Reality as a Vector in Hilbert Space

TL;DR

This paper advocates for a fundamental ontology where reality is represented by a vector in Hilbert space evolving via Schrödinger's equation, with emergent space and fields arising at higher levels.

Contribution

It proposes a radical ontological view that the universe's fundamental structure is a Hilbert space vector, emphasizing the role of the Hamiltonian's spectrum and emergent phenomena.

Findings

Reinforces the idea that the wavefunction's structure underpins physical reality.

Suggests space and fields are emergent from the Hilbert space framework.

Highlights the importance of the Hamiltonian's energy spectrum in physical laws.

Abstract

I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schr\"odinger 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.