I give a brief introduction to many worlds or "no wave function collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.
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.
This book examines a number of problems of quantum mechanics, most of which are not usually discussed. What is the origin of probabilities in the mechanics of the microworld? What is the nature of Planck's constant h? What is the nature of probability amplitudes? What is the wave function? A system of axioms for quantum theory is formulated. A model is studied according to which a classical oscillator in a thermostat can be interpreted as a quantum one. The measurement problem is discussed in detail.
For advanced undergraduate students, graduate students, and specialists interested in the foundations of quantum theory.
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The concept of entropic time is then introduced on the basis of information acquisition, which is argued to be effectively irreversible and consistent with both the Second Law of Thermodynamics and our psychological perception of time. This is distinguished from the notion of parametric time, which serves as the temporal parameter for the unitary evolution of a physical state in non-relativistic quantum mechanics. The interpretation of these ideas in terms of both subjective and objective collapse models is also discussed. It is shown that energy is conserved under subjective collapse schemes whereas, in general, under objective collapse it is not. This is consistent with the fact that the latter is inherently non-unitary and that energy conservation arises out of time symmetry in the first place.
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum theory could be, if not resolved, at least mitigated by a proper interpretation of probability. We rather show, through a historical and analytical overview of probability and quantum theory, that if some interpretations of the one and the other go along particularly well, none follows in a unique way.