  Anthony Aguirre and Max Tegmark have famously speculated that the Level I
Multiverse is the same as the Level III Multiverse. By this, they mean that the
parallel universes of the Level III Multiverse can be regarded as similar or
identical copies of our own Hubble volume distributed throughout the whole of
our (possibly infinite) bubble universe. However, we show that our bubble
universe is in a single quantum eigenstate that extends to regions of space
that are receding from each other at superluminal velocities because of general
relativistic expansion. Such a bubble universe cannot accommodate Hubble
volumes in the different orthogonal eigenstates required by the Level III
Multiverse. Instead, quantum uncertainty arises from large numbers of
alternative bubble universes in Hilbert space, isolated from each other. The
conclusion of the paper is that the Level I Multiverse is not the same as the
Level III Multiverse.
