Decoherence and Determinism in a One-Dimensional Cloud-Chamber Model

Abstract

The hypothesis [1] that the particular linear tracks appearing in the measurement of a spherically-emitting radioactive source in a cloud chamber are determined by the (random) positions of atoms or molecules inside the chamber is further explored in the framework of a recently established one-dimensional model [2]. In this model, meshes of localized spins 1/2 play the role of the cloudchamber atoms and the spherical wave is replaced by a linear superposition of two wave packets moving from the origin to the left and to the right, evolving deterministically according to the Schrödinger equation. We first revisit these results using a time-dependent approach, where the wave packets impinge on a symmetric two-sided detector. We discuss the evolution of the wave function in the configuration space and stress the interest of a non-symmetric detector in a quantum-measurement perspective. Next we use a time-independent approach to study the scattering of a plane wave on a single-sided detector. Preliminary results are obtained, analytically for the single-spin case and numerically for up to 8 spins. They show that the spin-excitation probabilities are sometimes very sensitive to the parameters of the model, which corroborates the idea that the measurement result could be determined by the atom positions. The possible origin of decoherence and entropy increase in future models is finally discussed.

Solvable model of a quantum particle in a detector

“…When the atoms are sufficiently far away from each other, the propagator G, which is inversely proportional to the interatomic distance L, can be treated as a perturbation compared to the diagonal term F −1 of the matrix M in Eq. (8). Such a situation is encountered when k 0 L 1, or κL 1, or γL 1, since F −1 goes as the parameters k 0 , κ, and γ.…”

“…In this work, we follow a similar approach. 8 We resort to a three-dimensional stationary scattering model of a detector made of N two-level atoms fixed in space.…”

“…The massive spinless particle interacts with the atoms through a zero-range potential. 2,3,6,[8][9][10] We derive the exact Lippmann-Schwinger equation of this multiple scattering problem. 11 It is then solved numerically in a non-perturbative way which holds for any coupling strength between the particle and the atoms.…”

“…An observable "track" is interpreted as a simultaneous excitation of close atoms. 6,8 Our purpose is to understand the formation of tracks in gaseous detectors from quantum-mechanical arguments. The influence of positions of atoms on the location of tracks is especially considered.…”

The two-spin model of a tracking chamber: a phase-space perspective

“…In particular, a one-dimensional model with N spins at fixed positions on each side of a central emitter has been theoretically and numerically studied in Refs. [3,4,11]. In this case, the particle "spherical wave" is represented by the superposition of two wave packets moving in opposite directions, and the detection of the particle corresponds to the spin flip.…”