Murray Gell-Mann formulated
his totalitarian
principle to address the fact that, when modelling a quantum mechanical
system, one must take account of every potential course of events which is not
actively forbidden. Every pathway that isn't forbidden is compulsory

– or, at least, happens enough of the time that you have to take it into
account. This is, in fact, an inevitable consequence of the system's
behaviour not depending on how we describe it.

As long as something isn't forbidden, it's possible: it may be highly
improbable (which influences how much effect it'll have when we *do*
take it into account), but it's possible. One's description of the quantum
system yields a basis of the available states. The states represented by
members of the basis are typically ones it's easy for puny human brains to
comprehend, one way or another, via the description. This makes these states
special to our puny human brains, but not to the quantum system. Our
description represents all the other possible states as linear combinations of
these basis states – mixing the comprehensible solutions in diverse
proportions (and phases) – and the system is almost certainly in one of
these mixed states, since there are infinitely more of them than there are
simple ones. Indeed, the system shall almost certainly be in one of the
superpositions that partakes of all of the basis members, for essentially the
same reason that a point chosen on a unit sphere at random has zero
probability of being on any particular great circle: all of the area of the
sphere is in the two hemispheres on either side of the circle. Some basis
states may be highly improbable but, as long as they're
not *forbidden*, they're included in the superposition, albeit only in
proportion to (the square root of) how probable they are.

Thus, when particles collide, munge together and come apart as something else, one's model of the intermediate munging must allow that every composite the particles could form is in fact expressed (albeit possibly only in a tiny proportion) in the transient state; and each such intermediate composite contributes its (sometimes little) part to the total probabilities of the various results once it all comes apart again.

Written by Eddy.