The First Droplet in a Cloud Chamber Track

Abstract

In a cloud chamber, the quantum measurement problem amounts to explaining the first droplet in a charged-particle track; subsequent droplets are explained by Mott’s 1929 wave-theoretic argument about collision-induced wavefunction collimation. I formulate a mechanism for how the first droplet in a cloud chamber track arises, making no reference to quantum measurement axioms. I look specifically at tracks of charged particles emitted in the simplest slow decays, because I can reason about rather than guess the form that wave packets take. The first visible droplet occurs when a randomly occurring, barely-subcritical vapor droplet is pushed past criticality by ionization triggered by the faint wavefunction of the emitted charged particle. This is possible because potential energy incurred when an ionized vapor molecule polarizes the other molecules in a droplet can balance the excitation energy needed for the emitted charged particle to create the ion in the first place. This degeneracy is a singular condition for Coulombic scattering, leading to infinite or near-infinite ionization cross sections, and from there to an emergent Born rule in position space, but not an operator projection as in the projection postulate. Analogous mechanisms may explain canonical quantum measurement behavior in detectors such as ionization chambers, proportional counters, photomultiplier tubes or bubble chambers. This work is important because attempts to understand canonical quantum measurement behavior and its limitations have become urgent in view of worldwide investment in quantum computing and in searches for super-rare processes (e.g., proton decay).