Abstract
We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is not a new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof.
Highlights
Completing the Realist ProgramThe ontic interpretation of quantum mechanics, that the wavefunction is an element of reality, is physically appealing because experience with other physical theories is that it is possible to describe real objects and fields mathematically, and it seems odd that only quantum mechanics should be different
Motivated yet again by a desire to have QM behave as other physical theories do, we propose that genuinely random variables are not root causes of physical phenomena, but underlying physical mechanisms may depend on uncontrolled or poorlyunderstood parameters such that a variety of outcomes are possible from experiments that appear to be identically prepared
The traditional challenge of quantum measurement is to explain the sensitivity of a quantum system to measurement, which changes its evolution from unitary evolution to collapse
Summary
Completing the Realist ProgramThe ontic interpretation of quantum mechanics, that the wavefunction is an element of reality, is physically appealing because experience with other physical theories is that it is possible to describe real objects and fields mathematically, and it seems odd that only quantum mechanics should be different. It ought to be possible to complete the realist program by providing an unambiguous mathematical description of the evolution of the wavefunction that deals with these challenges in a reasonable way and applies in all circumstances (that is, with or without measurement). There must exist a mathematical relationship among variables and functionals thereof (a “wave equation,” for short) that is valid at all times. It should describe the phenomena described by the wave equation in standard QM, and the measurement-induced transition from a superposition to a single (collapsed) eigenstate
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