How it works

Two theories. Special relativity, of 1905, is about things moving at steady speeds, and leaves gravity out. General relativity, finished in 1915, brings gravity in. For slow things and weak gravity it gives almost exactly the same answers as Newton, which is why Newton’s law is still used to fly spacecraft. The two differ where gravity is strong, where speeds are very high, or where the measuring is very fine.

The rubber sheet. The first picture in this lesson shows space as a sheet with a dip in it. It is the usual way to draw the idea, and it is only half right. It shows space being bent and leaves out time, which is bent as well. It also needs gravity underneath the sheet to make the ball roll, which is cheating. Take it as a sketch.

The test	What was found
Mercury’s orbit	It turns by 43 seconds of arc a century more than the other planets can explain. A second of arc is one 3,600th of a degree. Einstein’s theory gives 43
Starlight passing the Sun, 1919	Stars near the Sun’s edge were shifted by roughly the amount predicted, about twice what Newton’s gravity would give
Two clocks, 33 cm apart in height, 2010	The higher one ran faster. Over a life of 79 years the difference would come to about 90 billionths of a second
Clocks on navigation satellites	Fast by 45 millionths of a second a day from being higher up, and slow by 7 from their speed. Left alone, positions would drift by about 10 km a day

The 1919 expeditions. Two teams from Britain went to watch the eclipse, one to the island of Príncipe off West Africa and one to Sobral in Brazil. The Sun was hidden for nearly seven minutes, one of the longest eclipses of the century. They photographed the stars round the darkened Sun and compared the plates with the same stars photographed at night. The original glass plates are lost. The picture in this lesson was made from a copy of one of the Sobral plates kept at an observatory in Heidelberg.

What came out of it. Black holes, the expansion of the universe, the bending of light by galaxies and waves in space itself were all found first in Einstein’s equations and only later in the sky. Each has a lesson of its own.

Where it stops. General relativity has passed every test so far. It does not fit together with quantum theory, which describes the very small, and at the centre of a black hole its own sums stop making sense. Most physicists expect that a deeper theory lies underneath it, and nobody has found it yet.