This year is the centenary of the birth of the great logician Kurt Gödel. One of his greatest discoveries had nothing to do with mathematical logic. It was that Einstein's theory of relativity allows universes in which time travel is possible. We will describe Gödel's strange universe and discuss the history of the idea of time travel to the future and to the past in science fiction and science fact. In particular we will look at the traditional story line of 'back to the future' and show how it is possible to be part of the past but not to change the past, and what physicists think about time travel in the light of quantum theory.

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