Abstract
Entropic Dynamics is a framework in which dynamical laws 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 the constraints appropriate to the problem at hand. In this paper we review three examples of entropic dynamics. First we tackle the simpler case of a standard diffusion process which allows us to address the central issue of the nature of time. Then we show that imposing the additional constraint that the dynamics be non-dissipative leads to Hamiltonian dynamics. Finally, considerations from information geometry naturally lead to the type of Hamiltonian that describes quantum theory.
Highlights
The laws of physics, and in particular the laws of dynamics, have traditionally been seen as laws of nature
As with other applications of entropic methods, to derive dynamical laws we must first specify the microstates that are the subject of our inference — the subject matter — and we must specify the prior probabilities and the constraints that represent the information that is relevant to our problem. (See e.g., [2].) We consider N particles living in a flat Euclidean space X with metric δab
To motivate the particular choice of the functional F [ρ] that leads to quantum theory we appeal to information geometry once again
Summary
The laws of physics, and in particular the laws of dynamics, have traditionally been seen as laws of nature. We explore an alternative view in which the relation is considerably more indirect: The laws of physics provide a framework for processing information about nature From this perspective physical models are mere tools that are partly discovered and partly designed with our own very human purposes in mind. We focus on the derivation of the Schrödinger equation but the ED approach has been applied to several other topics in quantum mechanics that will not be reviewed here These include the quantum measurement problem [5,7,8]; momentum, angular momentum, their uncertainty relations, and spin [9,10]; relativistic scalar fields [11]; the Bohmian limit [12]; and the extension to curved spaces [13]. ED makes no reference to any sub-quantum dynamics whether classical, deterministic, or stochastic
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