Time and Space

Once again my friends and colleagues at Gogo Business Aviation in Broomfield Colorado indulged me, in the form of my alter-ego John Sloan, by letting me come and give a talk entitled Time & Space on the historical connection between precision timekeeping and navigation. They taped it and put it on the 'tube. I had a great time, and hopefully I wasn't the only one. Among lots of other things, I describe how both GPS and atomic clocks work.

I did, in my enthusiasm, misspeak a couple of times - that's the hazard of giving an hour long talk without slides or notes - and have made some corrections below.

A big Thank You to the folks at Gogo for sponsoring this.

Corrigendum

1. Despite my saying that the escapement wheel is not a gear (and it's not), I incorrectly referred to it as a gear once or twice.
2. When I gave the example about longitude, it would be 5 hours and 11 minutes before GMT, not after.
3. One of my Ph.D. physicist colleagues remarked that it's not really a different electron orbital shell to which the electron transitions but instead a hyperfine transition. (I'll have to look that up.)
4. In my excitement, I said neutrons have a positive charge when of course I meant it is protons which have a positive charge. (A particularly egregious mistake since I've know that since grade school.)
5. The GPS block IIF satellite has three atomic clocks. not four: two rubidium and one cesium. An earlier model GPS satellite I've studied has two of each.
6. There are a variety of algorithms used by GPS to determine your position; I described one class of algorithms. There are simpler closed-form solutions that work for time measurements from four satellites. And there are even simpler algorithms that work for three satellites, but which don't compute altitude. The iterative solution I describe is the most general one, solving for all three spatial coordinates, for time, and for as many satellites as can be observed.
7. I said the volume of the final GPS solution was fifteen meters across. It's actually about five meters across, or about fifteen feet. That jives with a timestamp resolution of about fifteen nanoseconds (light travels about a foot in a nanosecond), and not the 1.5 nanoseconds I quote in the talk. (Maybe I should break down and use notes or slides, huh?)