Abstract
Researchers propose a new ``many-interacting-worlds'' theory that could explain quantum mechanics in all its strangeness. Numerical simulations reproduce wave behavior in double-slit experiments assuming as few as 40 worlds.
Highlights
The role of the wave function differs markedly in various formulations of quantum mechanics
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical “worlds,” and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function
We introduce a simple model of such a “many interacting worlds” approach and show that it can reproduce some generic quantum phenomena—such as Ehrenfest’s theorem, wave packet spreading, barrier tunneling, and zero-point energy—as a direct consequence of mutual repulsion between worlds
Summary
The role of the wave function differs markedly in various formulations of quantum mechanics. In Madelung’s quantum hydrodynamics [5], Nelson’s stochastic dynamics [6], and Hall and Reginatto’s exact uncertainty approach [7], the fundamental equations of motion are formulated in terms of a configuration probability density P and a momentum potential S (or the gradient of the latter), with a purely formal translation to a wave function description via Ψ ≔ P1=2 exp1⁄2iS=ħ. Regarded as a fundamental physical theory in its own right, the MIW approach may lead to new predictions arising from the restriction to a finite number of worlds It provides a natural discretization of the Holland-Poirier approach, which may be useful for numerical purposes. Before considering how its dynamics might be mathematically formulated and used as a numerical tool, we give a brief discussion of how its ontology may appeal to those who favor realist interpretations
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