The paper takes up Bell's (1987) "Everett (?) theory" and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space - hence "Tychistic Bohmian Mechanics" (TBM). The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for a Bohmian theory within the Primitive Ontology framework (for which we offer a metaphysically more perspicuous formulation than is customary). TBM's formalism is that of ordinary Bohmian Mechanics (BM), without the postulate of continuous particle trajectories and their deterministic dynamics. This "rump formalism" receives, however, a different interpretation. We defend TBM as an empirically adequate and coherent quantum theory. Objections voiced by Bell and Maudlin are rebutted. The "for all practical purposes"-classical, Everettian worlds (i.e. quasi-classical histories) exist sequentially in TBM (rather than simultaneously, as in the Everett interpretation). In a temporally coarse-grained sense, they quasi-persist. By contrast, the individual particles themselves cease to persist.

Studies in History and Philosophy of Science Part AOct 25, 20215 citations

Worlds in a Stochastic Universe: On the Emergence of World Histories in Minimal Bohmian Mechanics

Alexander Ehmann

This thesis develops a detailed account of the emergence of for all practical purposes continuous, quasi-classical world histories from the discontinuous, stochastic micro dynamics of Minimal Bohmian Mechanics (MBM). MBM is a non-relativistic quantum theory. It results from excising the guiding equation from standard Bohmian Mechanics (BM) and reinterpreting the quantum equilibrium hypothesis as a stochastic guidance law for the random actualization of configurations of Bohmian particles. On MBM, there are no continuous trajectories linking up individual configurations. Instead, individual configurations are actualized independently of each other, carving out the decoherence-induced branching structure of the universal wave function. Yet, by contrast to the Everett interpretation, branches of the universal wave function are not actualized in parallel, i.e. all at the same time. Rather, world branches, on MBM, are actualized sequentially. For an introduction to MBM, the transition from BM to MBM is described, and their empirical equivalence is established. I present the conditions under which MBM can be classified as a primitive ontology (PO) theory, regarded as crucial for the acceptance of a theory as Bohmian by many proponents of BM. While rendering MBM compatible with the PO approach, it must not fall prey to the problem of communication, arising from the two-space reading of BM. The issue of temporal solipsism, identified by Bell as a serious problem for his “Everett (?) theory” – the historic predecessor of MBM – is discussed. I argue that Barbour’s time capsule approach does not provide a satisfactory solution. In particular, his adopting a more than minimal psychophysical parallelism between brain processes and experience of macroscopic change is argued to be reasonable in light of our current best neuroscience, yet problematic for theories relying solely on time capsules, understood as highly structured, individual, internally static configurations. As a solution, I introduce worlds, and world histories, as key concepts in providing a link between MBM’s micro dynamics and macroscopic phenomena. Worlds, other than time capsules, are coarse-grained regions in phase- or configuration space, defined as sets of possible micro states satisfying a relation of sufficient similarity from a macroscopic perspective, with respect to a given micro state. Hence, worlds may overlap. I argue that worlds thus construed are a reasonable option for replacing the disjoint macro regions of phase space, resulting from the usual way of partitioning phase space in the standard framework of Boltzmannian statistical mechanics. This move solves the issue of discontinuous change of macro variables upon the micro state crossing the boundary between different macro regions. I adapt this move for MBM’s discontinuous micro dynamics in configuration space. Issues revolving around the microscopic-macroscopic distinction, particle identity, impenetrability and haecceity in light of the desideratum of particle number conservation, etc., are discussed. I provide a detailed explanation of how overlapping worlds in MBM form world histories, thereby linking up macroscopically distinct worlds. Thus, the problem of temporal solipsism is resolved in a way that is compatible with a more than minimal psychophysical parallelism.

Jan 1, 20201 citation