Gauging Time Reversal Symmetry in Quantum Gravity

Arrow of Time from a Confinement–Deconfinement Transition

This repository contains the manuscript, figures, and supplementary materials for the paper "Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement–Deconfinement Transition" by Deepak Vaid.

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Abstract

This paper proposes that coherent cosmological time orientation can emerge as a gauge phenomenon. Binary tensor-network structure and paired signs of the LQG signed-volume operator motivate an effective $Z_2$ orientation field in a restricted four-valent $j=1/2$ spin-network sector. Adopting the minimal Wilson action gives a concrete mechanism:

• Confined phase — relative orientation cannot be transported coherently over macroscopic distances.
• Deconfined phase — long-distance orientation transport is coherent, as diagnosed by non-local gauge observables.

This is an effective proposal, not a completed derivation of the link field, Wilson coupling, semiclassical geometry, or cosmological trajectory from spin-foam dynamics. CZX is used as a controlled tensor-network reference construction, not identified with the projected LQG state. The numerical results are bounded controls of the adopted gauge theory and include a negative result for a tested signed-volume diagnostic.

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What's in This Repository

Path	Description
timesarrow.tex	Main LaTeX manuscript source (SciPost template)
arxiv_submission_v1/	Clean arXiv submission bundle (44 pages, 34 figures)
arxiv-submission-v1.tar.gz	Ready-to-upload tarball
figures/	TikZ source files and PNG diagrams
supplementary-calculations.tex	Detailed derivations for corrected arguments
web-static/	Static HTML web presentation of the paper
memory-bank/	Project memory bank (tasks, sessions, implementation docs)
ai-assistance-statement.md	Detailed statement of AI-assisted contributions
cover-letter.md	Submission cover letter for SciPost Physics

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Building the Paper

Requires a standard LaTeX distribution with biber (tested on TeX Live 2024):

# Build the manuscript
pdflatex timesarrow.tex
biber timesarrow
pdflatex timesarrow.tex
pdflatex timesarrow.tex

# Or use the build script
./buildtex

Note for Apple Silicon users: If biber fails with architecture mismatch, see memory-bank/implementation-details/biber-infrastructure-fix.md.

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Numerics & Simulation Code

This repository includes two numerical components for reproducing the paper's lattice gauge theory results:

TypeScript (numerics/)

• Purpose: Spin-network utilities, intertwiner computations, Z₂ lattice gauge theory configuration tools
• Requirements: Node.js 18+ (tested on Node.js 22.x)
• Build:

  cd numerics
  npm ci
  npx tsc --strict --noEmit

Rust (rust-lattice/)

• Purpose: High-performance Monte Carlo simulations of Z₂ lattice gauge theory (2D–4D)
• Requirements: Rust 1.92.0, pinned by rust-toolchain.toml (edition 2024)
• Build & test:

  cd rust-lattice
  cargo check
  cargo test

Full validation

Run ./scripts/validate.sh from the repository root to check the TypeScript build, Rust build, ordinary Rust tests, and Rust doctests. When local cargo/rustc proxy links are unavailable, the script resolves the pinned compiler tools directly through rustup. It exits with a non-zero status if any step fails.

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Key Results

1. Effective orientation proposal: a $Z_2$ link field motivated by binary bond data and paired signed-volume sectors in the restricted $j=1/2$ setting.
2. Concrete mechanism: confinement obstructs long-distance orientation comparison; deconfinement permits it, with Wilson and Polyakov observables providing gauge-invariant controls.
3. Microscopic boundary: an explicit operator calculation shows that the literal CZX unitary does not preserve the full $SU(2)$ singlet intertwiner subspace, so a new encoding map is required.
4. Reproducible numerical controls: canonical raw datasets and scripts locate the expected transition region; the tested signed-volume dressing is retained as a negative result.
5. Falsifiable next step: derive, modify, or rule out the effective field, action, and cosmological trajectory using microscopic spin-foam dynamics.

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Web Presentation

An interactive web presentation translating the paper's concepts for a broader audience is in development:

• Static version: web-static/ — deployed landing page
• Planned: Next.js interactive scrollytelling app with animated spin networks, vertex explorer, and tiered narrative (see memory-bank/implementation-details/gemini-web-presentation-plan.md)

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AI Assistance Statement

This manuscript originated as the author's independent work (2016–2018). During the April 2026 revision, Claude (Anthropic) was used as a writing assistant for formalization, LaTeX editing, bibliography management, and error correction. All physical ideas, arguments, and conclusions are the author's own.

A complete, commit-level account of AI-assisted contributions is available in:

• ai-assistance-statement.md
• The publicly auditable git history of this repository

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Citation

If you use this work, please cite:

@article{vaid2026gauging,
  title={Gauging Time Reversal Symmetry in Quantum Gravity: 
         Arrow of Time from a Confinement--Deconfinement Transition},
  author={Vaid, Deepak},
  journal={SciPost Physics},
  year={2026},
  url={https://github.com/space-cadet/timesarrow}
}

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Author

Deepak Vaid — Independent Researcher
📧 dvaid79@gmail.com
🌐 GitHub: @space-cadet

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License

The manuscript text and figures are © 2026 Deepak Vaid. Code and build scripts are released under the MIT License.