Born Rule Simulator
Interactive Simulation

The Born Rule as Physical Substrate Energy - Not a Postulate

What this simulator shows

Quantum mechanics has a mysterious rule: the probability of finding a particle at position x is proportional to |ψ(x)|² - the square of the wavefunction. Standard physics treats this as a postulate with no physical explanation for why it is the square.

This model, developed by Vijay Shankar Sharma, provides a physical answer. A particle is a distributed disturbance in a physical substrate - a real physical medium. Where the disturbance is stronger, it deposits more energy when it meets a detector. Energy scales as amplitude squared. The Born rule follows directly - it is not mysterious, it is wave physics.

Move the sliders. Watch where detection events (green dots) appear - always at the interference maxima where energy density is highest.

Vijay Shankar Sharma · ORCID 0009-0001-9622-6121
ρ_s = 5.9×10⁻²⁷ kg/m³ Substrate equilibrium density - the single physical constant from which all results are derived
Live outputs
Born peak |ψ|²
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Detection prob.
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Active fringes
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Regime
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Substrate deformation energy density |ψ(x)|²
Detector coupling g·|ψ|² vs position - green dots = detection events
Detection probability vs coupling strength g
Detection table
Position x|ψ(x)|²g·|ψ|² couplingDetection
This simulation underpins the following focused papers: P71  ·  All focused papers →