Abstract
It is often claimed that, from the abstract quantum state vector and Hamiltonian, everything emerges uniquely (for example the 3D-space, a preferred factorization of the Hilbert space, and a preferred basis). This thesis, called Hilbert-Space Fundamentalism (HSF), is assumed for example in Carroll and Singh’s “Mad-dog Everettianism”, some 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.I show that whenever the 3D-space, a preferred factorization, or any other structure emerges like this, there are infinitely many solutions. This refutes Hilbert-Space Fundamentalism.Implications for various research programs aiming to show that certain structures emerge uniquely, and for various interpretations of Quantum Mechanics, are discussed.
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