Collapse of the Wavefunction Following Destructive Interference with a Macroscopic Measuring Device

Abstract

Measurement in quantum mechanics is a long-standing issue, and the measurement problem consists of essentially two parts: 1) no matter what the initial wavefunction of an object, the result of a measurement always results in the observation of a single eigenstate (i.e., “wavefunction collapse”), and 2) once the wavefunction collapses it remains collapsed. Though there have been a number of proposed solutions to the measurement problem, none to date is without debate. Here we discuss a solution to the measurement problem that avoids some others’ difficulties. We assume that for every eigenvector of an operator there is a set of unique discrete phases, and that the phase sets among eigenvectors are disjoint. With this hypothesis it is possible to show that wavefunction collapse is a consequence of destructive interference when a quantum object interacts with the large set of “quantum-measurement mapping operators” that must comprise a classical measuring device.