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arXiv:gr-qc/9701027

Sources of Predictability

James B. Hartle

Published Jan 13, 1997• 0 citations
arXivHTMLPDF

Abstract

Sources of predictability in the basic laws of physics are described in the most general theoretical context -- the quantum theory of the universe as a whole. (To appear in the Proceedings of the conference on Fundamental Sources of Unpredictability held at the Santa Fe Institute, March 28 to 30, 1996 to be published by Complexity.)
DOI
10.48550/arxiv.gr-qc/9701027

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Sources of predictability

James B. Hartle

Sources of predictability in the basic laws of physics are described in the most general theoretical context -- the quantum theory of the universe as a whole. (To appear in the Proceedings of the conference on Fundamental Sources of Unpredictability held at the Santa Fe Institute, March 28 to 30, 1996 to be published by Complexity.)

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In discussing the fundamental sources of unpredictability, I shall concentrate on those indeterminacies that are definitely required by theory. Let me therefore begin \nby 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: \n1. 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. \n2. 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 \napproximate 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 \nbreaking 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. \n3. 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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In discussing the fundamental sources of unpredictability, I shall concentrate on those indeterminacies that are definitely required by theory. Let me therefore begin \nby 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: \n1. 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. \n2. 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 \napproximate 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 \nbreaking 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. \n3. 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.
It is a surprise that a theory that seems to be in conflict with so much of the real world continues to serve as the underpinning for our understanding of that world. Quantum Mechanics has been with us in its present form since the mid-1920's, and still serves as one of the two basic frameworks on which all meaningful physical theories must rest. The question persists: Can quantum mechanics fail to predict phenomena we can observe with new precision, or does it possibly have limits on its applicability? Or is it an approximation to a more general theory? With the recent advances in experimental techniques and in theoretical thinking, it seemed appropriate to examine these questions anew through the mechanism of an informal conference. The idea for holding a workshop now came from the recent advances in both theoretical studies of quantum mechanics, and in the new classes of experiments that can provide new tests or improve significantly on old ones. The papers in these Proceedings are divided between theoretical studies and discussions of experiments. Most of the theoretical work describes the quantum mechanical analysis of new systems not hitherto analyzed. Half (or more) of the experimental papers describe new tests of the predictions of quantum theory, either by employing new precision on existing experiments or by exploring new ground.