Entanglement and the quantum spatial continuum

John V. Corbett

doi:10.1063/1.3635841

Entanglement and the quantum spatial continuum

John V. Corbett^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

Abstract

The non-locality of entangled systems provides more evidence that the spatial continuum of quantum particles is not classical. We assume that physical quantities take Dedekind real numbers in a topos for their numerical values. This means that the quantum spatial continuum is isomorphic to R _D(E_J(M))³, where R_D(E _J(M)) the sheaf of Dedekind real numbers in the topos Shv(E _J(M) of sheaves on the state space of the quantum system. In such a continuum, a single particle can have a quantum trajectory which passes through two classically separated slits and two particles in an entangled condition stay close to each other in their quantum space and hence Einstein locality is retained.

Original language	English
Title of host publication	75 Years of Quantum Entanglement
Subtitle of host publication	Foundations and Information Theoretic Applications - S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium
Editors	Dipankar Home, Guruprasad Kar, Archan S. Majumdar
Place of Publication	College Park, MD
Publisher	American Institute of Physics
Pages	34-41
Number of pages	8
Volume	1384
ISBN (Print)	9780735409453
DOIs	https://doi.org/10.1063/1.3635841
Publication status	Published - 2011
Event	S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium on 75 Years of Quantum Entanglement: Foundations and Information Theoretic Applications - Kolkata, India Duration: 6 Jan 2011 → 10 Jun 2011

Other

Other	S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium on 75 Years of Quantum Entanglement: Foundations and Information Theoretic Applications
Country/Territory	India
City	Kolkata
Period	6/01/11 → 10/06/11

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title = "Entanglement and the quantum spatial continuum",

abstract = "The non-locality of entangled systems provides more evidence that the spatial continuum of quantum particles is not classical. We assume that physical quantities take Dedekind real numbers in a topos for their numerical values. This means that the quantum spatial continuum is isomorphic to R D(EJ(M))3, where RD(E J(M)) the sheaf of Dedekind real numbers in the topos Shv(E J(M) of sheaves on the state space of the quantum system. In such a continuum, a single particle can have a quantum trajectory which passes through two classically separated slits and two particles in an entangled condition stay close to each other in their quantum space and hence Einstein locality is retained.",

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year = "2011",

doi = "10.1063/1.3635841",

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booktitle = "75 Years of Quantum Entanglement",

publisher = "American Institute of Physics",

address = "United States",

note = "S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium on 75 Years of Quantum Entanglement: Foundations and Information Theoretic Applications ; Conference date: 06-01-2011 Through 10-06-2011",

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Corbett, JV 2011, Entanglement and the quantum spatial continuum. in D Home, G Kar & AS Majumdar (eds), 75 Years of Quantum Entanglement: Foundations and Information Theoretic Applications - S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium. vol. 1384, American Institute of Physics, College Park, MD, pp. 34-41, S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium on 75 Years of Quantum Entanglement: Foundations and Information Theoretic Applications, Kolkata, India, 6/01/11. https://doi.org/10.1063/1.3635841

Entanglement and the quantum spatial continuum. / Corbett, John V.
75 Years of Quantum Entanglement: Foundations and Information Theoretic Applications - S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium. ed. / Dipankar Home; Guruprasad Kar; Archan S. Majumdar. Vol. 1384 College Park, MD: American Institute of Physics, 2011. p. 34-41.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AB - The non-locality of entangled systems provides more evidence that the spatial continuum of quantum particles is not classical. We assume that physical quantities take Dedekind real numbers in a topos for their numerical values. This means that the quantum spatial continuum is isomorphic to R D(EJ(M))3, where RD(E J(M)) the sheaf of Dedekind real numbers in the topos Shv(E J(M) of sheaves on the state space of the quantum system. In such a continuum, a single particle can have a quantum trajectory which passes through two classically separated slits and two particles in an entangled condition stay close to each other in their quantum space and hence Einstein locality is retained.

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Entanglement and the quantum spatial continuum

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