Insufficiency of the Quantum State for Deducing Observational Probabilities

TL;DR

The paper argues that in a universe with many observers, the quantum state alone cannot determine observational probabilities, highlighting the need for additional rules beyond traditional quantum theory, which relates to the cosmological measure problem.

Contribution

It demonstrates that the quantum state is insufficient for deducing observational probabilities in large universes, emphasizing the necessity for supplementary rules.

Findings

Quantum state alone cannot determine observational probabilities in large universes.

Additional rules are required to connect quantum states to observations.

Addresses the measure problem in cosmology.

Abstract

It is usually assumed that the quantum state is sufficient for deducing all probabilities 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 an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to get the probabilities. What these rules are is not logically deducible from the quantum state, so the quantum state itself is insufficient for deducing observational probabilities. This is the measure problem of cosmology.