Multiple-time states and multiple-time measurements in quantum mechanics

5 Measurements continuous in time and a posteriori states in quantum mechanics

Measurements continuous in time were consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after the measurement when a certain trajec-tory of the measured observables is registered (the a posteriori states). In this paper a new derivation of filtering equations i...

Relativity as the quantum mechanics of space-time measurements

Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation formally stems from the First Relativity Postulate (FRP) alone if space-time quantization is a fundamental law of physics which must be included as part of the...

Time in quantum measurements.

We analyze canonical measurements involving momentum and position and show that they require a finite duration. A formalism that we have developed for a realistic description of quantum measurements is generalized to the multitime case. This enables us to derive rigorous and unambiguous time-energy uncertainty relations. For a free particle, we find that T6H 2 f, where 6H is the variance in the...

Arrival Time in Quantum Mechanics

Time, Quantum Mechanics, and Probability

A variety of ideas arisiüg in decoherence theory, and in the ongoing debate over Everett’s relative-state theory, can be linked to issues in relativity theory and the philosophy of time, speci…cally the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995, 1996a); in what follows we shall consider the same circle of id...