Quantum Mechanics: Modal Interpretation and Galilean Transformations

Abstract

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.

The nonrelativistic limit of (central-extended) Poincaré group and some consequences for quantum actualization

“…Through the assumption that in Quantum Field Theory the Casimir Operators of the Poincaré Group actualize, the non-relativistic limit of the latter group yields to the actualization of the Casimir operators of the Galilei Group, which is in agreement with the actualization rule of previous versions of modal Hamiltonian Interpretation [3]. …”

“…Following the lines of this MHI, it was further proved in [3] that for systems invariant under the Galilei group, the three Casimir operators of the central mass extended Galilei group, namely, the mass, the spin squared, and the internal energy W do actualize. Finally, the existence of a kinetic component in the Hamiltonian H was proved.…”

A modal-Hamiltonian interpretation of quantum mechanics

“…On the contrary, the MHI rule only depends on the system's Hamiltonian. Let us recall the main postulates of this intepretation ; see also Castagnino and Lombardi 2008;Ardenghi, Castagnino and Lombardi 2009;Lombardi, Castagnino and Ardenghi 2010) A quantum system S is a pair ( , ) On the basis of the above description, according to HMI two conditions define a quantum measurement:…”

Measurement, Interpretation and Information

“…But this conclusion does not take into account that Bohm's view is not the only reasonable possibility for a modal interpretation with a fixed preferred observable. In fact, the modal-Hamiltonian interpretation [25][26][27][28][29] endows the Hamiltonian with a determining role, both in the definition of systems and subsystems and in the selection of the preferred context.…”