In 1942, Paul Dirac wrote a paper: “The Physical Interpretation of Quantum Mechanics” where he introduced the concept of negative energies and negative probabilities:

“Negative energies and probabilities should not be considered as nonsense. They are well-defined concepts mathematically, like a negative of money.”

Negative probabilities have later been suggested to solve several problems and paradoxes. *Half-coins* provide simple examples for negative probabilities. These strange coins were introduced in 2005 by Gabor J. Szekely. *Half-coins* have infinitely many sides numbered with 0,1,2,… and the positive even numbers are taken with negative probabilities. Two half-coins make a complete coin in the sense that if we flip two half-coins then the sum of the outcomes is 0 or 1 with probability 1/2 as if we simply flipped a fair coin.

— Wikipedia on *Negative probability*

2011.05.19 Thursday ACHK