It's Not Exactly Modern Physics, But . . .

Pit of Babel does have a nice post, with well rendered equations, deriving the speed of light from Maxwell's Equations (which are definitely good T-shirt candidates -- even if you can't understand vector calculus, you should take a moment to wonder at how profoundly simple and beautiful the rules that govern much of electromagnetism are). This isn't anything new or revolutionary. It has been known for about a century. But, it does elegantly illustrate a few critical points.

One: Einstein's Theory of Special Relativity was already embedded into the structure of classical physics, although few people realized the full profundity of this fact initially.

Two: Classical Electomagnetic Theory requires a Minkowski background, not a Euclidian one (which is to say that time-space must have a geometry that accomodates special relativity wherein the speed of light is contant, while length and time may be distorted for observers moving relative to each other and the word "simultaneous" has only local meaning). It therefore follows that QED (quantum electrodynamics which is the quantum eletromagentic theory) must have a Minkowski background because QED must reduce to classical electromagentism at non-quantum scales.

Three: To the extent that Maxwell's equations are true at super-quantum scales, and we have no reason to doubt that they are based on voluminous experimental evidence, the speed of light can be measured indirectly with great precision by determining other more easily measured constants in Maxwell's Equations.

Again, none of this is revolutionary, but many people have trouble getting a comfort level with the idea that modern physics is real, and not just some crazy theory that may or may not be anywhere close to being true. Connecting mundane, classical physics like Maxwell's Equations, which you use to derive circuit equations, which electricians use every day in mundane applications, to modern physics concepts, can help provide that comfort level.