Born in an infinite universe: A cosmological interpretation of quantum mechanics
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for ca...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society (APS)
2012
|
| Online Access: | http://hdl.handle.net/1721.1/69847 https://orcid.org/0000-0001-7670-7190 |
| _version_ | 1826207574235545600 |
|---|---|
| author | Aguirre, Anthony Tegmark, Max Erik |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Aguirre, Anthony Tegmark, Max Erik |
| author_sort | Aguirre, Anthony |
| collection | MIT |
| description | We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave-function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad infinitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wave function, the remainder consists of a superposition of indistinguishable terms, so that arguably “collapse” of the wave function is irrelevant, and the “many worlds” of Everett’s interpretation are unified into one. Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection. |
| first_indexed | 2024-09-23T13:51:59Z |
| format | Article |
| id | mit-1721.1/69847 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:51:59Z |
| publishDate | 2012 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/698472022-10-01T17:35:10Z Born in an infinite universe: A cosmological interpretation of quantum mechanics Aguirre, Anthony Tegmark, Max Erik Massachusetts Institute of Technology. Department of Physics MIT Kavli Institute for Astrophysics and Space Research Tegmark, Max Erik Tegmark, Max Erik We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave-function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad infinitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wave function, the remainder consists of a superposition of indistinguishable terms, so that arguably “collapse” of the wave function is irrelevant, and the “many worlds” of Everett’s interpretation are unified into one. Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection. United States. National Aeronautics and Space Administration (Grant No. NAG5-11099) United States. National Aeronautics and Space Administration (Grant No. NNG 05G40G) National Science Foundation (U.S.) (Grant No. AST-0607597) National Science Foundation (U.S.) (Grant No. AST-0708534) National Science Foundation (U.S.) (Grant No. AST-0908848) National Science Foundation (U.S.) (Grant No. PHY-0855425) National Science Foundation (U.S.) (Grant No. PHY-0757912) Templeton Foundation (Foundational Questions in Physics and Cosmology grant) David & Lucile Packard Foundation Research Corporation 2012-03-23T19:03:37Z 2012-03-23T19:03:37Z 2011-11 2010-09 Article http://purl.org/eprint/type/JournalArticle 1550-7998 1089-4918 http://hdl.handle.net/1721.1/69847 Aguirre, Anthony, and Max Tegmark. “Born in an Infinite Universe: A Cosmological Interpretation of Quantum Mechanics.” Physical Review D 84.10 (2011): Web. 23 Mar. 2012. © 2011 American Physical Society https://orcid.org/0000-0001-7670-7190 en_US http://dx.doi.org/10.1103/PhysRevD.84.105002 Physical Review D Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society (APS) APS |
| spellingShingle | Aguirre, Anthony Tegmark, Max Erik Born in an infinite universe: A cosmological interpretation of quantum mechanics |
| title | Born in an infinite universe: A cosmological interpretation of quantum mechanics |
| title_full | Born in an infinite universe: A cosmological interpretation of quantum mechanics |
| title_fullStr | Born in an infinite universe: A cosmological interpretation of quantum mechanics |
| title_full_unstemmed | Born in an infinite universe: A cosmological interpretation of quantum mechanics |
| title_short | Born in an infinite universe: A cosmological interpretation of quantum mechanics |
| title_sort | born in an infinite universe a cosmological interpretation of quantum mechanics |
| url | http://hdl.handle.net/1721.1/69847 https://orcid.org/0000-0001-7670-7190 |
| work_keys_str_mv | AT aguirreanthony borninaninfiniteuniverseacosmologicalinterpretationofquantummechanics AT tegmarkmaxerik borninaninfiniteuniverseacosmologicalinterpretationofquantummechanics |