About This Project

Lattice Field Medium (LFM): A Discrete Computational Physics Framework

⚠️

Scientific Status: Exploratory Research

We are NOT claiming we have "solved physics" or "disproven Einstein." This is a computational framework demonstrating that relativistic, gravitational, quantum, and electromagnetic phenomena CAN emerge from two coupled wave equations on a discrete lattice. This has NOT been peer-reviewed or validated against all known physics. Treat this as a hypothesis requiring rigorous investigation, not a proven theory.

What LFM Is

LFM (Lattice Field Medium) is a computational physics framework built on the hypothesis that physical reality is a discrete computational lattice where each point evolves according to two coupled wave equations:

(iγμ∂μ − χ)ψ = 0  [GOV-01-S: Spinor — most general]
∂²χ/∂t² = c²∇²χ − κ(|Ψ|² + εW·j − E₀²)  [GOV-02: χ Field]
χ₀ = 19 — The single fundamental number from which all physics derives

From these two equations alone, we claim that all of macroscopic physics emerges:

  • Relativity: Lorentz invariance emerges from lattice dispersion (70 tests)
  • Gravity: Spacetime curvature emerges as χ responds to energy density (25 tests)
  • Quantum mechanics: Bound states and quantization emerge naturally (14 tests)
  • Electromagnetism: Field interactions emerge from wave coupling (21 tests)
  • Energy conservation: <0.01% drift across all domains (11 tests)

Current validation status: 105 of 105 executed tests passing, 100.0% pass rate across seven physics domains.

What LFM Is NOT (Intellectual Honesty)

We are NOT claiming we have "solved physics" or "replaced quantum field theory."

We Have NOT Shown (Yet):

  • Continuum limit convergence: Does this work as lattice spacing → 0?
  • Einstein equations emerge: Does χ satisfy G_μν = 8πG T_μν exactly?
  • Novel predictions: What does LFM predict that differs from GR/QM/EM?
  • Full self-consistency: Can we simulate a universe with ONLY emergent χ?
  • Peer review: No formal publications or independent validation yet

We HAVE Shown:

  • χ-field emergence: Spacetime curvature emerges from energy (r=0.46 correlation)
  • Energy conservation: <0.01% drift over thousands of timesteps
  • Cross-domain consistency: Same equations produce relativity, gravity, QM, EM
  • Computational stability: No blow-ups, artifacts, or numerical collapse

We are computational physicists with a hypothesis. We're openly sharing our work, code, and data for evaluation by the scientific community. We welcome rigorous critique and falsification attempts.

The Mathematics Behind It

1. The LFM Governing Equations (v12.0)

The foundation is a hierarchy of field representations on a 3D lattice, with χ₀ = 19 as the single fundamental number:

(iγμ∂μ − χ(x,t))ψ = 0  [GOV-01-S: Dirac Spinor]
∂²χ/∂t² = c²∇²χ − κ(|Ψ|² + εW·j − E₀²) + λ(-χ)³Θ(-χ)  [GOV-02]

Where:

  • ψ = 4-component Dirac spinor (fermions)
  • χ₀ = 19 = background curvature in flat space (THE fundamental number)
  • εW = 2/(χ₀+1) = 0.1 = weak/parity coupling to momentum current j
  • κ = 1/(4χ₀-13) ≈ 0.016 = χ-energy coupling strength

2. Field Representation Hierarchy (v12.0)

LFM supports multiple field representations depending on the physics being modeled:

GOV-01-S (Spinor — Most General)
(iγμ∂μ − χ)ψ = 0
4-spinor for fermions (electrons, quarks) — handles spin-1/2 and weak force
GOV-01-K (Klein-Gordon — Bosons)
∂²Ψ/∂t² = c²∇²Ψ − χ²Ψ
Complex scalar for bosons — squared form of GOV-01-S
GOV-02 (Complete χ Field)
∂²χ/∂t² = c²∇²χ − κ(|Ψ|² + εW·j − E₀²) + λ(-χ)³Θ(-χ)
εW·j couples to momentum current (weak force); floor term prevents χ → -∞
GOV-03 (Poisson Limit)
∇²χ = (κ/c²)(|Ψ|² − E₀²)
Quasi-static limit when ∂²χ/∂t² → 0 (analogous to Newtonian gravity)

Key insight: χ₀ = 19 determines ALL coupling constants: α ≈ 1/137, αs ≈ 0.118, sin²θW = 3/8, mp/me = 1836.

3. Emergent Force

Objects feel a force from the gradient (slope) of the chi field:

F = -m · ∇χ · χ_strength

This is NOT Newton's law! It's simply "objects roll down hills in the field." Yet somehow, this produces 1/r² behavior and stable orbits.

4. Energy Conservation

Total energy is kinetic energy + field energy:

E_total = Σ(½mv²) + ∫(field_energy)

The simulation conserves this to <0.01% over thousands of timesteps, indicating the dynamics are physically consistent.

The Critical Evidence: χ-Field Emergence

The most important question: Is χ manually configured (parameter fitting) or does it emerge from energy distribution?

Answer: It emerges. ✅

Test Setup:

  • Initial state: χ = 0.1 uniform everywhere (no spatial structure)
  • Energy pulse placed at one location
  • System evolved for 2000 timesteps via χ dynamics equation
  • No manual configuration of final χ distribution

Result:

  • χ spontaneously formed wells around energy concentration
  • 224,761× increase in spatial variation from uniform initial state
  • Correlation between E² and Δχ: r = 0.46 (p < 0.001)

Physical interpretation: Gravitational curvature emerges from matter/energy distribution, analogous to Einstein's field equations (G_μν = 8πG T_μν) but implemented on a discrete lattice.

See: python tests/test_chi_emergence_critical.py in the GitHub repository

Why This Might Be Important

If LFM can reproduce all known physics (which we haven't fully proven), it would suggest:

  • Unified foundation: Relativity, gravity, QM, and EM from two equations
  • Discrete reality: Physical spacetime is fundamentally quantized/computational
  • Emergent forces: What we call "forces" are lattice dynamics, not fundamental
  • Quantum-gravity compatible: Already discrete, avoids singularities
  • Computationally tractable: Easier to simulate than curved spacetime + quantum fields

But this is highly speculative. We're sharing our work to invite testing, validation, and especially falsification attempts from professional physicists.

Learn More & Verify

📄 Research Documentation

Detailed papers, test results, and methodology:

🔬Open Science Framework (OSF)→📖Framework Documentation (Zenodo)→📦Zenodo Archive (First Publication)→

💻 Source Code

All simulation code is open source. Verify there's no hidden gravity equations:

🐙GitHub Repository→

🤝 Collaboration

Are you a physicist? We want your feedback:

  • Can you find where this breaks?
  • Does it match or contradict known physics?
  • What experiments would validate/falsify this?

Contact: research@emergentphysicslab.com

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This project follows the principles of open science. All data, code, and methodology are freely available for replication and critique. We welcome skepticism and rigorous testing.

Last Updated: November 7, 2025