Dimensional Analysis Across the Landscape of Physics Classic Results, Textbook Examples, and Exploration of Research

Dimensional Analysis Across the Landscape of Physics introduces readers to the powerful idea that almost all physical quantities in science and engineering can be described using only five base dimensions: mass, length, time, charge, and temperature, and combinations thereof. Starting with the basics of how this foundational intellectual concept arises, it illustrates the use of dimensional analysis in approaching the solutions to textbook-level problems in physics and adjacent fields, ranging from introductory courses, through the advanced undergraduate curriculum, to advanced Physics electives.

It covers the core curricular topics of classical mechanics, electricity and magnetism, thermal physics, and quantum mechanics. It includes examples of the use of dimensional analysis applied to topics from other related fields such as geosciences, meteorology, engineering, and biophysics to emphasize the utility of such methods across the proverbial landscape of physics. There is also coverage of more specialized topics, such as advanced quantum mechanics, particle physics, field theory, condensed matter physics, and astrophysics and gravitation.

Many worked examples are included, as well as an extensive array of end-of-chapter problems, with a solution manual available to instructors. In addition to covering the standard topics in the undergraduate curriculum, the book explores how dimensional analysis has been used (and continues to be used) in research across all fields of physics, citing examples from the historical literature and from very recent research results. The work includes extensive references to the original papers for further study, as well as useful ancillary material, including a dimensional analysis 'dictionary', brief introductions to data-fitting, and connections to metrology. There is an emphasis throughout on the use of modern symbolic programming to streamline the process of the solving systems of linear equations needed for a dimensional analysis approach, with several Mathematica© templates provided for reader use.

Richard W. Robinett, Professor Emeritus, Department of Physics, Penn State University

Richard W. Robinett obtained his Ph. D. in theoretical physics from the University of Minnesota in 1981, followed by postdoctoral appointments at the University of Wisconsin Madison and the University of Massachusetts Amherst. He joined the faculty of the Physics Department at Penn State in 1986 as an Assistant Professor, and became a full Professor in 2000. He served as Interim Associate Dean of the Eberly College of Science twice, and as Associate Department Head for Undergraduate and Graduate Studies, until his retirement in 2023. He was selected a Fellow of the American Physical Society in 2003.

I Preparing to explore the landscape of physics1. Getting started2. Warm-up: Dimensional analysis confronts dataII The `quadrivium' of physics3. Classical mechanics: Point particles and continuum systems4. Electricity and magnetism5. Thermal physics6. Quantum mechanicsIII Exploring more advanced topics7. Advanced quantum mechanics8. Condensed matter physics9. Astrophysics and gravitationIV Resources for exploration10 Ancillary material