Probability in Physics—An Introductory Guide

Abstract

This book is not only valuable for undergraduate but also for graduate students and lecturers alike. Many physics curricula turn a mostly blind eye to probability; it might only appear in the context of experimental errors or in very specific examples in theoretical physics such as the Fermi-Dirac statistics. Andy Lawrence promises to provide a different approach and instead places probabilistic concepts at the heart of modern physics. After a short introduction to the most basic definitions from probability theory, the book quickly starts to model real physical phenomena and therefore introduces the reader to more advanced probability distributions and probabilistic techniques in a natural, hands-on way that is suitable for most physics students. Thermodynamics, quantum mechanical systems, and astronomy (Lawrence’s own field of expertise) provide numerous examples to motivate the use of more and more advanced techniques and equations. Thus, as early as in the 3rd of 14 chapters, Lawrence presents the first highlight of his book by deriving the Boltzmann distribution purely from this probabilistic point of view. Flexibly switching between the frequentist and Bayesian approach to probability, further chapters cover statistical hypothesis tests, model fitting, and brief glimpses into random processes in time. For curious students and for experienced lecturers, the last four chapters of Lawrence’s book provide thought-provoking discussions of the more philosophical aspects of probability theory, such as the arrow of time, information theory, and the inherent randomness in quantum mechanics. Although he touches on fractals, dynamical systems, and attractors, he unfortunately does not follow up with a chapter on the quasi-random behaviour of chaotic systems with strange attractors.