The Theory of Everything: Quantum and Relativity is everywhere – A Fermat Universe PDF
Preview The Theory of Everything: Quantum and Relativity is everywhere – A Fermat Universe
The Theory of Everything The Theory of Everything Quantum and Relativity is Everywhere – A Fermat Universe Norbert Schwarzer Published by JennyStanfordPublishingPte.Ltd. Level34,CentennialTower 3TemasekAvenue Singapore039190 Email:[email protected] Web:www.jennystanford.com British Library Cataloguing-in-Publication Data AcataloguerecordforthisbookisavailablefromtheBritishLibrary. The Theory of Everything: Quantum and Relativity is Everywhere – A Fermat Universe Copyright �c 2020JennyStanfordPublishingPte.Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughthe CopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.In thiscasepermissiontophotocopyisnotrequiredfromthepublisher. ISBN978-981-4774-47-5(Hardcover) ISBN978-1-315-09975-0(eBook) MeinenEltern,meinerFrauundunseren4Kindern Contents About Motivation and Luck xi 1 Brief Introduction 1 TheStamlerApproach:ABriefHistoricalOverviewofthe OriginalIdea 1 2 Theory 7 TheGeneralizedMetricDiracOperator 7 ScalarProductinLaplace–BeltramiForm 10 Example:SchwarzschildMetric 15 TransitiontotheMetricSchro¨dingerorCovariantSchro¨ dinger Equation 16 FurtherConsiderations 18 Example:TheClassicalDiracEquationintheMinkowski Space-TimeandItsExtensiontoArbitraryCoordinates 20 TheConnectiontotheEinsteinFieldEquations 24 SummingUptheRecipe:TheForwardDerivation 25 SummingUptheRecipe:TheBackwardDerivation 26 Example:TheHiggsField 27 Example:EigenvalueSolutionsforSimpleFieldswith K(f )= F (f ) ∗ f = p ∗ f 29 m m m m m 3 The 1D Quantum Oscillator in the Metric Picture 31 TheClassicalHarmonicQuantumOscillatorwithintheMetric PictureortheTheoryofEverything 32 Gaussian-LikeMetricApproach 41 viii Contents Cos-LikeMetricApproach 44 QuestionofQuantizingtheSolution 45 TheLevelUnderneath 50 Conclusionstothe“EinsteinOscillator” 52 4 The Quantized Schwarzschild Metric 55 TheQuantizationofTimeintheVicinityofaSchwarzschildObject 57 TheQuantizationofMassforaSchwarzschildObject 58 TheLevelUnderneath(seealso[16]orSection“The1DQuantum OscillatorintheMetricPicture”) 59 InvestigationsinConnectionwiththeSpeedofLightwithinthe LevelUnderneath 60 DiscussionwithRespecttor (n )/t(n)= c 62 s r t level2 DiscussionwithRespecttor (n ,n)/t(n , n)= c 63 end r t r t level2 HowtoEvaluatetheSpeedofLightoftheLevelUnderneath? 64 ConclusionstoQuantizedSchwarzschild 65 5 Matter–Antimatter Asymmetry 67 ApplicationtoDirac–SchwarzschildParticlesatRest 67 6 Generalization of “The Recipe”: From ���to the Planck Tensor 69 GeneralizationtoNon-diagonalMetrics 69 Generalizationofthe“CleverZero” 73 TheGeneralized“VectorialDiracRoot” 73 ExamplesforOther“VectorialDiracRoots” 77 Simplesquarerootwithshearcomponentwith(cid:2)(X )= X 2 77 Simplesquarerootwithshearcomponentwith(cid:2)(X )= X 2with virtualparametersE ofvariousordersof“virtuality” 77 i Simplecubicroot(cid:2)(X )= X 3 78 Simplecubicroot(cid:2)(X )= X 3withvirtualparameterc 79 Simplequarticroot(cid:2)(X )= X 4 79 Simplequarticroot(cid:2)(X )= X 4withvirtualparameterc 80 Extension/GeneralizationtoArbitraryFunctionalApproachesfor K(f ) 81 n ThePlanckfunctional 81 Extension/GeneralizationtoArbitraryDerivativeApproaches:The GeneralizedGradientof f 82 n Contents ix Extension/GeneralizationtoHigher-OrderPlanckTensors 83 SummingUptheGeneralizedRecipe:TheForwardDerivation 84 SummingUptheGeneralizedRecipe:TheBackwardDerivation 85 BackwardExample:TheHiggsFieldRevisited(Extended Considerationfrom[15]) 86 ForwardExample:TheHarmonicOscillatorandEigenvalue SolutionsforSimpleFieldswithK(f )= F (f ) ∗ f = p ∗ f m m m m m Revisited(ExtendedConsiderationfrom[10]) 94 Conclusionsto“GeneralizationoftheRecipe” 97 7 About Fermat’s Last Theorem 99 Introduction 99 Motivation 100 WhyisThat? 100 Fermat’sOwnProof? 101 8 Dirac Quantization of the Kerr Metric 103 TheGeneralizedMetricDiracOperatorforaKerrObject“atRest” 103 FurtherResultsandTrials 106 TheSpatialAppearanceoftheLeptons 109 ConclusionstotheQuantizedSchwarzschildandKerrObjects 111 9 The Photon 115 ThePhotonMetric 115 ConnectionswithMaxwell 119 TheOtherWaytoFulfilltheMaxwellEquationswithPlaneWaves 121 Illustrations 122 SpatialExtensionoftheSolutionandtheLocalizedPhoton 123 LocalizingthePhotonForcesIttoEvolveSpin 128 OptionA:LeadingtoMagneticCharges 130 OptionB:LeadingtoMagneticDisplacementCurrentDensity 131 OptionC:FindingtheCorrectMetric,aYetUnsolvedProblem 132 SuspicionaboutConnectionstoCompactifiedCoordinates 137 TheAlternativeInterpretationUsingRealandImaginaryPart 140 FurtherIllustrationsandaFewWordsabouttheAbsenceof MagneticMonopolesinOurObservableUniverse 143 TheTotalSpatialDisplacementforthePhoton 146 ConclusionstothePhoton 148
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