Why quantum mechanics indeed?

Gastón E. Giribet

This brief note has the didactical purpose of discussing the meaning of the uncertainty principle involving energy and time in quantum mechanics within the context of the seminal works on this subject. The importance of this topic is, indeed, frecuently neglected in several textbooks on quantum mechanics. Then, these pages are addressed to students attending to an undergraduate course on quantum mechanics; and the original aim is to present a list of references of the points which take part in the principal discussions on the subject. Principal attention is devoted to the discussion of the fallacies, which are indeed persistent in the literature.

P. T. Landsberg

Salvatore Capozzıello, Wladimir-Georges Boskoff

Leslie Ballentine, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

The concept of probability was prominent in the original foundations of quantum mechanics and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I argue that, although both objective and subjective probabilities have domains of relevance in QM, their roles are quite distinct. Even where both are legitimate, the objective and subjective probabilities differ, both conceptually and numerically. There are quantum probabilities that have no useful subjective interpretations, and there are subjective probabilities that cannot be realized as quantum probabilities.

Aristidis Arageorgis, John Earman

The popular impression of Bohmian mechanics is that it is standard quantum mechanics with the addition of some extra gadgets---exact particle positions and a guiding equation for particle trajectories---the advantages being that the gadgets pave the way for a resolution of the measurement problem that eschews state vector reduction while restoring the determinism lost in standard quantum mechanics. In fact, the Bohmian mechanics departs in significant ways from standard quantum mechanics. By itself this is not a basis for criticism; indeed, it makes Bohmian mechanics all the more interesting. But Bohmian mechanics is not, as the popular impression would have it, empirically equivalent to standard quantum mechanics in terms of probabilistic predictions for the outcomes of measurements of quantum observables. Indeed, in physically important applications to systems for which standard quantum mechanics delivers empirically well-confirmed probabilistic predictions, the sophisticated form of Bohmian mechanics designed to prove the global existence of Bohmian particle trajectories fails to deliver unequivocal predictions---of even a probabilistic variety---for the future behavior of said systems. Possible responses to this lacuna are discussed.