nLab Gell-Mann principle




Quantum systems

quantum logic

quantum physics

quantum probability theoryobservables and states

quantum information

quantum computation

quantum algorithms:



While the inherently probabilistic nature of quantum physics means, roughly, that as soon as there is more than one possibility, no quantum measurement outcome can be known with certainty; conversely this also means that all outcomes are possible with some probability. This converse statement had been stated by Gell-Mann 1956 for the case of quantum hadrodynamics (p. 859) in this form:

“Principle of Compulsory Strong Interactions”. Among baryons, antibaryons, and mesons, any process which is not forbidden by a conservation law actually does take place with appreciable probability.

The statement is recalled by Bunge 1976, p. 31 in the form:

Anything that is not forbidden is compulsory.

A more careful wording of the above principle is this: All possible repetitive chance events (in particular all those consistent with the conservation laws) are likely to occur in the long run.

and by Israel 1996 in the form:

What is not forbidden is compulsory.

For better or worse, Gell-Mann 1956 on that same page 859 found it helpful to add (about the contrapositive statement) that:

this is related to the state of affairs that is said to prevail in a perfect totalitarian state. Anything that is not compulsory is forbidden.

and some historians of science swallowed this red herring and ever since refer to Gell-Mann’s “principle of quantum compulsion” instead as the “totalitarian principle” (eg. Jaeger 2017, Wikipedia, cf. Kragh 2019a). See also the “principle of plenitude” (cf. Kragh 2019b).

Notice that Gell-Mann’s principle goes against the grain of the classical implication (see modal logic), which is the implication in the opposite direction:

necessary actual possible () () () \array{ necessary && actual && possible \\ \Box (-) &\rightarrow& (-) &\rightarrow& \lozenge (-) }

That in quantum physics this implication may in fact be reversed can be understood as ambidexterity

\lozenge \mathscr{H}_\bullet \;\simeq\; \Box \mathscr{H}_\bullet

of finite-dimensional dependent linear types \mathscr{H}_\bullet, see at quantum circuits via dependent linear types.


The original article:

Further discussion:

  • Mario Bunge, p. 31 in: Possibility and Probability, pp. 17-34 in: Foundations of Probability Theory, Statistical Interference, and Statistical Theories of Science Reidel (1976) [doi:10.1007/978-94-010-1438-0_2]

  • Werner Israel, p. 607 of: Imploding stars, shifting continents, and the inconstancy of matter, Foundations of Physics 26 (1996) 595–616 [doi:10.1007/BF02058234]

  • Gregg Jaeger, p. 5 of: Quantum randomness and unpredictability, Fortschr. Phys. 65 6-8 (2017) [doi:10.1002/prop.201600053]

  • Helge Kragh, Physics and the Totalitarian Principle [arXiv:1907.04623]

  • Helge Kragh, Plenitude Philosophy and Chemical Elements, International Journal for Philosophy of Chemistry 25 1 (2019) [pdf]

Last revised on October 3, 2022 at 13:39:26. See the history of this page for a list of all contributions to it.