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From Inference to Physics ∗

Ariel Caticha

Published Aug 4, 2013• 6 citations
OpenAlex

Abstract

Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system as it moves from given initial to final states. For an appropriately chosen configuration space the path of maximum probability reproduces Newtonian dynamics. 1

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From Inference to Physics

Ariel Caticha, Marcelo de Souza Lauretto, Carlos Alberto de Bragança Pereira +1 more

Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system as it moves from given initial to final states. For an appropriately chosen configuration space the path of maximum probability reproduces Newtonian dynamics.

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From Information Geometry to Newtonian Dynamics

Ariel Caticha, Carlo Cafaro, Kevin H. Knuth +3 more

Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by a probability distribution. The corresponding configuration space is a statistical manifold the geometry of which is defined by the information metric. The trajectory follows from a principle of inference, the method of Maximum Entropy No additional “physical” postulates such as an equation of motion, or an action principle, nor the concepts of momentum and of phase space, not even the notion of time, need to be postulated. The resulting entropic dynamics reproduces the Newtonian dynamics of any number of particles interacting among themselves and with external fields. Both the mass of the particles and their interactions are explained as a consequence of the underlying statistical manifold.

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Entropic Dynamics: Mechanics without Mechanism

Ariel Caticha

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.

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From Entropic Dynamics to Quantum Theory

Ariel Caticha, Paul M. Goggans, Chun-Yong Chan

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.

arXiv:0907.4335•AIP conference proceedings•Jan 1, 2009•3 citations

Entropic Dynamics

Ariel Caticha

Abstract 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 laws of motion such as those of classical mechanics are postulated. Instead, the dynamics is driven by entropy subject to constraints that reflect the information relevant to the problem at hand. In this chapter I review the derivation of three forms of mechanics. The first is a standard diffusion, the second is a form of Hamiltonian mechanics, and the third form is an argument from information geometry used to derive the special case known as quantum mechanics.

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Entropic quantization of scalar fields

Selman Ipek, Ariel Caticha

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.

arXiv:1412.5637•AIP conference proceedings•Jan 1, 2015•19 citations
Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system as it moves from given initial to final states. For an appropriately chosen configuration space the path of maximum probability reproduces Newtonian dynamics. 1
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by a probability distribution. The corresponding configuration space is a statistical manifold the geometry of which is defined by the information metric. The trajectory follows from a principle of inference, the method of Maximum Entropy No additional “physical” postulates such as an equation of motion, or an action principle, nor the concepts of momentum and of phase space, not even the notion of time, need to be postulated. The resulting entropic dynamics reproduces the Newtonian dynamics of any number of particles interacting among themselves and with external fields. Both the mass of the particles and their interactions are explained as a consequence of the underlying statistical manifold.
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.
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.
Abstract 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 laws of motion such as those of classical mechanics are postulated. Instead, the dynamics is driven by entropy subject to constraints that reflect the information relevant to the problem at hand. In this chapter I review the derivation of three forms of mechanics. The first is a standard diffusion, the second is a form of Hamiltonian mechanics, and the third form is an argument from information geometry used to derive the special case known as quantum mechanics.
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.