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December 2, 2015

The GPS in your smart phone and the General Theory of Relativity


Everyone knows that Albert Einstein was one of the greatest physicists of the early twentieth century. 2015 marks 100 years since he published his theory of gravitation, which keeps us on the floor and keeps the earth in its orbit around the Sun. He called this the general theory of relativity and we call it GR for short.


In 1915, Newton's laws of gravity had stood unchallenged for 250 years, and had explained the motion of the planets with great accuracy. Einstein's reason for wanting to replace it was his own discovery in 1905 that nothing could travel faster than light. In Newton's theory the effect of gravitation was instantaneous. Einstein replaced the force of gravity with a geometrical idea of curvature of space and time. The geometric  explained something that Newton had to postulate - particles of different masses move in the same way in the gravitational field of the earth, or the Sun.  In spite of being completely different from Newton's view of gravity, Einstein's theory was able to take over all its triumphs


But this was no mere rewriting of an old idea. GR explained the discrepancy in the motion of the planet Mercury and predicted that light rays passing near the Sun would be bent by a small angle. This experiment was carried out in 1919 by English astronomers, and proved Einstein right.  Friedmann, in Russia, showed that the theory could describe an expanding universe. This was confirmed a few years later by astronomical observations which showed distant galaxies moving away at speeds proportional to their distance from us.  


Fifty years after Einstein, Hawking and Penrose, were able to put the existence of black holes on a firm mathematical basis. A black hole is a sphere whose boundary is a one way membrane - anything entering it can never come out - not even light.  It results as the final stage of an object collapsing under its own gravity. Soon after this, astronomers found rapid motions and high energy radiation near the centres of galaxies.   The properties of these objects are best explained by the presence of black holes. Today, thousands of black holes are known and studied in great detail. GR is routinely used to understand the light, X-rays, and radio waves which astronomers receive from the centres of galaxies - these do not come from within the black hole, of course, but from material heated up while falling in. Currently, astronomers are poised to measure one more prediction of GR- waves in the gravitational field, traveling at the speed of light.


The effects of GR near the earth are very small - a few parts per billion, but very important practically. The GPS receiver in every smartphone has to use formulae based on GR, to locate you to within a few metres accuracy, with respect to satellites tens of thousands of kilometres away moving at tens of thousands of kilometres per hour.


GR is in your pocket today. What we celebrate is a milestone in human thought which has changed forever our view of space, time, gravity, and the universe.

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