Wavefunction collapse through backaction of counting weakly interacting photons

2016/01/31 by Lee E. Harrell
Computer Science · Medicine · Physics and Astronomy · #Biofield Effects and Biophysics #Classical mechanics #Matter wave #Photon #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum decoherence #Quantum dynamics #Quantum electrodynamics #Quantum mechanics #Quantum operation #Wave function #Wave function collapse #Wave packet #Wave–particle duality #quant-ph

paper · pdf · doi:10.1063/1.4944454

published as J. Math. Phys. 57(3), 032104 (2016) · 7 pages, 1 figure

openalex publication_date 2016/03/01 · arxiv created 2016/04/04 · arxiv updated 2016/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle’s wavefunction toward a narrow Gaussian wavepacket at the location xest determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle’s position, as calculated from the post-measurement wavefunction, agrees precisely with shot-noise limited uncertainty of the measured xest. Both the identification of the absolute square of the particle’s initial wavefunction as the probability density for xest and the de Broglie hypothesis emerge as consequences of interpreting the intensity of the optical field as proportional to the probability of detecting a photon. Linear momentum information that is encoded in the particle’s initial wavefunction survives the measurement, and the pre-measurement expectation values are preserved in the ensemble average.

Citations

• Quantum continual measurements and a posteriori collapse on CCR
• Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values
• Decomposing generalized measurements into continuous stochastic processes
• Testing Spontaneous Wave-Function Collapse Models on Classical Mechanical Oscillators
• Weak Measurements Are Universal
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• Translation of Lueders' "Uber die Zustandsanderung durch den Messprozess"