The undivided universe. (English) Zbl 0990.81503

Bohm, D.; Hiley, B. J.

London: Routledge. xii, 397 p. (1995).

This volume, completed just prior to Bohm’s death, is a comprehensive exposition of Bohm’s “ontological” interpretation of quantum mechanics. The interpretation takes the wave function as an incomplete description of the world. In the case of particles, exact particle positions exist as well. In the case of boson fields, the field magnitudes are the additional “beables”. The wave function plays a dual role in this account. On the one hand it is a “guidance” field for the particles (fields), mapping particle position into velocity (or, alternatively in some cases, providing a “quantum potential” whose gradient is a force additional to the usual imposed forces accelerating the particle). On the other hand it is the wave function that provides the correct statistical distribution over initial particle positions for identically prepared systems. The book has four general sections. The first, Chapters 2 through 5, gives the basic interpretation. Successive chapters provide an historical introduction, give the ontological interpretation for one particle, extend it to many particle systems, and describe transitions in this framework. The second section, Chapters 6 through 8, deals with “general implications” of the interpretation. Measurement is characterized by the “undivided wholeness of systems and measuring apparatus”. Nonlocality in the theory is described in detail. Because the guiding wave function for a multi-particle system is in configuration space, an interference with one particle can affect another at a spatial distance instantaneously, so long as the wave function for the particles is an “entangled” one. The classical limit is described as seen in this interpretation.
The third section, Chapters 9 through 12, treats extensions of the approach. The first chapter deals with the wave function in its role of probability distribution over initial conditions. The next treats the Pauli equation and spin. Next the introduction of the boson field magnitudes as the elements of reality (as opposed to particle positions) and its guidance by the “quantum superpotential” is discussed. Finally the issue of relativistic invariance is treated. In the interpretation the fundamental theory is not Lorentz invariant due to the instantaneous non-local interactions. All statistical results, however, do obey Lorentz invariance.
The final, fourth, section, Chapters 13 through 15, discusses other interpretations of quantum theory and their relations to the “ontological” interpretation. The first of these chapters deals with “many worlds” interpretations. The second takes up the interpretation of Ghirardi-Rimini-Weber and that of “decoherent histories” in the version of Gell-Mann and Hartle. The final chapter deals with the overall “metaphysics” behind the interpretation. Here the emphasis is on the “implicate order” of the world, as represented by the folded-in order of the entangled wave functions that guide the, only apparently separable, “beables” of the world.
Many deep and important aspects of the interpretation are given lucid and revealing treatments. Among these are (1) the nature of the wave function as joint guiding field and probability distribution over initial conditions; (2) the fact that in measurement only position measurements can be thought of as revealing pre-existing states of the system measured (the other features being the result of the joint system and apparatus interaction); (3) the several ways in which one might try to rationalize the wave function’s role as “equilibrium” probability distribution (chaotic evolution vs. underlying “osmotic field” as stochastic driver to equilibrium); (4) the place of non-locality in this interpretation and in other interpretations of quantum theory; (5) the way in which interpretation preserves relativistic invariance at the level of observable statistics while denying it at the level of fundamental processes; and (6) the general virtues of this interpretation as providing an intuitive understanding of the quantum world while at the same time finding a more natural place for the manifest classical world than is available for it in some other interpretations.
Bohm’s heroic efforts in carrying to fruition this perspective on quantum theory, an interpretation stemming from that of de Broglie which was rejected early in the history of the subject because of its inability to deal with such issues as multi-particle systems, are ideally summed up in this very readable and fully comprehensive treatment of the subject. The “ontological” interpretation is now the subject of much vigorous attention, in no small part due to the availability of this masterful exposition of its technical and philosophical aspects. The book is absolutely essential reading for anyone interested in the foundations of quantum theory.

Reviewer: Lawrence Sklar (MR 96i:81008)

MSC:

81Pxx	Foundations, quantum information and its processing, quantum axioms, and philosophy
00A30	Philosophy of mathematics
81-02	Research exposition (monographs, survey articles) pertaining to quantum theory
00A79	Physics