Searcharxiv⌕ Search

arXiv subjects

Ariel Caticha

Publications and source records attributed to Ariel Caticha.

At least 37 records · Page 2Linked to original sources
arXiv2017

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

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.

quant-ph↗
arXiv2017

Exact Renormalization Groups as a form of Entropic Dynamics

The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom. What all these methods have in common -- which is what explains their success -- is that they allow a systematic search for those degrees of freedom that happen to be relevant to the phenomena in question. In the standard approaches the RG transformations are implemented by either coarse graining or by changes of variables. When these transformations are infinitesimal the formalism can be described as a continuous dynamical flow in a fictitious time parameter. It is generally the case that these exact RG equations are functional diffusion equations. In this paper we show that the exact RG equations can be derived using entropic methods. The RG flow is then described as a form of entropic dynamics of field configurations. Although equivalent to other versions of the RG, in this approach the RG transformations receive a purely inferential interpretation that establishes a clear link to information theory.

cond-mat.stat-mech↗
arXiv2017

Changes of Variables and the Renormalization Group

A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a saddle point approximation is more accurate, becoming, in some cases asymptotically exact as the transformations are iterated. The formalism provides a simplified and unified approach to several known renormalization groups. It also suggests some new ways in which renormalization group methods might successfully be applied. In particular, an exact gauge covariant renormalization group transformation is constructed. Solutions for a scalar field theory are obtained both as an expansion in ε=4-d and as an expansion in a single coupling constant.

hep-th↗
arXiv2017

The Classical Limit of Entropic Quantum Dynamics

The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that Planck's constant remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.

quant-ph↗
arXiv2017

Entropic Dynamics: The Schroedinger equation and its Bohmian limit

In the Entropic Dynamics (ED) derivation of the Schroedinger equation the physical input is introduced through constraints that are implemented using Lagrange multipliers. There is one constraint involving a "drift" potential that correlates the motions of different particles and is ultimately responsible for entanglement. The purpose of this work is to deepen our understanding of the corresponding multiplier. Its main effect is to control the strength of the drift relative to the fluctuations. We show that ED exhibits a symmetry: models with different values of the multiplier can lead to the same Schroedinger equation; different "microscopic" or sub-quantum models lead to the same "macroscopic" or quantum behavior. As the multiplier tends to infinity the drift prevails over the fluctuations and the particles tend to move along the smooth probability flow lines. Thus ED includes the causal or Bohmian form of quantum mechanics as a special limiting case.

quant-ph↗
arXiv2017

Quantum Measurement and Weak Values in Entropic Dynamics

The problem of measurement in quantum mechanics is studied within the Entropic Dynamics framework. We discuss von Neumann and Weak measurements, wavefunction collapse, and Weak Values as examples of bayesian and entropic inference.

quant-ph↗
arXiv2016

Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class

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 Schroedinger 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 Schroedinger 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 non-dissipative 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.

quant-ph↗
arXiv2016

Entropic Dynamics on Curved Spaces

Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic dynamics of $N$ particles to curved spaces. The important new feature is that the displacement of a particle does not transform like a vector because fluctuations can be large enough to feel the effects of curvature. The final result is a modified Schrödinger equation in which the usual Laplacian is replaced by the Laplace-Beltrami operator.

quant-ph↗
arXiv2016

Relational Entropic Dynamics of Particles

The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a system. This leads to an entropic version of the classical best matching technique developed by J. Barbour and collaborators. The procedure is illustrated in the simple case of a system of N particles with global translational symmetry. The generalization to other symmetries whether global (rotational invariance) or local (gauge invariance) is straightforward. The entropic best matching allows a quantum implementation Mach's principles of spatial and temporal relationalism and provides the foundation for a method of handling gauge theories in an informational framework.

quant-ph↗
arXiv2015

Geometry from Information Geometry

We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.

gr-qc↗
arXiv2015

Entropic Dynamics

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.

quant-ph↗
arXiv2014

Towards an Informational Pragmatic Realism

I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More specifically: (1) Probability theory is designed as the uniquely natural tool for representing states of incomplete information. (2) An epistemic notion of information is defined in terms of its relation to the Bayesian beliefs of ideally rational agents. (3) The method of updating from a prior to a posterior probability distribution is designed through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting framework includes as special cases both MaxEnt and Bayes' rule. It therefore unifies entropic and Bayesian methods into a single general inference scheme. I find that similar pragmatic elements are an integral part of Putnam's internal realism, of Floridi's informational structural realism, and also of van Fraasen's empiricist structuralism. I conclude with the conjecture that their valuable insights can be incorporated into a single coherent doctrine - an informational pragmatic realism.

physics.hist-ph↗
arXiv2014

The Basics of Information Geometry

To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".

physics.data-an↗
arXiv2014

Entropic Dynamics: from Entropy and Information Geometry to Hamiltonians and Quantum Mechanics

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.

quant-ph↗
arXiv2014

Entropic Quantization of Scalar Fields

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 Schroedinger representation.

quant-ph↗
arXiv2012

The Entropic Dynamics of Relativistic Quantum Fields

The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field configurations. On extending the notion of entropic time to the relativistic regime we find that the field fluctuations provide the clock that sets the scale of duration. We also find that the usual divergences that affect all quantum field theories do not refer to the real values of physical quantities but rather to epistemic quantities invariably associated to unphysical probability distributions such as variances and other measures of uncertainty.

quant-ph↗
arXiv2012

Entropic Inference: some pitfalls and paradoxes we can avoid

The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes provide us with valuable learning opportunities to sharpen our skills in the proper way to deploy entropic methods. The central theme of this paper revolves around the different ways in which constraints are used to capture the information that is relevant to a problem. This leads us to focus on four epistemically different types of constraints. I propose that the failure to recognize the distinctions between them is a prime source of errors. I explicitly discuss two examples. One concerns the dangers involved in replacing expected values with sample averages. The other revolves around misunderstanding ignorance. I discuss the Friedman-Shimony paradox as it is manifested in the three-sided die problem and also in its original thermodynamic formulation.

physics.data-an↗