measurement postulate

The measurement postulate is the rule that bridges the abstract wavefunction and the concrete numbers a laboratory reads off. It states that the possible results of measuring an observable are its eigenvalues, and that the probability of getting any particular one is given by the Born rule — the squared magnitude of the corresponding amplitude in the state. Without this rule, the wavefunction would be a beautiful but mute object; with it, the theory makes testable predictions.

Alongside the probabilities, the postulate also specifies what becomes of the system afterward: having obtained a given result, the state is updated to the eigenstate that belongs to it. This is the part often called collapse or state reduction. So the postulate does two jobs at once — it tells you the odds of each outcome, and it tells you the state you are left holding once an outcome occurs.

This postulate sits a little uneasily beside the rest of the theory. The other rules describe smooth, deterministic, reversible evolution, while the measurement postulate introduces probability, abruptness, and a special role for 'observation'. That tension is precisely the measurement problem. Pragmatically the postulate works flawlessly; philosophically it raises the question of why nature should need a separate rule for looking at all.