Loss of quantum-mechanical coherence in a measurement process

A quantum-mechanical measurement process is analyzed in terms of a model Hamiltonian describing the interaction between a quantum system (a particle) and a macroscopic apparatus (a detector), which is assumed to be made up of N two-level elementary constituents (molecules). The description of the molecule locations introduces an effective fluctuating coupling constant, and this provokes a loss of quantum-mechanical coherence in the limit of large N. It is argued that coherence is lost statistically, as a result of the interaction: The collapse of the wave function is indeed obtained when the same experiment is performed many times, as a result of the microscopic differences among macroscopically identical initial states of the detector. In this way, insight is obtained into the mechanism engendering the loss of coherence suffered by a quantum-mechanical system when interacting with a macroscopic apparatus, and the concept of wave-function collapse is replaced by that of a statistically defined dephasing process. No classical behavior of the detection system is postulated and the presence of no external observer is required.