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Einstein continued to work on the problem in Berlin, undisturbed by domestic matters and largely unaffected by the war, until he finally found the right equations, in November 1915. Einstein had discussed his ideas with the mathematician David Hilbert during a visit to the University of Gottingen in the summer of 1915, and Hilbert independently found the same equations a few days before Einstein. Nevertheless, as Hilbert admitted, the credit for the new theory belonged to Einstein. It was his idea to relate gravity to the warping of space-time. It is a tribute to the civilized state of Germany in this period that such scientific discussions and exchanges could go on undisturbed even in wartime. What a contrast to 20 years later!

The new theory of curved space-time was called general relativity to distinguish it from the original theory without gravity, which was now known as special relativity. It was confirmed in spectacular fashion in 1919, when a British expedition to West Africa observed a slight shift in the position of stars near the sun during an eclipse. Their light, as Einstein had predicted, was bent as it passed the sun. Here was direct evidence that space and time are warped, the greatest change in our perception of the arena in which we live since Euclid wrote his Elements about 300 B.C.

Einstein's general theory of relativity transformed space and time from a passive background in which events take place to active participants in the dynamics of the cosmos. This led to a great problem that is still at the forefront of physics at the end of the 20th century. The universe is full of matter, and matter warps space-time so that bodies fall together. Einstein found that his equations didn't have a solution that described a universe that was unchanging in time. Rather than give up a static and everlasting universe, which he and most other people believed in at that time, he fudged the equations by adding a term called the cosmological constant, which warped space-time the other way so that bodies move apart. The repulsive effect of the cosmological constant would balance the attractive effect of matter and allow for a universe that lasts for all time.

This turned out to be one of the great missed opportunities of theoretical physics. If Einstein had stuck with his original equations, he could have predicted that the universe must be either expanding or contracting. As it was, the possibility of a time-dependent universe wasn't taken seriously until observations were made in the 1920s with the 100-in. telescope on Mount Wilson. These revealed that the farther other galaxies are from us, the faster they are moving away. In other words, the universe is expanding and the distance between any two galaxies is steadily increasing with time. Einstein later called the cosmological constant the greatest mistake of his life.