On the Time Orientation of Probabilistic Theories

An influential theorem by Satosi Watanabe convinced many that there can be no physical probabilistic theory with both non-trivial forward and backward transition probabilities. We show that this conclusion does not follow from the theorem. We point out the flaw in the argument, and we showcase examples of theories with well-defined backward and forward transition probabilities.
Comment: 10 single column pages, no figures, version accepted for publication, improved thanks to peer review