1998/06/24 by Bruno Galvan, Galvan, Bruno
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9806083
32 pages, LaTex
arxiv created 1998/06/24 · openalex publication_date 1998/06/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of defining the boundary conditions for the universe is considered here in the framework of a classical dynamical theory, pointing out that a measure on boundary conditions must be included in the theory in order to explain the statistical regularities of evolution. It is then suggested that quantum statistical regularities also could derive from this measure. An explicit definition of such a measure is proposed, using both a simplified model of the universe based on classical mechanics and the non-relativistic quantum mechanics formalism. The peculiarity of such a measure is that it does not apply to the initial conditions of the universe, i.e. to the initial positions and momenta of particles, but to their initial and final positions, from which the path is derived by means of the least action principle. This formulation of the problem is crucial and it is supported by the observation that it is incorrect to liken the determination of the boundary conditions of the universe to the preparation of a laboratory system, in which the initial conditions of the system are obviously determined. Some possible objections to this theory are then discussed. Specifically, the EPR paradox is discussed, and it is explained by showing that, in general, a measure on the boundary conditions of the universe generates preinteractive correlations, and that in the presence of such correlations Bell's inequality can no longer be proven true. Finally, it is shown that if one broadens the dynamical scheme of the theory to encompass phenomena such as particle decay and annihilation, the least action principle allows for an indeterministic evolution of the system.