nLab Gell-Mann principle

Idea

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:

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

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.

References

The original article:

• Murray Gell-Mann, The interpretation of the new particles as displaced charge multiplets, Nuovo Cim 4 2 (1956) 848–866 [doi:10.1007/BF02748000]

Further discussion:

• Mario Bunge, p. 31 in: Possibility and Probability, in: Foundations of Probability Theory, Statistical Interference, and Statistical Theories of Science Reidel (1976) 17-34 [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]