Fundamental Sources of Unpredictability

Abstract

In discussing the fundamental sources of unpredictability, I shall concentrate on those indeterminacies that are definitely required by theory. Let me therefore begin by eliminating from consideration supposed indeterminacies stemming from doubts that some people may entertain about basic principles or from certain kinds of ignorance that I believe to be temporary and likely to be remedied in the relatively near future. I assume the following: 1. Quantum mechanics is correct. The formulation and interpretation of quantum mechanics are still undergoing some necessary evolution, especially in order to accommodate quantum cosmology in a comfortable way, but the basic character of quantum mechanics has always been the same and we may suppose it will remain unchanged. 2. The elementary particles and their interactions obey a definite dynamical law, discoverable by inquiring complex adaptive systems such as the human scientific enterprise. Although the process of discovery involves a sequence of approximate schemata, there is an endpoint to the process after a finite amount of research. (Of course, it can never be possible to prove that the resulting unified theory is perfect; one can only verify it in the usual way by comparing predictions to available observations.) Humans may already have found this unified quantum field theory in the form of superstring theory, which has, to begin with, no arbitrary parameters. (Of course, spontaneous symmetry breaking may give rise to some parameters and even to a choice of solutions, with probabilities for the various alternatives. I will deal with that possibility further on.) This second assumption is equivalent to stating that there is no necessary fundamental unpredictability stemming from ignorance of the universal dynamical law. 3. The density matrix (in the Schrödinger picture) of the universe near the beginning of its expansion is also knowable. It must in any case be comparatively simple and very far from equilibrium. The second law of thermodynamics and the other associated arrows of time are explained by these properties of the initial density matrix along with the fact that the universe is still very young—the interval of ten billion years is extremely short compared with the relaxation time from the special initial condition.

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