# Analysis of double-slit interference experiment at the atomic level

## TL;DR

This paper proposes that the core features of the double-slit experiment can be explained solely by Schrödinger's equation when considering small energy gaps in detector atoms, offering a potential solution to the measurement problem.

## Contribution

It introduces a toy model of a detector based on isolated energy levels, demonstrating how the Born rule emerges from unitary quantum mechanics without collapse.

## Key findings

- The model reproduces the Born rule probability distribution.
- Analysis aligns with neutron interference experiments.
- The approach avoids hidden variables and irreversibility issues.

## Abstract

I argue that the marquis characteristics of the quantum-mechanical double-slit experiment (point detection, random distribution, Born rule) can be explained using Schroedinger's equation alone, if one takes into account that, for any atom in a detector, there is a small but nonzero gap between its excitation energy and the excitation energies of all other relevant atoms in the detector (isolated-levels assumption). To illustrate the point I introduce a toy model of a detector. The form of the model follows common practice in quantum optics and cavity QED. Each detector atom can be resonantly excited by the incoming particle, and then emit a detection signature (e.g. bright flash of light) or dissipate its energy thermally. Different atoms have slightly different resonant energies per the isolated-levels assumption, and the projectile preferentially excites the atom with the closest energy match. The toy model permits one easily to estimate the probability that any atom is resonantly excited, and also that a detection signature is produced before being overtaken by thermal dissipation. The end-to-end detection probability is the product of these two probabilities, and is proportional to the absolute square of the incoming wavefunction at the atom in question, i.e. the Born rule. I consider how closely a published neutron-interference experiment conforms to the picture developed here; I show how this paper's analysis steers clear of creating a scenario with local hidden variables; I show how the analysis steers clear of the irreversibility implicit in the projection postulate; and I discuss possible experimental tests of this paper's ideas. Hopefully, this is a significant step toward realizing the program of solving the measurement problem within unitary quantum mechanics envisioned by Landsman, among others.

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Source: https://tomesphere.com/paper/1905.00277