Wave function evolution

The orthodox account has two rules: unitary evolution between measurements, and collapse at measurement. Only the first is deterministic and reversible; the second is neither, and the theory never states which applies when. That gap is the measurement problem in one sentence, and every other interpretation on this page is an attempt to remove one of the two rules or to explain how they fit together.

Everett's proposal is precisely to delete the second rule. Measurement becomes an ordinary interaction in which observer and system become entangled, and what looks like collapse from inside is a record that has branched. Because the dynamics never stop being unitary, information is never destroyed — an assumption that reaches well beyond interpretation, since the same commitment drives the black-hole information debate. What supporters must still supply is why branch weights should be experienced as probabilities.

Given the wave function and the initial configuration, de Broglie–Bohm fixes everything that follows. Quantum randomness enters only as ignorance of that initial configuration, distributed according to the Born rule, so what looks like indeterminism is classical-style uncertainty about a starting point. Reversibility holds for wave and particles together. The cost, again, is that the guidance equation depends instantly on the whole configuration however far apart its parts are.

GRW and CSL modify the equation rather than interpreting it, adding a stochastic term whose rate scales with the number of particles involved. Evolution is therefore not exactly unitary and information is not exactly preserved, which is what makes these models testable and what makes reconciling them with relativity difficult. Below the microscopic scale the deviation sits far under anything measurable; for anything macroscopic it dominates completely.

QBism reads unitary evolution as a normative rule for updating a personal state assignment in the absence of new experience, closely analogous to the way a Bayesian carries a probability forward when nothing has been observed. Measurement is the one step that is not reversible, precisely because it is the step where experience arrives and the books are rewritten. What the world is like, such that agents must keep their books this way and no other, is the question QBism leaves open.

On Rovelli's account the wave function is not an absolute object but the way one system encodes information about another. Unitary evolution describes that relation while no new interaction occurs; a measurement is an interaction, and it establishes a value relative to the systems involved. Consistency survives because any comparison of two records is itself an interaction. What is given up is the idea of a single observer-independent history into which everything must fit.

The formalism assigns amplitudes to sequences of events using the unitary dynamics, then checks whether the histories in a family interfere. If they do not, ordinary probabilities apply and measurement appears as physics inside a history rather than as an intervention from outside it. Because probabilities belong to complete histories, the split between smooth evolution and irreversible outcome reflects the family chosen, not the dynamics. The unresolved point is that many incompatible families are equally consistent.