In quantum mechanics, Gell-Mann's Totalitarian Principle states: "Everything not forbidden is compulsory." Physicist Murray Gell-Mann borrowed this expression from T. H. White's The Once and Future King to describe the state of particle physics around the time he was formulating the Eightfold Way, a precursor to the quark-model of hadrons.
The statement is in reference to a surprising feature of particle interactions: that any interaction which is not forbidden by a small number of simple conservation laws is not only allowed, but must be included in the sum over all "paths" which contribute to the outcome of the interaction. Hence if it isn't forbidden, there is some probability amplitude for it to happen.
In any of the Everett-based interpretations of quantum mechanics, such as Bryce DeWitt's many worlds or Gell-Mann and Hartle's consistent histories interpretation, the principle has a more literal meaning: that every possibility at every interaction which is not forbidden by such a conservation law will actually happen (in some branch of the wavefunction).
- See footnote on p. 859 in Gell-Mann, M. (1956). "The interpretation of the new particles as displaced charge multiplets" (PDF). Il Nuovo Cimento. 4: 848. doi:10.1007/BF02748000.
Among baryons, antibaryons, and mesons, any process which is not forbidden by a conservation law actually does take place with appreciable probability. We have made liberal and tacit use of this assumption, which is related to the state of affairs that is said to prevail in a perfect totalitarian state. Anything that is not compulsory is forbidden. Use of this principle is somewhat dangerous, since it may be that while the laws proposed in this communication are correct, there are others, yet to be discussed, which forbid some of the processes that we suppose to be allowed.
- White, T.H. (1996). The Once and Future King (Reprint ed.). Ace Trade. p. 121. ISBN 978-0441003839. The passage describes an ant-hill from the point of view of an ant: "The fortress was entered by tunnels in the rock, and, over the entrance to each tunnel, there was a notice which said: EVERYTHING NOT FORBIDDEN IS COMPULSORY."
- Johnson, G. (1999). Strange Beauty: Murray Gell-Mann and the Revolution in Twentieth-Century Physics. Knopf. p. 224. ISBN 978-0-679-43764-2. Johnson describes Gell-Mann's application of the quote to physics, but incorrectly attributes the original to Orwell.