The Infinite Improbability Drive

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The Infinite Improbability Drive is a faster-than-light drive. The most prominent usage of the drive is in the starship Heart of Gold. It is based on a particular perception of quantum theory: a subatomic particle is most likely to be in a particular place, such as near the nucleus of an atom, but there is also an infinitesimally small probability of it being found very far from its point of origin (for example close to a distant star). Thus, a body could travel from place to place without passing through the intervening space (or hyperspace, for that matter), if you had sufficient control of probability. According to the Guide, the drive "passes through every conceivable point in every conceivable universe almost simultaneously," meaning that you are "never sure where you'll end up or even what species you'll be when they get there" and "it's therefore important to dress accordingly".
The Guide's entry on the drive also states that it was invented "following research into finite improbability, which was often used to break the ice at parties by making all the molecules in the hostess' undergarments leap one foot simultaneously to the left, in accordance with the theory of indeterminacy". It further explains that many respectable physicists wouldn't stand for that sort of thing, "partly because it was a debasement of science, but mostly because they didn't get invited to those sort of parties."

(source: Wikipedia)

The first application of the concept behind the infinite improbability drive comes from an old experiment from the 20th century:

Well, some researchers were once conducting such an experiment, but when they opened up the box, the cat was neither alive nor dead but was in fact completely missing, and they called me in to investigate. I was able to deduce that nothing very dramatic had happened. The cat had merely got fed up with being repeatedly locked up in a box and occasionally gassed and had taken the first opportunity to hoof it through the window. It was for me the work of a moment to set a saucer of milk by the window and call "Bernice" in an enticing voice -- the cat's name was Bernice, you understand -- and the cat was soon restored.

(from Dirk Gently's Holistic Detective Agency by Douglas Adams)