Refutation of Hilbert Space Fundamentalism

Abstract: According to the "Hilbert Space Fundamentalism" Thesis, all features of a physical system, including the 3D-space, a preferred basis, and factorization into subsystems, uniquely emerge from the state vector and the Hamiltonian alone. I give a simplified account of the proof from arXiv:2102.08620 showing that such emerging structures cannot be both unique and physically relevant.