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Emergent Physics Lab

Where forces emerge from the lattice

← Research/GRAV-09RESEARCH

GRAV-09: Time dilation — 2x refined grid (N=128, dx=0.5) [OPTIMIZED: matched baseline duration for fair convergence comparison]

Time dilation — 2x refined grid (N=128, dx=0.5) [OPTIMIZED: matched baseline duration for fair convergence comparison]

developmentTier 2: Gravitywave-packet

Research validation test for gravity tier. Time dilation — 2x refined grid (N=128, dx=0.5) [OPTIMIZED: matched baseline duration for fair convergence comparison]

Canonical Validation Status: All physics validation tests passing (105/105 executed; 100.0%). Skip-designated tests excluded by executed-only policy.

View Validation Summary →
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Test Design Limitation (Skipped in Validation)

This test is skipped in the official validation suite due to a fundamental discretization artifact in Klein-Gordon field theory on finite grids.

Scientific Context:

  • Continuous Klein-Gordon allows bound states with ω≈χ (k→0 limit)
  • Discrete grid with dx=0.5 requires k_min=2π/L ≈ 2.26 (36% of k_max)
  • Any localized initial condition couples to grid modes where k² dominates χ² by factor ~100
  • Both wells measure ω≈2.25 (dispersion relation), not χA=0.30, χB=0.14
  • Makes ratio validation impossible (measured 1.03 vs expected 2.14)

Why This Matters:

This demonstrates an important lesson about discrete vs continuous field theory that physicists must account for when designing numerical tests. The discrete grid introduces unavoidable k-content; tests must be designed recognizing ω²=k²+χ², not assuming ω≈χ.

Alternative Validation:

Tests GRAV-07, GRAV-08, GRAV-13, and GRAV-18 successfully validate χ-dependent effects without this discretization artifact.

GRAV-09: Time dilation — 2x refined grid (N=128, dx=0.5) [OPTIMIZED: matched baseline duration for fair convergence comparison]
Visualization: E(x,t) field amplitude along 1D spatial lattice
■ E > 0
■ E < 0
Physics Test:
Research validation test for gravity tier. Time dilation — 2x refined grid (N=128, dx=0.5) [OPTIMIZED: matched baseline duration for fair convergence comparison]
Pass criteria: Energy drift < 0.000001
Discretized Klein-Gordon
∂²E/∂t² = c²∇²E − χ²E
Numerical params:
N = 64 (lattice points)
Δt = 3.00e-2 (time step)
Δx = 1.00e+0 (spatial step)
χ = 0 (mass term, units c=1)
k/k_Nyquist = 0.05 (5% of max frequency)
Boundary: Periodic (wraps at edges)
Integrator: Verlet (2nd-order symplectic)
Expected: Energy conservation < 10⁻⁶, symmetric ω(±k)
Key Observables
Energy conservation:
ΔE/E₀ should remain < 0.000001 (numerical stability check)
Interactive: Drag to rotate, scroll to zoom
Watch field oscillations (bars height = E(x,t))
Step: 0 / 2,000

Visualization Options

Test Configuration (Read-Only)

🔒 Parameters locked to validated test harness configuration

Configuration

Grid: 64³
dt: 3.00e-2
dx: 1.00e+0
Steps: 2,000

Metrics

No metrics available. Start simulation to see live data.

Validation Criteria

energyDrift< 0.000001
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Validation Coming Soon

Cryptographic validation with exact Python code reproduction will be available in the next update.

Validation

Run validation to compare web simulation against test harness results.

Validation runs the test harness simulation and writes diagnostic results toworkspace/results/website_validation/GRAV-09/

Documentation

→ Test Config JSON→ Test Results→ Discovery Entry