Bohmian mechanics is, it seems to me, by far the simplest and clearest version of quantum theory. Nonetheless, with its additional variables and equations beyond those of standard quantum mechanics, Bohmian mechanics has seemed to most physicists to involve too radical a departure from quantum modes of thought. The approaches of spontaneous localization and decoherent histories have achieved much wider acceptance among physicists, the former because it ostensibly involves only wave functions, effectively collapsing upon measurement in the usual text-book manner, and the latter because it apparently is defined solely in terms of standard quantum mechanical machinery--i.e., the quantum measurement formulas of the orthodox theory, involving wave functions and sequences of Heisenberg projection operators.

However, SL clearly involves equations beyond those of orthodox quantum theory, and, as I've argued, DH must also be regarded in this way. I have also argued that neither for DH nor even for SL can the wave function be regarded as providing the complete description of a physical system. Thus, while there are significant differences in detail, the three approaches discussed here have much more in common than is usually acknowledged. Each involves additional equations and additional variables; the latter are the fundamental variables, describing the primitive ontology--what the theory is fundamentally about. The behavior of the fundamental variables is governed by laws expressed in terms of the wave function, which thus simply plays a dynamical role.

As to detail, Bohmian mechanics shows that if we don't insist upon
patterning these laws upon familiar formulas such as those of the quantum
measurement formalism, surprising simplicity can be achieved. GRW,
particularly a la Bell, shows that these laws may be of a most unusual
variety, with unexpected implications for the symmetry of the theory
[1, page 209,]. And DH introduces a fundamental irreducible
coarse-graining and, if it should turn out that more than one family
satisfies DC+, suggests that a fundamental stochastic theory need not
assign probabilities to everything that can happen--for example, to
histories of the form ``*h* and '' where *h* and
belong to different DC+ families, while the history ``*h* and ''
belongs to no such family.

None of the theories sketched here is Lorentz invariant. There is a good reason for this: the intrinsic nonlocality of quantum theory presents formidable difficulties for the development of a Lorentz invariant formulation that avoids the vagueness of the orthodox version. I believe, however, that such a theory is possible, and that the three approaches I've discussed here have much to teach us about how we might go about finding one.

Wed Aug 13 17:22:41 EDT 1997