The World Formula: A Late Recognition of David Hilbert's Stroke of Genius

625 Pages·2022·39.948 MB·English

by  Norbert Schwarzer

The World Formula

The World Formula
A Late Recognition of David Hilbert’s
Stroke of Genius
Norbert Schwarzer
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TheWorldFormula:ALateRecognitionofDavidHilbert’sStrokeofGenius
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Dedication
Tothevictimsofignorantpoliticians.
Wewillnotforget.Wewillnotforgive.

Contents
Acknowledgment xvii
AbouttheBook xix
PersonalMotivation 1
SomeFundamentalMotivation 3
TheEighthDay(FromT.Bodan,withThanks) 11
PrefacetoTheEighthDay 11
PrefacetoTheFirstSevenDays 12
Why 13
EighthDay 13
Reichskristallnacht 16
ACourageousJewess 18
TheTwoBrothersandtheEinstein–HilbertAction 19
Judith,theLittleSister 28
BriefHoursofScholarship 29
TheEvacuation 33
BeforetheEndLiesaWaythroughFractalDimensions 36
TheLastPiece 45
TRIALS
1 TheHistoryofOurDevelopments 51
viii Contents
2 AnUnusualIntroduction 53
2.1 DerivationofElectromagneticInteraction(andMatter)viaa
SetofCreativeTransformations 55
2.1.1 IntelligentZeroApproaches:JustOneExample 63
2.1.2 IntroductionSummedUp 72
3 HowManyTheoriesofEverythingAreThere? 73
3.1 AbouttheTheoryofEverything 73
3.2 AMostFundamentalStartingPointandHowtoProceedfrom
There 74
3.3 TheRicciScalarQuantization 77
3.3.1 AbouttheOriginofMatter 78
3.3.2 PostulationofaConstantRicciScalar 84
3.3.3 IntermediateSum-Up 86
3.3.4 TheSituationinnDimensions 86
3.3.4.1 The2-dimensionalspace 87
3.3.4.2 The3-dimensionalspace 87
3.3.4.3 The4-dimensionalspace 87
3.3.4.4 The5-dimensionalspace 87
3.3.4.5 The6-dimensionalspace 88
3.3.4.6 The7-dimensionalspace 88
3.3.4.7 The8-dimensionalspace 89
3.3.4.8 The9-dimensionalspace 89
3.3.4.9 The10-dimensionalspace 89
3.3.5 PeriodicSpace-TimeSolutions 90
3.3.6 SphericalCoordinates 92
3.3.7 CartesianCoordinates 101
3.3.7.1 Asomewhatmoregeneralcase 101
3.3.7.2 The1Dharmonicoscillator 102
3.3.7.3 Thetotalvacuumcase 105
3.3.8 CylindricalCoordinates 105
3.3.9 SchwarzschildMetricinItsQuantumTransformed
Form 106
3.3.9.1 Discussion 112
3.3.9.2 Theotherquantumnumber 116
3.4 TheOtherHydrogen 121
3.4.1 MainlyGeometricInterpretation 123
3.4.2 Particles 132
Contents ix
3.4.3 Quarks? 136
3.4.4 TimeIndependentFermions? 138
3.4.5 TheOtherHydrogen:Conclusions 140
3.4.6 Appendix:AboutSpin1/2,3/2,5/2andsoon 141
3.5 ConsiderationoftheEinstein–HilbertSurfaceTerm 155
3.6 AsanExample:Considerationin4Dimensions 160
3.7 HeisenbergUncertaintyduetotheWigglyBackground 166
3.7.1 ConnectiontotheClassicalHeisenbergUncertainty
Principle 167
3.7.2 FindingOtherPrincipleLimits 169
3.8 VariationwithRespecttotheNumberofDimensions 170
3.8.1 SchwarzschildMetricasanExample 171
3.8.2 SolvingtheSingularityProblemforBlackHoles 173
3.9 UsingtheGeneralEinstein–HilbertActionwith f[R] 175
3.10 TheVariationoftheMetricTensor:BriefIntroduction 179
3.11 TheAdditiveVariationoftheMetricTensor 180
3.11.1 ASlightlyPhilisophicalStartingPoint 180
3.11.2 CombinationwithQuantumTheoryviatheVariation
ofBaseVectors—GettingStarted 181
3.11.3 ClassicalSolutionsinConnectionwiththeFlatSpace
Limit 185
3.11.4 SymmetryIssues 189
3.11.5 ExtensionandGeneralizationoftheQuantum
TransformationRules—SymmetricinCo-and
Contra-Variance 189
3.11.6 ExtensionandGeneralizationoftheQuantum
TransformationRules—AsymmetryinCo-and
Contra-Variance 197
3.11.7 Dirac’sPeculiar“Accident” 200
3.11.8 TheSpecialCaseoftheSchro¨dingerEquation—PartI 204
3.11.9 Klein–GordonandDiracEquationsofZero,First,
Second,andn-thOrder 207
3.11.9.1 L-Equations 208
3.11.9.2 Klein–Gordonequations 208
3.11.9.3 Diracequations 209
3.11.10WorldFormulae(?)—SummingUpandRepetitionof
theSimplest(Scalar)Form 211
3.12 ConnectionwiththeExtendedEinstein–HilbertVariation 213