Galactic Positioning System

No, that title is not a mistake.  Of course, most people by now are familiar with the idea of another GPS, the Global Positioning System, which uses a “constellation” of satellites in Earth orbit, fitted with high–accuracy atomic clocks, to enable a terrestrial receiver to determine its position.

According to a note posted on the Physics ArXiv blog at the MIT Technology Review Web site, a couple of French researchers have published a short paper [PDF – quite technical] proposing that a similar system could be constructed on a much larger scale, using natural objects in place of the satellites:

Today, Bertolomé Coll at the Observatoire de Paris in France and a friend propose an interstellar GPS system that has the ability to determine the position of any point in the galaxy to within a metre.

The proposed system would use signals from a set of four pulsars, which lie approximately in a tetrahedron centered on the Solar System.  (A pulsar is a rotating neutron star, with a very high magnetic field, which emits a strong beam of electromagnetic radiation.  Because, as with the Earth, the magnetic axis does not correspond exactly with the rotational axis, the signal appears to “blink” on and off, as a lighthouse might.  This “blinking”, for at least some individual pulsars, has a very stable period, to within a few nanoseconds.)

Because of the distances involved, and the fact that the signals travel at the speed of light, General Relativity has to be taken into account:

Why four pulsars? Coll points out that on these scales relativity has to be taken into account when processing the signals and to do this, the protocol has to specify a position in space-time, which requires four signals.

Basically the corrections must account for the relativistic time dilation, and the curvature of space-time caused by gravity (sometimes called the gravitational blue-shift).

Many people (myself included) are surprised to find that the existing GPS also has to take relativity into account.  The current system’s undithered signals (the ones used by the military) permit determining location to about a 1 meter radius.  In order to do this, time must be measured to an accuracy of about 1 part in 1013.  But if relativistic effects were ignored, that would introduce an error of about 1 part in 1010, or 1000 times as much.  Over the course of a day, you could accumulate a position error of ~10 kilometers.  (Source: Warped Passages, by Lisa Randall, ISBN 0-06-053109-6.)

I’ve mentioned before how parts of modern physics take us away from the domain where our instincts and intuition work.  This is another aspect of that same paradox: the ideas underlying General Relativity (such as curved, non-Euclidean space-time) seem exotic, and the mathematics is formidable.  Yet the little box you may have in your dashboard has to “know” all about it.

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