Pebble in the Sky

Caught up in an experiment gone wrong, Joseph Schwartz is transported forward in time from post-war Chicago to the heyday of the first Galactic Empire.
Earth, he soon learns, is a backwater, despised by the other two hundred million planets of the Empire because its people dare to claim it as the original home of man.
And Earth is poor, with great areas of radioactivity ruining much of its soil - so poor that everyone is sentenced to death at the age of sixty.
And Joseph Schwartz is sixty-two