How Einstein helps tractor drivers
“Turn off SATNAV” – advice during Farnborough Air Show to allow for the various road closures and diversions which are meant to facilitate traffic flow. Many people would find it hard to imagine life now without SATNAV and all the other functions which the GPS system allows. Presumably Einstein would have found it even harder to imagine that his work on relativity in the early years of the 20th Century would play an essential part in enabling a must-have device of the 21st to work correctly. Malcolm MacCallum, Emeritus Professor at Queen Mary College London and our July 2014 meeting speaker, gave us a talk entitled “Was Einstein right?” and included the idea that we are in effect testing the special and the general theory of relativity every time we used the GPS – and this testing includes the most modern tractors which are equipped with GPS-linked sensors which enable them to steer with great accuracy, ensuring there are no wasteful overlaps or unwanted gaps while sowing seed.
First, a quick summary of how GPS works and then some comments about the link between GPS and Einstein. The GPS system is a set of 24 satellites. Each one is sending down signals identifying itself and giving the time that the signal is sent. A GPS receiver on the ground picks up this signal a split second later. It knows what time it receives the signal so it knows from the time delay how far away it is from the satellite. It has also identified the satellite and, as it is orbiting in a well-defined pattern, it knows from the time information where the satellite was when it transmitted the signal. Hence it knows all of its possible locations relative to that satellite. These positions lie on a sphere, so the information from four satellites is combined to pinpoint the receiver position.
It is fundamental to the operation of GPS that the clocks giving the time information on the satellites remain exactly synchronised with clocks in the Earth-bound GPS receivers. This is where Einstein and relativity come in. It is at this point that I will give a quote I found while doing some research for this post –“it is beyond the scope of this article to go into details about these [relativistic] effects”. In my case, it is beyond the scope of the author, so forgive me when I just state conclusions.
One feature of the special theory of relativity, which deals with objects moving relative to one another at constant speed, is illustrated by the famous (or should that be infamous?) twins paradox which states that if a twin sets off on a space journey and then returns , he or she will not have aged as much as the Earth-bound twin. The GPS version of this is that a clock on a satellite will “tick” more slowly than one on Earth because of the speed at which the satellite orbits. The error would amount to about 7000 nanoseconds each day. Not good news for GPS accuracy!
Even worse news for GPS accuracy is a conclusion from the general theory of relativity, which takes into account the effects of gravitational fields. This predicts that clocks run more slowly where the gravitational field is stronger. For our Earth-bound receiver and satellite pair, it is now the Earth-bound one which is running slower, in this case by about 45,000 nanoseconds /day. The combined result of the two opposing time effects means that the satellite-based clock would get ahead of that on Earth by 38,000 nanoseconds/day, enough to introduce an error of about 10km in day.
The solution is to change the definition of 1 second on the atomic clock on each satellite. The need is to slow down the rate of “ticking” and this is achieved by increasing the number of electron transitions within caesium atoms used to define the satellite-clock “tick”. If the satellite was to remain on Earth, then its clock would be observed to run too slowly. Once up in space, the alteration allows for the different time effects of both theories of relativity and the satellite-clock stays synchronised with the Earth-bound GPS receiver.
I’ll close with another quote, taken from the article which I found very helpful in getting my ideas about this topic straight, by Richard W Pogge of Ohio State University : ‘ People often ask “What good is Relativity?” It is a commonplace to think of Relativity as an abstract and highly arcane mathematical theory that has no consequences for everyday life. This is in fact far from the truth.’ I confess my instinct has always been to agree with the first part of this statement, but I will now try to reflect on the second part when I am eating some bread which might have been made from wheat sown by a GPS-controlled tractor.
Click here to read more of this article.
I also found an article on the Metasearch website useful. Click here to see this
Talk given by Emeritus Professor Malcolm MacCallum of Queen Mary College London
Post written by Katherine Rusbridge
July 2014