Foundations of Physics 37 (1):3-39 (2007)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented
Keywords measurement problem  Born rule  Berry’s phase  EPR-paradox
Categories (categorize this paper)
DOI 10.1007/s10701-006-9093-5
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,178
Through your library

References found in this work BETA

Add more references

Citations of this work BETA

Add more citations

Similar books and articles


Added to PP index

Total views
80 ( #135,916 of 2,454,924 )

Recent downloads (6 months)
3 ( #225,801 of 2,454,924 )

How can I increase my downloads?


My notes