Typical Quantum States of the Universe are Observationally Indistinguishable

This paper is about the epistemology of quantum theory. We establish a new result about a limitation to knowledge of its central object -- the quantum state of the universe. We show that, if the universal quantum state can be assumed to be a typical unit vector from a high-dimensional subspace of Hilbert space (such as the subspace defined by a low-entropy macro-state as prescribed by the Past Hypothesis), then no observation can determine (or even just narrow down significantly) which vector it is. Typical state vectors, in other words, are observationally indistinguishable from each other. Our argument is based on a typicality theorem from quantum statistical mechanics, known as distribution typicality. That is in a sense the strongest known result about a limitation to knowledge in a quantum universe. Assuming the universe we inhabit is typical, our observational data alone will tell us very little about exactly which one it is that we inhabit. We also discuss how theoretical considerations that go beyond the empirical evidence might bear on this fact and on our knowledge of the universal quantum state.