Thoughts on math and physics.
On April 24, 2026, we are required as educators to comply with the new ADA Title II standards which adhere to Web Content Accessibility Guidelines (WCAG) 2.1 Level AA. I regularly prepare mathematical and physics-heavy teaching materials using GitHub, Overleaf, and LaTeX. Because these documents often contain substantial mathematical notation, accessibility requires some extra care.
The following derivation is the outcome of my own personal journey in trying to learn more group theory (and representation theory) which appears in many areas of physics. Despite the importance of groups in physics, I don’t believe physicists are well-educated at the university level on this topic (or at least I wasn’t) unless they go out of their way.
It’s easy to notice that the famous equation \(E = mc^2\) is similar to the classical expression for kinetic energy \(T = \frac{1}{2}mv^2\). Both are proportional to mass, and both have a “speed” (\(c\) or \(v\)) which is squared. That they are alike might prompt the question: why doesn’t Einstein’s equation include the factor of \(1/2\) like kinetic energy does? Did Einstein overlook this factor?
A graviton \(G\) is a theoretical quantum of the gravitational field, which presumably exists if gravity can indeed be quantized. There remains an important question regarding this fundamental particle: Can we ever detect a single graviton?