Apparently Pound and Rebka were the first to measure it using gamma rays going up 72 feet (that's 22m in new money). They did it in the Jefferson laboratory (pictured) at Harvard in 1959. That's about 40 years after Einstein predicted it. The change in the wavelength was 2 parts in a thousand trillion (##2## in ##10^{15}##). They measured it by wiggling the source of the gamma rays about in a speaker cone and seeing when the Doppler shift cancelled the gravitational shift!

The calculations are quite simple (and I got the right answer without cheating!) but I really needed to understand a few other things which sent me right back to chapters 3 and then 1. It all concerns the energy-momentum vector for a massive particle and then a massless e.g. gamma ray) particle and how the energy and therefore frequency fits into that. Light dawned.

The basic calculations: Commentary 5.5 Gravitational Redshift.pdf (2 pages)

On four-momentum and energy: Commentary 3.4 Particle energy.pdf (6 pages)