Bach and Physics

BachPhysics is a long-term collection of essays on physics and mathematics, written for readers who want to understand difficult topics in detail and from first principles. The intended audience is primarily advanced undergraduate and graduate students, as well as self-learners who are comfortable following mathematical arguments closely.

The guiding philosophy is understanding through derivation. The goal is not simply to state results, but to follow the path that leads to them. Equations are developed carefully, intermediate steps are shown whenever possible, and the connections between mathematical structure and physical meaning are made explicit.

Many physics texts move quickly from one equation to the next, often omitting passages that are essential for real understanding. BachPhysics is built around the opposite approach: derivations should be readable, reproducible, and detailed enough that a careful student can follow each step.

The project is intentionally a work in progress. Its scope includes selected parts of classical mechanics, electromagnetism, relativity, quantum mechanics, and the mathematical tools needed to study them, including calculus, linear algebra, differential equations, tensor analysis, and differential geometry.

The site is not meant to be complete in the encyclopedic sense. Its purpose is clarity rather than coverage: to develop selected topics slowly, explicitly, and with enough mathematical detail to make the physics genuinely transparent.

Despite every effort to ensure accuracy and completeness, errors and omissions may remain. The reader is asked to regard these notes as a work in progress and to excuse any shortcomings that may be encountered.

The essays collected here are written by a theoretical physicist with a longstanding interest in the mathematical foundations of physics. They are offered in the hope that others may find in them some of the same joy, wonder, and illumination that accompany the patient study of mathematics and the laws of nature. Perhaps, in time, others who share this spirit will join in expanding and enriching the collection. More information can be found on the About page.

Physics understood one derivation at a time.

Notes on Mathematics, Physics, and Harmony

A closing cadence for essays shaped by mathematics, physics, and music.