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arXiv:1502.07092 · Journal of Physics Conference Series

Time symmetry in wave function collapse models

Daniel Bedingham

Published Jul 3, 2015• 0 citations
arXivHTMLPDF

Abstract

A framework for wave function collapse models that is symmetric under time reversal is presented. Within this framework there are equivalent pictures of collapsing wave functions evolving in both time directions. The backwards-in-time Born rule can be broken by an initial condition on the Universe resulting in asymmetric behaviour. Similarly the forwards- in-time Born rule can in principle be broken by a final condition on the Universe.

DOI
10.1088/1742-6596/626/1/012007

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A framework for wave function collapse models that is symmetric under time reversal is presented. Within this framework there are equivalent pictures of collapsing wave functions evolving in both time directions. The backwards-in-time Born rule can be broken by an initial condition on the Universe resulting in asymmetric behaviour. Similarly the forwards- in-time Born rule can in principle be broken by a final condition on the Universe.
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Dynamical collapse models embody the idea of a physical collapse of the wave function in a mathematically well-defined way. They involve modifications to the standard rules of quantum theory in order to describe collapse as a physical process. This appears to introduce a time reversal asymmetry into the dynamics since the state at any given time depends on collapses in the past but not in the future. Here we challenge this conclusion by demonstrating that, subject to specified model constraints, collapse models can be given a structurally time symmetric formulation in which the collapse events are the primitive objects of the theory. Three different examples of time asymmetries associated with collapse models are then examined and in each case it is shown that the same dynamical rule determining the collapse events works in both the forward and backward in time directions. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws.
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function so as to give a dynamical account of collapse. The resulting dynamics is at first sight time asymmetric for the simple reason that the wave function depends on those collapse events in the past but not those in the future. Here we show that dynamical wave-function collapse models admit a general description that has no built-in direction of time. Given some simple constraints, we show that there exist empirically equivalent pictures of collapsing wave functions in both time directions, each satisfying the same dynamical rules. A preferred direction is singled out only by the asymmetric initial and final time constraints on the state of the universe.
Although quantum mathematics is the most successful science ever, that does not mean we live in the universe described by quantum mechanics. This article is entirely based on symmetry. Two symmetrical universes could have exactly the same mathematics, but differ in other respects. The motivation for seeking symmetry inside quantum mathematics is that the QM picture of nature is bizarre. Richard Feynman says no one can understand it. We propose that the quantum world is not bizarre. QM portrays the wrong universe: the symmetrical one, not the one we inhabit. If quantum waves travel in the opposite direction as what is expected, then we would have the same math but a different universe, one that is recognizable and familiar. Wave equations are symmetrical with respect to time reversal. This means they are symmetrical with respect to wave direction reversal (with time going forwards). This wave equation symmetry is the basis of the symmetry of two models of the universe, only one of which is congruent with the universe we inhabit.