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arXiv:1403.3822 · Journal of Physics Conference Series

Entropic Dynamics: an inference approach to quantum theory, time and measurement

Ariel Caticha

Published Apr 14, 2014• 23 citations
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Abstract

We review the derivation of quantum theory as an application of entropic methods of inference. The new contribution in this paper is a streamlined derivation of the Schrödinger equation based on a different choice of microstates and constraints.
DOI
10.1088/1742-6596/504/1/012009

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Entropic Dynamics is a framework in which dynamical laws such as those that arise in physics are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to constraints reflecting the information that is relevant to the problem at hand. In this work I review the derivation of quantum theory but the fact that Entropic Dynamics is based on inference methods that are of universal applicability suggests that it may be possible to adapt these methods to fields other than physics.
Entropic Dynamics is an information-based framework that seeks to derive the laws of physics as an application of the methods of entropic inference. The dynamics is derived by maximizing an entropy subject to constraints that represent the physically relevant information that the motion is continuous and non-dissipative. Here we focus on the quantum theory of scalar fields. We provide an entropic derivation of Hamiltonian dynamics and using concepts from information geometry derive the standard quantum field theory in the Schrödinger representation.
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the particles of interest x there exist extra variables y whose entropy S ( x ) depends on x . The Schrödinger equation follows from their coupled dynamics: the entropy S ( x ) drives the dynamics of the particles x while they in their turn determine the evolution of S ( x ). In this 'entropic dynamics' time is introduced as a device to keep track of change. A welcome feature of such an entropic time is that it naturally incorporates an arrow of time. Both the magnitude and the phase of the wavefunction are given statistical interpretations: the magnitude gives the distribution of x in agreement with the usual Born rule and the phase carries information about the entropy S ( x ) of the extra variables. Extending the model to include external electromagnetic fields yields further insight into the nature of the quantum phase.
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the particles of interest x there exist extra variables y whose entropy S(x) depends on x. The Schr\"odinger equation follows from their coupled dynamics: the entropy S(x) drives the dynamics of the particles x while they in their turn determine the evolution of S(x). In this "entropic dynamics" time is introduced as a device to keep track of change. A welcome feature of such an entropic time is that it naturally incorporates an arrow of time. Both the magnitude and the phase of the wave function are given statistical interpretations: the magnitude gives the distribution of x in agreement with the usual Born rule and the phase carries information about the entropy S(x) of the extra variables. Extending the model to include external electromagnetic fields yields further insight into the nature of the quantum phase.
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schroedinger equation follows naturally from information geometry.
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration space and the corresponding probability distributions constitute a statistical manifold. The dynamics follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. A welcome feature is that the entropic dynamics notion of time incorporates a natural distinction between past and future. The statistical manifold is assumed to be a dynamical entity: its curved and evolving geometry determines the evolution of the particles which, in their turn, react back and determine the evolution of the geometry. Imposing that the dynamics conserve energy leads to the Schroedinger equation and to a natural explanation of its linearity, its unitarity, and of the role of complex numbers. The phase of the wave function is explained as a feature of purely statistical origin. There is a quantum analogue to the gravitational equivalence principle.