The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism

I prove the existence of infinitely many physically distinct worlds represented by the same state vector and evolving according to the same law. This gives a constructive refutation of "Hilbert-space fundamentalism", the hypothesis that from the abstract state vector and the Hamiltonian all features of the physical world emerge uniquely, including space, all physical objects and their properties, and the decomposition into subsystems (Carroll, arXiv:2103.09780). This thesis was previously refuted in (arXiv:2102.08620) in full generality, but the proof was mathematically very abstract, while the present constructive proof is, hopefully, easily accessible to the down-to-earth intuition of the working physicists and philosophers of physics