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It is usually assumed that the quantum state is sufficient for deducing allprobabilities for a system. This may be true when there is a single observer,but it is not true in a universe large enough that there are many copies of anobserver. Then the probability of an observation cannot be deduced simply fromthe quantum state (say as the expectation value of the projection operator forthe observation, as in traditional quantum theory). One needs additional rulesto get the probabilities. What these rules are is not logically deducible fromthe quantum state, so the quantum state itself is insufficient for deducingobservational probabilities. This is the measure problem of cosmology.

Insufficiency of the Quantum State for Deducing Observational Probabilities