Refutation of Hilbert Space Fundamentalism

TL;DR

This paper critically examines the claim that all features of physical systems, including space and subsystems, uniquely emerge from quantum state vectors and Hamiltonians, arguing that such emergence cannot be both unique and physically meaningful.

Contribution

It provides a simplified proof demonstrating that the emergence of space and subsystems from quantum states cannot be both unique and physically relevant, challenging the Hilbert Space Fundamentalism thesis.

Findings

Emerging structures from quantum states are not both unique and physically relevant.

The proof simplifies previous arguments against Hilbert Space Fundamentalism.

Challenges the idea that all physical features derive solely from the state vector and Hamiltonian.

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.