ASPECTS OF DETERMINISM IN MODERN PHYSICS
John Earman
1 INTRODUCTION
The aims of this chapter are to review some aspects of determinism that are famil- iar to physicists but are little discussed in the philosophical literature and to show how these aspects connect determinism to issues about symmetries in physics, the structure and ontological status of spacetime, predictability, and computability.1 It will emerge that in some respects determinism is a robust doctrine and is quite hard to kill, while in other respects it is fragile and requires various enabling as- sumptions to give it a fighting chance. It will also be seen that determinism is far from a dead issue. Whether or not ordinary non-relativistic quantum mechanics (QM) admits a viable deterministic underpinning is still a matter of debate. Less well known is the fact that in some cases QM turns out to be more deterministic than its classical counterpart. Quantum field theory (QFT) assumes determinism, at least at the classical level, in order to construct the field algebra of quantum observables. Determinism is at the heart of the cosmic censorship hypothesis, the most important unsolved issue in classical general relativity theory (GTR). And issues about the nature and status of determinism lie at the heart of key foundation issues in the search for a theory of quantum gravity.
2 PRELIMINARIES
2.1 The metaphysics of determinism The proposal is to begin by getting a grip on the doctrine of determinism as it was understood pre-GTR and pre-QM, and then subsequently to try to understand how the doctrine has to be adjusted to accommodate these theories. In pre-GTR physics, spacetime serves as a fixed background against which the drama of physics is enacted. In pre-QM physics it was also assumed that there is a set O of gen- uine physical magnitudes (a.k.a. “observables”) each of which takes a determinate
1Recent surveys of determinism are found in Butterfield [1998], Earman [2004a], and Hoefer [2003]. A collection of articles on various aspects of determinism is found in Atmanspacher and Bishop [2002].
Handbook of the Philosophy of Science. Volume 2: Philosophy of Physics Volume editors: John Earman and Jeremy Butterfield. Handbook editors: Dov M. Gabbay, Paul Thagard and John Woods. c 2006 Elsevier BV. All rights reserved. 1370 John Earman value at every moment of time; call these the occurrent magnitudes. Other phys- ical magnitudes may be dispositional in character and may take on determinate values only in appropriate contexts; but it was assumed that these dispositional magnitudes supervene on the nondispositional magnitudes.2 A history H is a map from R to tuples of values of the basic magnitudes, where for any t ∈ R the state H(t) gives a snapshot of behavior of the basic magnitudes at time t. The world is Laplacian deterministic with respect to O just in case for any pair of histories H1, H2 satisfying the laws of physics, if H1(t)=H2(t) for some t, then H1(t)=H2(t) for all t. Several remarks are in order. First, the ‘t’ which appears in the above definition is supposed to be a global time function. This notion can be defined in a manner that applies to classical, special relativistic, and general relativistic spacetimes: a global time function is a smooth map t : M→R, where M is the spacetime manifold, such that for any p, q ∈M, t(p)