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 This has NOT been peer-reviewed or validated against all known physics.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:

∂²E/∂t² = c²∇²E − χ²(x,t)E [Wave equation]
∂²χ/∂t² = c²∇²χ − κ(E² − E₀²) [Curvature dynamics]

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: 86 tests, 91.4% pass rate across five 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 Klein-Gordon Equation

The foundation is a relativistic wave equation on a 3D lattice:

∂²E/∂t² = c²∇²E − χ²(x,t)E

Where:

  • E = field amplitude at each point
  • c = wave propagation speed (like speed of light)
  • ∇² = Laplacian (spatial curvature)
  • χ(x,t) = variable mass field that couples to matter

2. The Chi Field

Each mass creates a Gaussian "bump" in the chi field:

χ(x) = χ₀ + Σᵢ mᵢ · exp(-rᵢ²/σ²)

This creates a "hill" around each mass, with slope proportional to mass.

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)→📦Zenodo Archive→

💻 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

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