A brief introductory lecture on the Global Positioning System (GPS), and how both Einstein's special and general theories of relativity need to be considered to ensure that it works properly. We describe the satellite set-up of GPS, the use of cesium atomic clocks to transmit time and position information, and the geometry of why four satellite positions determine where we are. Precursors to this system include LORAN (Long Range Navigation system) of beacons used at sea, and earlier audio systems used in WW1 to try to determine enemy gun positions by measuring differences of distances from observers. We discuss the accuracy of the clocks, and why Einstein's Special theory (SR) and General theory (GR) of relativity both are affecting this situation. We present simplified views of SR and GR, starting with the Michaelson-Morley experiment which showed that the speed of light was constant in different uniform motion coordinate systems, then Einstein's remarkable conclusion that there is no fixed reference coordinate system for the world: the laws of physics are the same for different observers moving at uniform motion with respect to each other. A bizarre consequence is that simultaneity of events is a relative notion. GR is explained in terms of the Equivalence Principle relating observers in accelerated frames and in gravitational fields: this allows us to apply the (relativistic) Doppler effect to conclude that clocks higher in a gravitational field appear to run faster. Both of these effects have effects on the running of the atomic clocks in the GPS satellites--in fact they work in opposite directions, and their cumulative effect must be taken into account by the engineers who manage the system.

• published: 24 Nov 2013
• views: 743