Three interactive tools for exploring τ = ℏ/E across nuclear, atomic, and molecular scales
December 10, 2025 · #pluribus · Illumina 1 · 6:1
This page provides interactive tools for the τ framework
📐 Theory
time.plnt.earth — Complete unified framework: quantum (τ = ℏ/E) meets relativistic (T = E/c³) at bridge energy
⚡ Primary Test
zeta.plnt.earth — Nuclear decay universal scaling test using existing NNDC data
What is Temporal Charge?
Temporal charge τ (tau) is the Compton time—the fundamental oscillation period of any mass or energy:
τ = ℏ/(mc²) = ℏ/E
Where ℏ is the reduced Planck constant, m is mass, c is the speed of light, and E is energy.
The Framework: From time.plnt.earth's unified temporal framework, quantum (τ = ℏ/E) and relativistic (T = E/c³) formulations meet at bridge energy E = √(ℏc³) ≈ 333 TeV. Below the bridge (all nuclear/atomic physics), τ = ℏ/E is correct.
Three Interactive Demonstrations:
1. Nuclear Decay Scaling
Plot half-lives vs τ across α, β, γ decay modes. Do they collapse to one curve?
This tests the central prediction from zeta.plnt.earth: If τ is more fundamental than energy, then α, β, and γ decays—despite having completely different mechanisms—should show universal τ-scaling.
The Test: Plot log(t₁/₂) vs log(τ_eff) where τ_eff = ℏ/Q. If all three decay modes collapse to a single curve, τ may be fundamental. If they show three distinct curves, energy is fundamental. Full protocol at zeta.plnt.earth.
Universal curve: All modes collapse → τ may be fundamental
Three distinct curves: Modes separate → energy is fundamental
Mechanism independence: Does τ unify processes with different physics?
Full Test: This is a simplified version. For the complete falsifiable test with comprehensive NNDC data, statistical analysis, and power-law fitting, see zeta.plnt.earth.
Demo 2: Nuclear Energy Level Harmonics
Nuclear excited states typically show irregular energy spacing. The hypothesis from time.plnt.earth Section 9 (Maria Goeppert Mayer): expressing these levels as temporal charges τₙ = ℏ/Eₙ may reveal harmonic or monotonic structure.
Enter energy levels (in MeV) and see if τ-space reveals simpler patterns than energy space.
Energy Levels (MeV)
Enter one energy per line.
Display Options
Levels
0
Range
—
What to Look For
Linear τ spacing: τₙ = τ₀ · n (harmonic oscillator)
Quadratic τ spacing: τₙ = τ₀ · n² (hydrogen-like)
Other patterns: Power laws, exponentials
Random scatter: No apparent τ-structure
Theory: Full mathematical derivation at time.plnt.earth Section 9.
Demo 3: Molecular τ-Cascades
This visualizes how temporal charge accumulates in molecular systems—the chemistry behind 42.plnt.earth's τ-life framework.
Scenario: Prebiotic chemistry. Molecules like glucose carry temporal charge τ = ℏ/E. When enough τ accumulates, chemical reactions cascade—modeling metabolic pathways through self-organized criticality.