Path integral approach to space-time probabilities: a theory without pitfalls but with strict rules

Abstract

Following the renewed interest in the topic [1], we revisit the problem of assigning probabilities to classes of Feynman paths passing through specified space-time regions. We show that by assigning of probabilities to interfering alternatives, one already makes an assumption that the interference has been destroyed through interaction with an environment, or a meter. Including the effects of the meter allows to construct a consistent theory, free of logical 'pitfalls' identified in Ref. [1]. Wherever a meter cannot be constructed, or cannot be set to perform the desired decoherence, formally constructed probabilities have no clear physical meaning, and can violate the necessary sum rules. We illustrate the above approach by analysing the three examples considered in [1].

References in corpus (3)

• Quasiclassical Coarse Graining and Thermodynamic Entropy
• Quantum Mechanics with Extended Probabilities
• Pitfalls of Path Integrals: Amplitudes for Spacetime Regions and the Quantum Zeno Effect

Cited by in corpus (7)

• Full distribution of work done on a quantum system for arbitrary initial states
• Von Neumann spin measurements with Rashba fields
• The Salecker-Wigner-Peres clock, Feynman paths, and a tunnelling time that should not exist
• Electron traversal times in disordered graphene nanoribbons
• Spin measurements and control of cold atoms using spin-orbit fields
• Classical Limit of the Quantum Zeno Effect by Environmental Decoherence
• Unitary evolution and elements of reality in consecutive quantum measurements