Precision QED

In my class on quantum field theory I have been lecturing on renormalization of QED (Quantum Electrodynamics, which describes the interaction of photons with charged particles). As far as I know, QED is the most precisely tested theory of nature humans have ever developed. For example, using QED one can compute the magnetic moment of the electron mu to accuracy of about 1 part in 10^{-12}, using inputs such as the fine structure constant alpha, the mass of the electron, etc. The difficult part of the calculation involves quantum fluctuations of the photon as well as virtual charged particles and antiparticles.

The theoretical result is in good agreement with the experimental measurement: mu = 1.001159652187 ± 0.000000000004 in units of Bohr magnetons. The deviation from unity is due to the quantum effects I mentioned.

You can see here what is involved in a state of the art precision QED calculation: a teraflop cluster, 400,000 CPU hours to evaluate 200 10-dimensional Feynman integrals using Monte Carlo. (Don't forget the 128 bit arithmetic to maintain sufficient accuracy!)

Feynman, Schwinger and Tomonaga, the main architects of QED, are legendary figures of modern physics. For a superb intellectual history of the development of QED, see QED and the Men who Made It by S. Schweber. Schweber is a historian of science and theoretical physicist.