Michael J. W. Hall, Dirk-André Deckert, and Howard M. Wiseman,

Quantum phenomena modelled by interactions between many classical worlds. Phys. Rev. X 4 041013 [17 pages] (2014).

At the request of Dr Shan Gao, I’m posting here a short discussion of this new paper.

This work is motivated by the quantum measurement problem, which suggests that orthodox quantum mechanics does not provide a realistic model of the universe. We postulate an ontology which is radically different from any other interpretation. In particular there is no wave-function, only a vast collection of essentially classical worlds, all real, which interact. Our world is but one of them. We call our theory an approach to, rather than an interpretation of, quantum mechanics, because it has the potential to lead to new predictions. It also has potential as a numerical tool.

For commentaries, see:

1. Bill Poirier, The Many Interacting Worlds Approach to Quantum Mechanics

Phys. Rev. X 4 040002 (2014) [Commentary as part of Editorial]

2. Alexandra Witze, A quantum world arising from many ordinary ones? Nature News (24 October, 2014)

3. me, “When parallel worlds collide … quantum mechanics is born“, The Conversation (24 October, 2014)

Our many interacting worlds (MIW) approach is most closely related to some earlier approaches using the hydrodynamic formulation of QM, which made a tentative connection between streamlines and worlds (see the commentary by Bill Poirier for references.) We postulate discrete interacting worlds, and are not tentative in our interpretation. The paragraphs below are based on those on page 2 of the published paper.

At the current stage, the MIW approach is not yet well enough developed to be considered on equal grounds with other long-established realistic approaches to quantum mechanics such as the de~Broglie-Bohm (dBB) and many-worlds (MW) interpretations. We have outlined the theory only for scalar non-relativistic particles, and for fields. We have done explicit calculations reproducing quantum statistics only for a single particle. Nevertheless it is worth comparing its ontology with those of these better known approaches.

In our MIW approach there is no wave-function, only a very large number (not a continuum!) of classical-like worlds with definite configurations that evolves deterministically. Probabilities arise only because observers are ignorant of which world they actually occupy, and so assign an equal weighting to all worlds compatible with the macroscopic state of affairs they perceive. In a typical quantum experiment, where the outcome is indeterminate in orthodox quantum mechanics, the final configurations of the worlds in the MIW approach can be grouped into different classes based on macroscopic properties corresponding to the different possible outcomes. The orthodox quantum probabilities will then be approximately proportional to the number of worlds in each class.

In contrast, the dBB interpretation postulates a single classical-like world, deterministically guided by a physical universal wave function. This world — a single point of configuration space — does not exert any back reaction on the guiding wave, which has no source but which occupies the entire configuration space. This makes it challenging to give an ontology for the wave function in parts of configuration space so remote from the `real’ configuration that it will never affect its trajectory. Furthermore, this wave function also determines a probability density for the initial world configuration. From a Bayesian perspective on probability this dual role is not easy to reconcile.

In the Everett or MW interpretation, the `worlds’ are orthogonal components of a universal wave function . The particular decomposition at any time, and the identity of worlds through time is argued to be defined (at least well-enough for practical purposes) by the quantum dynamics which generates essentially independent evolution of these quasiclassical worlds into the future (a phenomenon called effective decoherence). The inherent fuzziness of Everettian worlds is in contrast to the corresponding concepts in the MIW approach, of a well-defined group of deterministically-evolving configurations. In the MW interpretation it is meaningless to ask exactly how many worlds there are at a given time, or exactly when a branching event into subcomponents occurs, leading to criticisms that there is no precise ontology. Another difficult issue is that worlds are not equally `real’ in the MW interpretation, but are `weighted’ by the modulus squared of the corresponding superposition coefficients. As noted above, in the MIW approach all worlds are equally weighted, so that Laplace’s theory of probability is sufficient to account for our experience and expectations.

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