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arXiv:2208.02156 · International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt)

Entropic Dynamics and Quantum “Measurement”

Ariel Caticha

Published Dec 15, 2022• 3 citations
arXivHTMLPDF

Abstract

The entropic dynamics (ED) approach to quantum mechanics is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The approach succeeds because ED achieves a clear-cut separation between ontic and epistemic elements: positions are ontic, while probabilities and wave functions are epistemic. Thus, ED is a viable realist ψ-epistemic model. Such models are widely assumed to be ruled out by various no-go theorems. We show that ED evades those theorems by adopting purely epistemic dynamics and denying the existence of an ontic dynamics at the subquantum level.

DOI
10.3390/psf2022005036

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The entropic dynamics (ED) approach to quantum mechanics is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The approach succeeds because ED achieves a clear-cut separation between ontic and epistemic elements: positions are ontic, while probabilities and wave functions are epistemic. Thus, ED is a viable realist ψ-epistemic model. Such models are widely assumed to be ruled out by various no-go theorems. We show that ED evades those theorems by adopting purely epistemic dynamics and denying the existence of an ontic dynamics at the subquantum level.
Abstract Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single‐valuedness of wave functions.
Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures—which is a Hamilton-Killing flow in phase space—is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations.
In the Entropic Dynamics (ED) approach, quantum mechanics is derived from the principles of entropic inference and information geometry. The ED approach differs from other interpretations by making a clear commitment to distinguishing which variables are ontic (real) and which are epistemic. The classical limit for the center of mass (CM) coordinate is achieved for a large number of particles, M →∞, while Planck’s constant ℏ remains finite. Typically, the emergence of the classical limit requires decoherence through interactions with the external environment. In this work, we investigate whether the classical behavior of the CM coordinate in a mesoscopic system can instead be achieved through internal decoherence resulting from interactions of the CM with the particles of the system itself. Within the framework of entropic dynamics, we study how correlations between a system’s center of mass and its internal coordinates impact this transition. We look at mesoscopic systems placed in both uniform and non-uniform gravitational potentials using probabilistic forms of the Hamilton–Jacobi equation. In uniform fields, the center of mass remains independent of internal coordinates, maintaining quantum coherence. Meanwhile, non-uniform potentials create coupling that induces decoherence, leading to classical behavior. These results show correlation-induced information loss as a natural process for the quantum-to-classical transition and clarify how entropic dynamics provide a coherent, information-theoretic link between quantum and classical realms.
Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson’s stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.
Standard Quantum Mechanics, although successful in terms of calculating and predicting results, is inherently difficult to understand and can suffer from misinterpretation.Entropic Dynamics is an epistemic approach to quantum mechanics based on logical inference.It incorporates the probabilities that naturally arise in situations in which there is missing information.It is the author's opinion that an advantage of this approach is that it provides a clearer mental image with which to picture quantum mechanics.This may provide anWe then move on to applying Entropic Dynamics to several of the paradigmatic examples used to explain quantum mechanics.The first of these is wave packet expansion.The second is interference, which is the basis behind many of the important phenomena in quantum mechanics.The third is the double slit experiment, which provides some interesting insight into the subject of interference.In particular, we look at the way in which minima can occur without a mechanism for destructive interference, since probabilities only add.The idea of probability flow is very apparent at this point in the discussion.The next example is that of the harmonic oscillator.This leads to an interesting insight concerning rotation and angular momentum as it corresponds to the flow of probability.The last example explored is that of entanglement.The discussion begins with a review of EPR, but then comes to the interesting conclusion that many of the problems inherent in the traditional approach to entanglement do not exist in Entropic Dynamics.The last topic covered in this thesis consists of some remarks concerning the state of education research as it pertains to quantum mechanics and the ways in which Entropic Dynamics might address them.iii viii 9.3.
Entropic Dynamics (ED) is a framework that allows the formulation of dynamical theories as an application of entropic methods of inference. In the generic application of ED to derive the Schrödinger equation for N particles the dynamics is a non-dissipative diffusion in which the system follows a "Brownian" trajectory with fluctuations superposed on a smooth drift. We show that there is a family of ED models that differ at the "microscopic" or sub-quantum level in that one can enhance or suppress the fluctuations relative to the drift. Nevertheless, members of this family belong to the same universality class in that they all lead to the same emergent Schrödinger behavior at the "macroscopic" or quantum level. The model in which fluctuations are totally suppressed is of particular interest: the system evolves along the smooth lines of probability flow. Thus ED includes the Bohmian or causal form of quantum mechanics as a special limiting case. We briefly explore a different universality class - a nondissipative dynamics with microscopic fluctuations but no quantum potential. The Bohmian limit of these hybrid models is equivalent to classical mechanics. Finally we show that the Heisenberg uncertainty relation is unaffected either by enhancing or suppressing microscopic fluctuations or by switching off the quantum potential.