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The Foundations of Inference and Its Application to Fundamental Physics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Foundations of Inference and Its Application to Fundamental Physics./
Author:	Carrara, Nicholas.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	459 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-02, Section: A.
Contained By:	Dissertations Abstracts International83-02A.
Subject:	Theoretical physics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28548123
ISBN:	9798534665598

The Foundations of Inference and Its Application to Fundamental Physics.
Carrara, Nicholas.

The Foundations of Inference and Its Application to Fundamental Physics. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 459 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: A.

Thesis (Ph.D.)--State University of New York at Albany, 2021.

This item must not be sold to any third party vendors.

This thesis concerns the foundations of inference-probability theory, entropic inference, information geometry, etc. - and its application to the Entropic Dynamics (ED) approach to Quantum Mechanics (QM). The first half of this thesis, chapters 2-6, concern the development of the inference framework. We begin in chapter 2 by discussing deductive inference, which involves formal logic and it's role in accessing the truth of propositions. We eventually discover that deductive inference is incomplete, in that it can't address situations in which we have incomplete information. This necessitates a theory of inductive inference (probability theory), which is developed in chapter 3. Probability theory is derived as a framework for manipulating degrees of belief of propositions, in a way which is consistent with its deductive counterpart. In chapter 4 we review the construction of entropic inference as a means for updating our beliefs in the presence o new information. The entropy functional is designed through the process of eliminative induction by imposing a principle of minimal updating (PMU) and various constraints. Chapter 5 considers the design of another entropic functional, the total correlation and all its variants, for the purposes of ranking join distributions with respect to their correlations. Finally, in chapter 6, we discuss the application of a special case of the correlation functionals from chapter 5, the mutual information, to problems in experimental physics and machine learning. The second half of this thesis, chapters 7-9, concerns the ED approach to QM. In particular, chapters 8 and 9 involve the inclusion of particles with spin 1/2 into the framework. These developments are the main contribution of this thesis to the body of work in the ED approach. The problem is defined as an application of inference to the dynamics of quantum particles which have definite yet unknown positions and follow continuous trajectories. Through the method of maximum entropy developed in chapter 4, we can determine the transition probability that these particles will move from one location to another. Geometric algebra (GA) is chosen as the preferred representation for the algebra of spin, which is then introduced through constraints in the maximum entropy method. Aquantum mechanics is subsequently developed by constructing an epistemic phase space of probabilities and constraints and imposing that the physically relevant flows in this space are those which preserve a particular metric and symplectic form. These flows lead to a linear Pauli equation for one and two particles with spin.

ISBN: 9798534665598Subjects--Topical Terms:

2144760
Theoretical physics.
Subjects--Index Terms:

Entropy

The Foundations of Inference and Its Application to Fundamental Physics.
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300 $a 459 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: A.
500 $a Advisor: Ernst, Jesse;Caticha, Ariel.
502 $a Thesis (Ph.D.)--State University of New York at Albany, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis concerns the foundations of inference-probability theory, entropic inference, information geometry, etc. - and its application to the Entropic Dynamics (ED) approach to Quantum Mechanics (QM). The first half of this thesis, chapters 2-6, concern the development of the inference framework. We begin in chapter 2 by discussing deductive inference, which involves formal logic and it's role in accessing the truth of propositions. We eventually discover that deductive inference is incomplete, in that it can't address situations in which we have incomplete information. This necessitates a theory of inductive inference (probability theory), which is developed in chapter 3. Probability theory is derived as a framework for manipulating degrees of belief of propositions, in a way which is consistent with its deductive counterpart. In chapter 4 we review the construction of entropic inference as a means for updating our beliefs in the presence o new information. The entropy functional is designed through the process of eliminative induction by imposing a principle of minimal updating (PMU) and various constraints. Chapter 5 considers the design of another entropic functional, the total correlation and all its variants, for the purposes of ranking join distributions with respect to their correlations. Finally, in chapter 6, we discuss the application of a special case of the correlation functionals from chapter 5, the mutual information, to problems in experimental physics and machine learning. The second half of this thesis, chapters 7-9, concerns the ED approach to QM. In particular, chapters 8 and 9 involve the inclusion of particles with spin 1/2 into the framework. These developments are the main contribution of this thesis to the body of work in the ED approach. The problem is defined as an application of inference to the dynamics of quantum particles which have definite yet unknown positions and follow continuous trajectories. Through the method of maximum entropy developed in chapter 4, we can determine the transition probability that these particles will move from one location to another. Geometric algebra (GA) is chosen as the preferred representation for the algebra of spin, which is then introduced through constraints in the maximum entropy method. Aquantum mechanics is subsequently developed by constructing an epistemic phase space of probabilities and constraints and imposing that the physically relevant flows in this space are those which preserve a particular metric and symplectic form. These flows lead to a linear Pauli equation for one and two particles with spin.
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