Principio hamilton

ARTICLE IN PRESS

Studies in History and Philosophy of Modern Physics 39 (2008) 380–443 www.elsevier.com/locate/shpsb

A modal-Hamiltonian interpretation of quantum mechanics$
Olimpia Lombardia,Ã, Mario Castagninob
b a ´logo Larralde 3440, 1430 Buenos Aires, Argentina CONICET, Universidad de Buenos Aires, Criso CONICET-IAFE, Universidad de Buenos Aires, Casilla de Correos 67, Sucursal 28,1428 Buenos Aires, Argentina

Received 28 December 2006; received in revised form 10 January 2008

Abstract The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valuedobservables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of theontology referred to by the theory, where quantum systems turn out to be bundles of possible properties. r 2008 Elsevier Ltd. All rights reserved.
Keywords: Quantum mechanics; Modal interpretation; Hamiltonian; Quantum measurement; Decoherence; Classical limit; Quantum ontology

When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics

$ÃCorresponding author.

This work is fully collaborative: the order of the names does not mean priority.

E-mail addresses: olimpiafilo@arnet.com.ar (O. Lombardi), mariocastagnino@citynet.net.ar (M. Castagnino). 1355-2198/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.shpsb.2008.01.003

ARTICLE IN PRESS
O. Lombardi, M. Castagnino / Studies in History and Philosophyof Modern Physics 39 (2008) 380–443 381

Contents 1. 2. 3. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Why modal? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure and content of quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 3.1. Formal structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Physical content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The modal-Hamiltonian interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Properties, systems and subsystems. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Possible facts and propensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Actual facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Actualization rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thephysical relevance of the interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Free particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Free particle with spin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Harmonic oscillator. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Free hydrogen atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Zeeman effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. Fine structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....