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.