Reality as a Vector in Hilbert Space

2021/03/17 by Sean M. Carroll, Carroll, Sean M. · 4 voices · 7 citations
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Hamiltonian (control theory) #Hilbert space #Mathematics #Physical law #Physics #Position (finance) #Pure mathematics #Quantum Mechanics and Applications #Quantum mechanics #Reproducing kernel Hilbert space #Rigged Hilbert space #Sketch #Space (punctuation) #Theoretical physics #Vector space #gr-qc #hep-th #physics.hist-ph #quant-ph

paper · pdf · doi:10.48550/arxiv.2103.09780

published in arXiv (Cornell University) (Cornell University) · Invited contribution to the volume Quantum Mechanics and Fundamentality: Naturalizing Quantum Theory Between Scientific Realism and Ontological Indeterminacy; Valia Allori (ed.)

arxiv created 2021/03/17 · openalex publication_date 2021/03/17 · arxiv updated 2021/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined solely by the energy eigenspectrum of the Hamiltonian. The structure of our observed world, including space and fields living within it, should arise as a higher-level emergent description. I sketch how this might come about, although much work remains to be done.

Cited by

• Causality from the spectrum: Emergence of causal order from process-matrix mereology
• Toward a Phenomenologically Acceptable Quantum Cyclic Universe
• The Standard Model Symmetry and Qubit Entanglement
• Realism and Ontology in Quantum Mechanics and String Theory
• On the emergence of preferred structures in quantum theory
• Disentangling tensor product structures
• The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism

Discussions

• Reality as a Vector in Hilbert Space [hn, 51 points, 45 comments]
• My own view is that reality is represented by the quantum state, a vector in Hilbert space. It is often helpful to think of that state in the quantum-field basis, but that's just a convenient choice. [bsky, 13 points, 3 comments]
• Also in the physics-y vein, I finally got to @seanmcarroll.bsky.social 's Reality as a Vector in Hilbert Space over the weekend arxiv.org/abs/2103.09780 [bsky, 2 points, 1 comments]
• Reality as a Vector in Hilbert Space [hn, 2 points, 0 comments]

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