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The Born Rule from Electromagnetic Detection and Single-Event Exclusivity

Paul Monforton, Sarah Monforton

Published Mar 23, 2026• 0 citations
Publisher

Abstract

We derive the Born rule for single-event electromagnetic detection from four physical premises: (i) electromagnetic field modes satisfy Maxwell's equations in the apparatus geometry, (ii) the energy flux at each detection endpoint is given by the Poynting vector, (iii) each detector is a physical system with internal stochastic degrees of freedom characterised by a finite correlation time, and (iv) an individual emission produces an individual detection event (winner-take-all competition). The single non-classical input is that individual emissions produce individual detection events — one emission, one click. In the weak-field regime, the detector response is linear in the incident flux, and the Poisson limit theorem converts many independent sub-threshold crossing attempts into a Poisson process at each endpoint with rate proportional to the local field intensity |a(y)|². The competing-exponentials theorem then gives the detection probability P(y) = |a(y)|²/∫|a|²dy'. The Born rule is not assumed but derived, reducing a quantitative law over a continuous domain to a single non-classical input — discrete, exclusive detection events — combined with classical electromagnetism and detector physics. The result holds for any apparatus geometry governed by the free Helmholtz equation with electromagnetic boundary conditions, any detector material, and any internal noise distribution. We show that the Born rule is the unique detection statistics compatible with electromagnetic energy transport, linear detector response, and single-event exclusivity.

DOI
10.5281/zenodo.19195972

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