An Introduction to Covariant Quantum Mechanics

Geza Szamosi

U. Kasper, Eckhard Kreisel, H.‐J. Treder

N. Ionescu-Pallas, I. Gottlieb

Horst E. Wilhelm

A formulation of the quantum mechanics of charged particles in time‐dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocity w is in magnitude comparable with the velocity of light c. The electromagnetic substratum velocity w occurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.

Rodolfo Gambini, Jorge A. Pullin

We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework that was recently introduced by Höhn, Smith, and Lock to treat the problem of time in generally covariant systems. These new methods, which solve several problems in the introduction of a notion of time in such systems, do not change the main results of the Montevideo Interpretation. The use of the new formalism makes the construction more general and valid for any system in a quantum generally covariant theory. We find that, as in the original formulation, a fundamental mechanism of decoherence emerges that allows for supplementing ordinary environmental decoherence and avoiding its criticisms. The recent results on quantum complexity provide additional support to the type of global protocols that are used to prove that within ordinary—unitary—quantum mechanics, no definite event—an outcome to which a probability can be associated—occurs. In lieu of this, states that start in a coherent superposition of possible outcomes always remain as a superposition. We show that, if one takes into account fundamental inescapable uncertainties in measuring length and time intervals due to general relativity and quantum mechanics, the previously mentioned global protocols no longer allow for distinguishing whether the state is in a superposition or not. One is left with a formulation of quantum mechanics purely defined in quantum mechanical terms without any reference to the classical world and with an intrinsic operational definition of quantum events that does not need external observers.

Alessandro Teta