Space-Time Geometry Framework

Overview

This repository contains the Space-Time Geometry Framework for visualizing quantum wavefunctions with time treated as a spatial-like dimension. The framework uses a polar (or cylindrical) coordinate representation of spacetime, incorporates phase encoding via hue, and provides both a theoretical foundation and practical examples (e.g., Klein–Gordon, Dirac, double-slit, tunneling scenarios).

Key Features

• Polar-Coordinate Wavefunction Mapping: Transforms (x,t) to (r,theta) to unify time and space in a single 2D or 3D plot.
• Phase Encoding: Visualizes quantum interference through a hue-based color map.
• Relativistic Extensions: Includes discussions on Minkowski spacetime, Lorentz invariance, and conceptual paths toward curved metrics in general relativity.
• Many-Worlds Interpretation (MWI): Demonstrates how separate “branches” can be represented as orthogonal angular sectors.

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Repository Structure

.
├── appendices
│   ├── 1_detailed_mathematical_derivations
│   ├── 2_mwi_visualization_and_case_studies
│   ├── 3_code_implementation_considerations
│   └── 4_extensions_to_general_relativity_and_metric_comparisons
│
├── paper
│   ├── images               # Placeholder or actual figures for the paper
│   ├── references.bib       # BibTeX references
│   ├── ripples_in_spacetime.pdf   # Compiled PDF
│   ├── ripples_in_spacetime.tex   # Main LaTeX source
│
├── draft_paper.ipynb       # Jupyter notebook for prototyping or data analysis
├── profile.prof            # Profiling output (if relevant to performance tests)
├── README.md               # This README
└── requirements.txt        # Python/LaTeX packages if needed for easy setup

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Description of Major Components

1. appendices/

   • Each appendix is split into its own file/folder for detailed derivations, MWI discussion, implementation notes, and relativistic extensions.
   • 1_detailed_mathematical_derivations: Covers rigorous proofs of wavefunction normalization, coordinate transformations, phase encoding, etc.
   • 2_mwi_visualization_and_case_studies: Showcases Gaussian packets, double-slit experiments, entanglement, and more—mapped into the polar/hue space.
   • 3_code_implementation_considerations: Addresses performance, parallelization, color map strategies, and integration with simulation libraries.
   • 4_extensions_to_general_relativity_and_metric_comparisons: Explores applying the framework to curved spacetimes and advanced GR scenarios.

2. paper/

   • Houses the main LaTeX paper (ripples_in_spacetime.tex), which compiles into ripples_in_spacetime.pdf.
   • images/ is a placeholder (or actual) directory for figures referenced in the paper.
   • The auxiliary files (.aux, .bbl, .blg, .log, .toc, etc.) are auto-generated by LaTeX.
   • references.bib contains all citations used in the paper (BibTeX format).

3. draft_paper.ipynb

   • An optional Jupyter notebook for prototyping, data analysis, or interactive exploration of wavefunction transformations.
   • May also store small code snippets for testing numeric methods.

4. profile.prof

   • Profiling data for performance (if you used a profiler on any code).
   • Might help optimize wavefunction simulations or large-scale rendering.

5. requirements.txt

   • Lists Python or LaTeX packages (if any) required to replicate the environment.
   • If the project uses a Python-based simulation, this helps others install dependencies easily (e.g., pip install -r requirements.txt).

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