  The quantum world is described by a unit vector in the Hilbert space and the
Hamiltonian. Do they, as abstract basis-independent objects, give a complete
description of the physical world, or should we include observables like
positions and momenta and the decomposition into subsystems? According to
"Hilbert-space fundamentalism" they give a complete description, and all other
features of the physical world emerge from them (Carroll, arXiv:2103.09780).
This thesis was previously refuted in (arXiv:2102.08620) in full generality.
But being an abstract non-uniqueness proof, and not a constructive one, it may
not be convincing enough to the busy reader who wants to avoid mathematical
details.
  Here I give a simpler, intuitive and constructive refutation, by showing that
concrete physically distinct worlds can be described by the same unit vector
and evolve according to the same law.
