Carrol - Reality as a Vector in a Hilbert Space.pdf -...

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CALT-TH-2021-010Reality as a Vector in Hilbert SpaceSean M. Carroll1Walter Burke Institute for Theoretical PhysicsCalifornia Institute of Technology, Pasadena, CA 91125and Santa Fe Institute, Santa Fe, NM 87501AbstractI defend the extremist position that the fundamental ontology of the world consists of avector in Hilbert space evolving according to the Schr¨odinger equation. The laws of physicsare determined solely by the energy eigenspectrum of the Hamiltonian. The structure ofour observed world, including space and fields living within it, should arise as a higher-levelemergent description. I sketch how this might come about, although much work remainsto be done.Invited contribution to the volumeQuantum Mechanics and Fundamentality: NaturalizingQuantum Theory Between Scientific Realism and Ontological Indeterminacy; Valia Allori(ed.).1e-mail:[email protected]arXiv:2103.09780v1[quant-ph]17 Mar 2021
[I]t would be naive in the extreme to be a ‘Hilbert-space-vector realist’: to reify Hilbertspace, and take it as analogous to physical space.– Wallace (2017)In Hilbert space, nobody can hear you scream.– Aharonov & Rohrlich (2005)Almost a century after the 1927 Solvay Conference, the question of the ultimate ontologyof quantum mechanics remains unsettled. Essentially all formulations of quantum theory relyon the use of a wave function or state vector (or mathematically equivalent structures). Butresearchers do not agree on whether the state vector is a complete and exact representation ofreality, whether it represents part of reality but needs to be augmented by additional variablesto be complete, or whether it is an epistemic tool rather than a representation of reality at all.And they further do not agree on whether the state vector should be thought of as purely anelement of some abstract Hilbert space, or whether there is some fundamental ontological statusto a particular representation of that vector in terms of something more directly physical, suchas configuration space or particles or fields in honest three-dimensional “space.”Here I want to argue for the plausibility of an extreme position among these alternatives, thatthe fundamental ontology of the world is completely and exactly represented by a vector in anabstract Hilbert space, evolving in time according to unitary Schr¨odinger dynamics. Everythingelse, from particles and fields to space itself, is rightly thought of as emergent from that austereset of ingredients. This approach has been called “Mad-Dog Everettianism” (Carroll & Singh,2019) although “Hilbert Space Fundamentalism” would be equally accurate.Let’s see how one might end up seduced by an ideology that is so radically different fromour direct experience of the world. When we are first taught quantum mechanics, we are shownhow to construct quantum theories by taking classical models and quantizing them. Imaginewe have a classical precursor theory defined on some phase space, expressed mathematically as

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Term
Spring
Professor
WilliamL.Andersen
Tags
The Bear, Hilbert space

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