Bohmian mechanics (BM) draws a picture of nature, which is completely different from that drawn by standard quantum mechanics (SQM): Particles are at any time at a definite position, and the universe evolves deterministically. Astonishingly, accordin
g to a proof by Bohm the empirical predictions of these two very different theories coincide. From the very beginning, BM has faced all kinds of criticism, most of which are either technical or philosophical. There is, however, a criticism first raised by Correggi et al. (2002) and recently strengthened by Kiukas and Werner (2010), which holds that, in spite of Bohms proof, the predictions of BM do not agree with those of SQM in the case of local position measurements on entangled particles in a stationary state. Hence, given that SQM has been proven to be tremendously successful in the past, BM could most likely not be considered an empirically adequate theory. My aim is to resolve the conflict by showing that 1) it relies on hidden differences in the conceptual thinking, and that 2) the predictions of both theories approximately coincide if the process of measurement is adequately accounted for. My analysis makes no use of any sort of wavefunction collapse, refuting a widespread belief that an effective collapse is needed to reconcile BM with the predictions of SQM.
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about object
s in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points, both time and world are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everetts many-worlds interpretation, it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everetts approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random collapse of the wavefunction caused by the measurement, while still being an objectively deterministic theory.
