Einstein at Work on Unified Field Theory : The Five-Dimensional Einstein-Bergmann Approach

✍ Scribed by Tobias Schütz

• Publisher: Springer Nature Switzerland
• Year: 2024
• Tongue: English
• Leaves: 362
• Category: Library

✦ Table of Contents

Acknowledgments
Contents
List of Figures
List of Tables
1 Introduction
1.1 Motivation and Sources
1.1.1 The Collected Papers and the Princeton Manuscripts
1.1.2 Prague Notebook
1.2 Overview of Research Notes
1.3 Einstein's Education and His Way to General Relativity with a Special Focus on Mathematics
1.3.1 Primary and Secondary School in Munich, Milano, and Aarau
1.3.2 Einstein's Studies at ETH
1.3.3 Summary on Einstein's Education
1.3.4 Einstein's Way to General Relativity
1.3.4.1 Annus Mirabilis 1905
1.3.4.2 The Equivalence Principle and Its Consequences
1.3.4.3 Einstein's First Gravitational Theories and Comments on Abraham's Mathematical Approach
1.3.4.4 Nordström's First Theory on Gravitation
1.3.4.5 Einstein's Turn to Mathematics, the Zurich Notebook, and the Entwurf Theory
1.3.4.6 Nordström's Further Works and His Five-Dimensional Approach
1.3.4.7 Einstein's Final Steps to the Theory of General Relativity
1.4 Einstein's Unified Field Theory Program
1.5 Outline of Einstein's 1938 Program Based on SubsequentAnalysis
1.6 Einstein's Princeton Assistants
1.6.1 Peter Gabriel Bergmann
1.6.2 Valentine Bargmann
1.7 Structure of the Book
2 Einstein and Projective Geometry
2.1 Sources
2.1.1 The Prague Notebook and the Princeton Manuscripts
2.1.2 Projective Relativity and the Pasadena Diary
2.1.3 Bergmann Correspondence and the Point at Infinity
2.2 Theoretical Background
2.2.1 Literature
2.2.2 Notations
2.2.3 Pascal Line and Involution on a Conic
2.3 Analysis of Princeton Manuscripts and Further Working Sheets
2.3.1 AEA 62-785r
2.3.2 AEA 62-787r
2.3.3 AEA 62-789
2.3.4 AEA 62-789r
2.3.5 AEA 124-446
2.3.6 Further Notes
2.4 Summary of the Analysis
2.5 Prague Notebook and Its Connection with Princeton Manuscripts
2.6 Concluding Remarks
2.6.1 Conjecture on the Purpose of Einstein's Ideas About Projective Geometry
3 Different Pathways to the Generalization of Kaluza's Theory
3.1 Einstein's Field Equations of General Relativity
3.2 Einstein and Bergmann's Generalized Kaluza Theory
3.2.1 Space Structure and Properties
3.2.2 Field Equations of General Relativity
3.2.3 Field Equations in Generalized Kaluza Theory
3.2.3.1 First Action
3.2.3.2 Second Action
3.2.3.3 Third Action
3.2.3.4 Fourth Action
3.2.3.5 The Field Equations
3.2.3.6 The Identities
3.3 Einstein's Opinion on the New Theory
3.4 Einstein's Washington Manuscript
3.4.1 Einstein and Bergmann Correspondence
3.4.2 The Donation to the Library of Congress
3.4.3 Differences Between the Two Versions of the Manuscript
3.4.4 Axiomatic Structure of the Manuscript and its Differences to the Publication
3.4.4.1 The Title and Authorship
3.4.4.2 The Axiomatic Structure
3.4.4.3 The Mathematical Appendix
3.4.4.4 Further Differences
3.4.5 A Correction to the Proofs
3.5 Concluding Remarks on the Washington Manuscript
3.6 Manuscript Pages Dealing with the 1938 Theory
3.6.1 AEA 62-789
3.6.2 AEA 62-798
3.6.3 AEA 62-802 and AEA 62-794
3.6.3.1 Neglecting the Derivatives of the Christoffel Symbols
3.6.4 AEA 62-785
3.7 Concluding Remarks
4 Einstein's Further Considerations on the Generalized Kaluza Theory
4.1 Einstein and Bergmann's Correspondence: Dating the Letters
4.2 Context of Einstein's Further Calculations
4.2.1 Most Important Relations of the Generalized Kaluza Theory
4.2.2 Wave Equations and the Stromgleichung
4.2.3 The Usage of Different Notations
4.2.4 Einstein's Ansatz
4.2.4.1 Interpretation of the Stromgleichung
4.2.4.2 The Potential
4.2.4.3 Ansatz in Bargmann Correspondence, 1939
4.2.4.4 Ansatz in P. Bergmann Correspondence 1938
4.2.4.5 The Ansatz: Combining the Two Approaches
4.2.4.6 How to Derive the Stromgleichung
4.2.4.7 A Second Approach
4.3 Manuscript Pages Related to Publication, Correspondence, and Further Development
4.3.1 Sheets Containing Sketches on Projective Geometry
4.3.1.1 AEA 62-785r
4.3.1.2 AEA 62-787r
4.3.1.3 AEA 62-789r
4.3.1.4 Dating All Manuscript Pages on Projective Geometry
4.3.1.5 Additional Remarks to the Conjecture on the Purpose of Einstein's Ideas on Projective Geometry
4.3.2 Power Series Expansions of beta and eta at Zero and Infinity
4.3.3 Calculations on F1 to F4 and on the Laplace Operator
4.3.4 Rewriting the Equations in Terms of Rho
4.3.5 Sheets Containing Idiosyncratic Relations and Considerations
4.3.6 Considerations on Different Expressions for Rho
4.3.7 AEA 62-791: An Example for Both Mistakes and Skills
4.3.8 Further Sheets
4.4 Concluding Remarks
5 Considerations on Delta Functions
5.1 Theoretical Background
5.2 Analysis of Related Manuscript Pages and Correspondence
5.2.1 AEA 62-783
5.2.2 Related Correspondence
5.2.3 An Expression for the Functions a, b, d, and e
5.2.3.1 Further Procedure
5.2.4 AEA 62-795
5.2.5 AEA 62-795r
5.2.6 An Expression Similar to Delta-Function from 1938
5.2.7 Further Manuscript Pages
5.2.8 AEA 63-058r
5.3 Concluding Remarks
6 Conclusion
References
Index of Research Notes, Letters, and Further Documents