Bohmian mechanics and consistent histories

The interpretations of a particular quantum gedanken experiment provided by Bohmian mechanics and consistent histories are shown to contradict each other, both in the absence and in the presence of a measuring device. The consistent history result seems closer to standard quantum mechanics, and shows no evidence of the mysterious nonlocal influences present in the Bohmian description. Bohmian mechanics [1, 2, 3, 4] provides a realistic interpretation of quantum theory by means of additional “hidden” variables, not part of the standard Hilbert space of wave functions, representing the positions of particles which make up a quantum system. All the particles have well-defined positions at all times, and follow trajectories as a function of time which are determined by the quantum wave function; the unitary time development of the latter is governed by Schrödinger’s equation. These particle trajectories, along with the quantum wave function, provide the basic ontology of the theory. Measurements do not play a fundamental role in Bohmian mechanics; they are simply particular examples of physical processes. Hence it is quite possible in this approach to model the measurement of a particle’s position, and ask whether the outcome of the measurement reveals the property of the measured particle or gives a spurious result. It was on this basis that the physical reality of Bohmian particle trajectories was challenged by Englert et al. [5]. They asserted that the Bohm trajectory of a particle in a bubble chamber does not necessarily coincide with the track of bubbles it produces. Although they did not carry out a calculation to directly support this particular assertion, they gave detailed calculations for some other situations in which a detector can be triggered without the trajectory of the particle passing through it. Their conclusion was that Bohmian trajectory is more a metaphysical construction than an aspect of physical reality. See [6] for a response to this work by proponents of Bohmian mechanics, and [7] for a reply by Englert et al. Somewhat later, Aharonov and Vaidman [8] made a simplified model of a bubble chamber track and reached the same conclusion as Englert et al. In addition, Dewdney, Hardy and Squires [9], themselves quite sympathetic to Bohm’s approach, carried out a detailed calculation on a simple model, in essence that shown in Fig. 1, and confirmed that a quantum particle ∗Electronic mail: [email protected]