— DOWNLOADABLE SECTIONS AND SUBSECTIONS —
Full Paper
1. INTRODUCTION
1.1 Background and Motivations
2.1 Review of General Relativity
2.2 Einstein’s Field Equations
2.3 Extending the Framework of Dimensions
2.4 Foundational Criteria for Dimensions
2.5 Implications of the New Dimensions
2.6 Manifestations of the New Dimensions
3. DEVELOPMENT OF A 7-DIMENSIONAL HYPOTHESIS
3.1 Emergence of Dimensions and the Foundations of Physical Law
3.2 Mathematical Framework for a 7-Dimensional Universe
3.3 Modified Field Equations in 7 Dimensions
3.4 Using the modified field equations to explain expansion
3.5 Modified Equations and Singularities in the Universe
3.6 The Role of Chance: Quantum Mechanics and the 7dU
3.7 Implications for the Quantum Scale
4. INTEGRATION OF THE SCHRÖDINGER EQUATION
4.1 The Standard Schrödinger Equation
4.2 The Dimension of Chance and Quantum Mechanics
4.3 Physical Interpretation of Chance
4.4 Implications for Quantum Mechanics
4.6 Mathematical Consistency in the 7dU
5.0 THE HEISENBERG UNCERTAINTY PRINCIPLE IN A 7dU
5.1 Heisenberg Uncertainty Principle
5.2 Impact of the Dimension of Chance
5.3 Generalized Uncertainty Relation
5.4 Mathematical Derivation in the Framework
5.5 Physical Implications of the Modified HUP
5.7 Complementarity with the 7dU Framework
6.0 UNIFYING QUANTUM MECHANICS AND GENERAL RELATIVITY
6.1 Introduction to Unification
6.2 Geometric Basis for Quantum Randomness
6.3 Coupling Quantum Mechanics with General Relativity
6.4 Implications for Quantum Gravity
7. TESTING THE 7-DIMENSIONAL UNIVERSE
7.1 Comparison with Observational Data
7.2 Proposed Experiments to Test the 7dU Hypotheses
7.3 Implications for the Quantum Scale
8. DISCUSSION AND INTERPRETATION OF RESULTS
8.1 Implications of Living in a 7dU
8.2 Philosophical Implications of a 7dU
9. CONCLUSION
9.2 Implications for Cosmology and Quantum Mechanics
9.4 A Final Prompt
Appendix Directory – Field Notes – Proofs
Appendix 1 – On Absolute Absence – FN
Appendix 2 – On Absolutely Everything – FN
Appendix 3 – On Chance – FN
Appendix 4 – On Zero – FN
Appendix 5 – On Infinity – FN
Appendix 6 – On Pi – FN
Appendix 7 – On Time – FN
Appendix 8 – On Spatial Dimensionality – FN
Appendix 9 – On Absolutely Something – FN
Appendix 10 – Force Unification via Probabilistic Scaling
Appendix 11 – Dimensional Reduction of 7dU to General Relativity
Appendix 12 – Dark Geometry and Expansion
Appendix 13 – The Emergence of Quantum Gravity
Other Works, Field Notes, Proofs, etc.