Toy Models

SPT Lab

Interactive mathematical toy models — drag a slider, watch the equations update live, validate against known physics results with PASS / FAIL badges.

Master toy

DANode Master Simulator

One (or two) Tai Chi nodes, three switchable lenses — derive wave-particle duality, in-phase / anti-phase forces, and curved spacetime from one membrane mechanism.

  • Lens A — Wave-Particle Duality (Englert / Davisson–Germer)
  • Lens B — Phase-Locking → Force (Newton / Coulomb)
  • Lens C — Membrane Twist → Curved Spacetime (Eddington / Mercury / GPS)
  • Lagrangian + energy-momentum + ghost / tachyon soundness checks

Photon — Flip & Spin

A single photon with controllable flip-rate and spin-rate. Derives E = ℏω, p = ℏk, λ, and m = 0 from the SPT motion-budget constraint.

  • Photoelectric effect — Einstein 1905, Millikan 1916
  • Photon mass = 0 → v = c exactly
  • de Broglie wavelength λ = h/p
  • Chain mode: light ray propagating with phase = ωt − kx

Entanglement — Bell / CHSH

Two DANodes share one phase. Measuring one side instantly reflects on the other. Violates Bell, reaches Tsirelson bound 2√2.

  • CHSH inequality |S| > 2 (Aspect 1982)
  • Singlet correlation E = −cos(θ_A − θ_B)
  • Tsirelson bound 2√2 ≈ 2.828
  • No-signalling preserved (causality)

Black Hole — Phase-Reversal Unitary

Membrane folds at the event horizon. Hawking radiation = unitary phase reversal → information preserved, BH paradox resolved.

  • Hawking T_H = ℏc³/(8πGM k_B)
  • Bekenstein S_BH = A/(4 ℓ_P²)
  • Page curve — info returns after t_Page
  • Unitarity preserved (no paradox)

Gravity — Large-N Phase-Mixing

Gravity = residual after N phase-mixed nodes mostly cancel. Solves 10⁴² hierarchy, recovers G and Hubble H₀.

  • G_eff = G_Pl/N — phase-mixing residual
  • Hierarchy 10⁻⁴² gravity:EM solved naturally
  • Hubble H₀ = 67.4 km/s/Mpc recovered
  • 1/r² preserved at all N
Methodology

Each toy model is built on an explicit SPT Lagrangian. Equations of motion and observables are derived directly from that Lagrangian. Numerical results are compared against famous physics experiments. The goal is not to generate new physics — it is to demonstrate that one geometric mechanism (membrane flip + spin + phase-coupling) recovers all the known laws.