Spacetime symmetries in quantum mechanics

CRISTIAN LÓPEZ; OLIMPIA LOMBARDI

Quantum Worlds: Perspective on the Ontology of Quantum Mechanics

Cambridge University Press

Lugar: Cambridge; Año: 2019; p. 269 - 293

In the last decades, the philosophy of physics has begun to pay attention to themeaning and the role of symmetries, an issue that has, however, had a greatrelevance in physics since, at least, the middle of the twentieth century. Notwithstanding this fact, this increasing interest in symmetries has not yet been transferred to the field of the interpretation of quantum mechanics. Although it is usually accepted that the Galilean group is the group of invariance of the theory, discussions about interpretations of quantum mechanics, with very few exceptions, have not taken into account symmetry considerations. But the invariance of a theory under a group does not guarantee the invariance of its interpretations, as they usually add interpretive assumptions to the formal structure of the theory. Symmetry considerations should thus be seriously taken into account in the field of the interpretation of quantum mechanics.For this reason, in this chapter we shall focus on the spacetime symmetries ofquantum mechanics. After briefly introducing certain terminological clarifications, we shall focus on two aspects of spacetime transformations. First, we shall consider the behavior of nonrelativistic quantum mechanics under the Galilean group, aiming at assessing its Galilean invariance in relation to interpretive concerns. Second, we shall analyze the widely-accepted view about the invariance of the Schrödinger equation under time reversal, in order to unveil some implicit assumptions underlying such a claim.