonionic E8 Root Vector Lagrangian ... page 38 !!! Subtle Supersymmetry (Octonionic) ... page 41 !! Quaternionic E8 Root Vector Lagrangian ... page 43 57 !!! Nambu-Jona-Lasinio Higgs-Truth Quark System ... page 59 !!!! CMS HIggs Histograms ... page 63 !!!! Fermilab Truth Quark data ... page 69 !!!!! Varnes Ph.D. Thesis ... page 70 !!!!! Dalitz, Goldstein, and Fermilab ... page 76 !!! Two D4 of D8 / D4xD4 ... page 78 !!! Schwinger Sources ... page 81 !!!! Visualization ... page 81 !!!! Symmetry of Sources ... page 87 !!!! Kernel and Green's Functions ... page 88 !!!! Masses and Force Strengths ... page 103 !!!! Size and Internal Structure ... page 106 !!!! Indra's Net Blockchain ... page 107 2 Table of Contents (cont'd) !!! Wyler Calculations of Force Strengths, Masses, etc ... page 122 !!!! Gauge Boson Geometry ... page 123 !!!! Force Strengths ... page 125 !!!! Higgs, W+, W-, Z0 Masses ... page 131 !!!! Fermion Masses ... page 136 !! !!! Kobayashi-Maskawa Parameters ... page 148 !!! Neutrino Masses beyond Tree Level ... page 158 !!! Proton-Neutron Mass Difference ... page 163 !!! Pion as Sine-Gordon Breather ... page 164 !!! Planck Mass ... page 169 !!! Conformal Gravity + Dark Energy and DE : DM : OM ... page 170 !!Results of Calculations, Coleman-Mandula, Chirality, !!! Spin-Statistics, 3 Generations ... pages 180-183 ! ClI(16) TriVectors = Fr3(O) 26D String=World-Line Theory ... page 184 !! Construction from J3(O)o ... page 188 !! Construction from E8 Redundancy ... page 193 !! Many-Worlds ... page 195 !!Creation/Annihilation and E8 Maximal Contraction ... page 197 !! Bohm Sutherland Lagrangian and Sarfatti Back-Reaction ... page 198 !! Algebraic Quantum Field Theory (AQFT) ... page 200 !! Penrose-Hameroff Quantum Consciousness ... page 205 Part III - Cl(16) and Art, Music, and Archetypes of Jung's Red Book ! Duchamp's Large Glass ... page 221 ! Beethoven's Grosse Fugue ... page 275 ! Jung's Red Book ... page 302 Part IV - History ! Universe from Big Bang to Manetho's Rule of Gods ... page 307 ! Humanity from Manetho's Decline of Gods to Now ... page 315 ! some of my family history ... page 349 Part V - Deuterium Fusion in Palladium Clusters !! by Klein Paradox Quantum Tunnelling ... page 377 3 Part I Real Clifford Algebras describe the algebra and geometry of vector spaces and their subspaces. They are matrix algebras whose entries are either Real Numbers (green in the diagram on the following page), Complex Numbers (white) or Quaternions (yellow). The diagram shows some Real Clifford Algebras Cl(p,q) for real vector spaces of signature (p,q). The p=0 line is Cl(0,q) = Cl(q). The diagram also shows the chain of Real Clifford Algebras used by David Finkelstein to describe the Origin of Our Universe: VOID Cl(VOID) = Z = Integers = 0-dimensional Cl(0) = R = Real Numbers = 1-dimensional Cl(1) = C = Complex Numbers = 2-dimensional Cl(2) = H = Quaternions = 4-dimensional Cl(4) = M2(H) = 2x2x4 = 16-dimensional Cl(16) = M256(R) = 256x256 = 65,536-dimensional The Finkelstein Clifford Iteration Process stops at Cl(16) because its 16-dim Vector part has Zero Divisors (arXiv math/0512517) given by fibration Spin(7) / Spin(5) = V(7,2) -> G2 -> S3 with symmetry of 10-dim Lie Sphere Spin(7) / Spin(5)xU(1) corresponding to Cl(1,9) = Cl(2,8) = M32(R) Conformal over Cl(1,7) = Cl(0,8) = M16(R) . The 16-dim Sedenion Zero Divisors have 7+28 = 35 Associative Triples. Further, although by 8-Periodicity Cl(16) = tensor product Cl(8) ✇ Cl(8) , neither Cl(8) = M16(R) nor 8-dim Vectors of Cl(8) are a Division Algebra . Cl(8) Vectors = Cl(3) = 8-dim associative algebra not the nonassociative Octonions . 4 5 Some details of Cl(n) describing algebra and geometry of n-dim space are: For the VOID that is just the Empty Set Cl(VOID) has no graded structure Cl(VOID) algebra = 0-dim Integers For 0-dim Space that is just a point Cl(0) has graded structure 0 where grade 0 = 1 type of 0-dim point algebra = Real Numbers with basis { 1 } Cl(0) algebra = 2^0 = 1-dim Real Numbers with basis { 1 } For 1-dim Space with coordinate x Cl(1) has graded structure 0 1 where grade 0 = 1 type of 0-dim point algebra = Real Numbers with basis { 1 } grade 1 = 1 type of 1-dim line algebra = Imaginary Numbers with basis { i } Cl(1) algebra = 2^1 = 2-dim Complex Numbers with basis { 1 i } For 2-dim Space with coordinates x y Cl(2) has graded structure 0 1 2 where grade 0 = 1 type of 0-dim point algebra = Real Numbers with basis { 1 } grade 1 = 2 types of 1-dim line algebra = Imaginary Numbers with basis { i j } grade 2 = 1 type of 2-dim area algebra = Imaginary Numbers with basis { k } Cl(2) algebra = 2^2 = 4-dim Quaternions with basis { 1 i j k } 6 For 3-dim Space with coordinates x y z Cl(3) has graded structure 0 1 2 3 where grade 0 = 1 type of 0-dim point grade 1 = 3 types of 1-dim line grade 2 = 3 types of 2-dim area grade 3 = 1 type of 3-dim volume Cl(3) algebra = 2^3 = 8 = (4+4)-dim Pair of Quaternions with basis { 1 i j k ; K J I E } Cl(3) is associative and differs from non-associative Octonions.
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