  Hilbert-Space Fundamentalism (HSF) states that the only fundamental
structures are the quantum state vector and the Hamiltonian, and from them
everything else emerge uniquely, including the 3D-space, a preferred basis, and
a preferred factorization of the Hilbert space.
  In this article it is shown that whenever such a structure emerges from the
Hamiltonian and the state vector alone, if it is physically relevant, it is not
unique.
  Moreover, HSF leads to strange effects like "passive" travel in time and in
alternative realities, realized simply by passive transformations of the
Hilbert space.
  The results from this article affect all theories that adhere to HSF, whether
they assume branching or state vector reduction (in particular the version of
Everett's Interpretation coined by Carroll and Singh "Mad-dog Everettianism"),
various proposals based on decoherence, proposals that aim to describe
everything by the quantum structure alone, and proposals that spacetime emerges
from a purely quantum theory of gravity.
