Time, Quantum Mechanics, and Probability

Carl Friedrich von Weizsäcker

Jiří Souček

Quantum Mechanics (QM) is primarily a probabilistic theory. The standard Kolmogorov probability theory is not suitable for this goal since it does not offer the possibility of the reversible time evolution. This implies the need to construct a new probability theory which is able to model the reversible time evolution. I have proposed such an Extended probability theory. The main goal of this project is to understand what QM is. In this note I shall describe the program of the research which is already partially realized.

Diederik Aerts

E. C. G. Sudarshan

It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of probabilities and then use it to describe quantum dynamics? What is the origin of the probability distribution for a maximally specified quantum state? Is quantum mechanics `local' or is there an essential nonlocality (nonseparability) inherent in quantum mechanics? These questions are discussed in this paper. The decay of an unstable quantum state and the time dependence of a minimum uncertainty states for future times as well as past times are also discussed.

Hrvoje Nikolić

This chapter considers a more realistic variation of the measuring procedure, taking into account the fact that the measured particles become entangled with the measuring apparatus at some finite time. The results are also generalized to quantum field theory, where quantum states are represented by wave functions depending on an infinite number of space-time coordinates. Thus, to make Bohmian mechanics covariant, one needs first to reformulate the standard quantum mechanics (QM) in a covariant way such that time is treated on an equal footing with space. Another physically interesting situation is when the entanglement with the environment takes the form, where are coherent states. In general, in the Bohmian interpretation all the other quantities may have a distribution totally different from those predicted by purely probabilistic QM. The space probability density should be generalized to the space-time probability density.

Simon W. Saunders