In quantum mechanics, the totalitarian principle states: "Everything not forbidden is compulsory." Physicists including Murray Gell-Mann borrowed this expression, and its satirical reference to totalitarianism, from the popular culture of the early twentieth century.
The statement is in reference to a surprising feature of particle interactions: that any interaction that 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" that contribute to the outcome of the interaction. Hence if it is not forbidden, there is some probability amplitude for it to happen.
In the many-worlds interpretation of quantum mechanics, the principle has a more literal meaning: that every possibility at every interaction that is not forbidden by such a conservation law will actually happen (in some branch of the wave function).
Origin of the phrase
Neither the phrase nor its application to quantum physics originated with Gell-Mann, but a 1956 paper by him contains the first published use of the phrase as a description of quantum physics. Gell-Mann used it to describe the state of particle physics around the time he was formulating the Eightfold Way, a precursor to the quark-model of hadrons.
Formulations close to Gell-Mann's are used in T. H. White's 1958 (not 1938-39) version of The Once and Future King and in Robert Heinlein's 1940 short story "Coventry." They differ in details such as the order of the words "forbidden" and "compulsory," and Gell-Mann's footnote uses the words in both orders, although only one of these orders captures his precise logical meaning. The phrase, and variations on it, appear to have been common in this period, and probably trace back to an older legal principle, that everything which is not forbidden is allowed. Since White did not use the phrase in any published work until two years after Gell-Mann's paper, White cannot have been Gell-Mann's source. It is likely that writers such as White, Heinlein, and Gell-Mann were all simply making use of a phrase that was a part of popular culture at the time.
- Kragh, Helge. "Physics and the Totalitarian Principle". arXiv:1907.04623. Cite journal requires
- 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. Bibcode:1956NCim....4S.848G. 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.
- 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.
- 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." This passage does not appear in the 1938 and 1939 editions of The Sword and the Stone, but only in the 1958 revision incorporated into The Once and Future King.
- Anthologized in Robert A. Heinlein, The Past Through Tomorrow, Berkley Medallion mass-market paperback edition, 1967, p. 600. "The state was thought of as a single organism with a single head, a single brain, and a single purpose. Anything not compulsory was forbidden.."