Quantum Mechanics: Modal Interpretation and Galilean Transformations

The aim of this paper is to consider in what sense the modal-Hamiltonian interpretation of quantum mechanics satisfies the physical constraints imposed by the Galilean group. In particular, we show that the only apparent conflict, which follows from boost-transformations, can be overcome when the definition of quantum systems and subsystems is taken into account. On this basis, we apply the interpretation to different well-known models, in order to obtain concrete examples of the previous conceptual conclusions. Finally, we consider the role played by the Casimir operators of the Galilean group in the interpretation.

[1]  Bas C. van Fraassen,et al.  The Einstein-Podolsky-Rosen Paradox , 1974 .

[2]  J. Lévy-Leblond.  Galilei Group and Nonrelativistic Quantum Mechanics , 1963 .

[3]  O. Lombardi,et al.  The role of the Hamiltonian in the interpretation of quantum mechanics , 2008 .

[4]  S. Bose.  The galilean group in 2+1 space-times and its central extension , 1995 .

[5]  C. cohen-tannoudji,et al.  Quantum Mechanics: , 2020, Fundamentals of Physics II.

[6]  N L Harshman,et al.  Galilean and dynamical invariance of entanglement in particle scattering. , 2007, Physical review letters.

[7]  Pieter E. Vermaas,et al.  The Modal Interpretation of Quantum Mechanics , 1998 .

[8]  N. L. Harshman,et al.  Tensor Product Structures, Entanglement, and Particle Scattering , 2007, Open Syst. Inf. Dyn..

[9]  Jeffrey Bub,et al.  Paradigms and Paradoxes: The philosophical challenge of the quantum domain , 1976 .

[10]  M. Tinkham.  Group Theory and Quantum Mechanics , 1964 .

[11]  L. Ballentine.  Quantum mechanics : a modern development , 1998 .

[12]  Mario Bunge,et al.  Philosophy of Physics , 1972 .

[13]  E. Specker,et al.  The Problem of Hidden Variables in Quantum Mechanics , 1967 .

[14]  Eugene P. Wigner,et al.  80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group" , 2021 .

[15]  Bas C. van Fraassen.  Semantic Analysis of Quantum Logic , 1973 .

[16]  C. Hooker,et al.  Contemporary research in the foundations and philosophy of quantum theory : proceedings of a conference held at the University of Western Ontario, London, Canada , 1973 .

[17]  W. Scott,et al.  Group Theory. , 1964 .

[18]  Y. Peleg,et al.  Schaum's outline of theory and problems of quantum mechanics , 1998 .

[19]  Wu-Ki Tung,et al.  Group Theory in Physics , 1985 .

[20]  Olimpia Lombardi,et al.  A modal-Hamiltonian interpretation of quantum mechanics , 2006, quant-ph/0610121.

[21]  Wu-Ki Tung,et al.  Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions in Classical and Quantum Physics , 1985 .

[22]  Katherine Brading,et al.  Symmetries and invariances in classical physics , 2005 .

[23]  V. Bargmann,et al.  On Unitary ray representations of continuous groups , 1954 .