The disappearance of causality at small scale in almost-commutative manifolds

This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by the so-called isocones which generalize to the noncommutative setting the convex cones of order-preserving functions. In this paper we will consid...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical physics 2017-09, Vol.58 (9), p.1
Hauptverfasser: Bizi, Nadir, Besnard, Fabien
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 9
container_start_page 1
container_title Journal of mathematical physics
container_volume 58
creator Bizi, Nadir
Besnard, Fabien
description This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by the so-called isocones which generalize to the noncommutative setting the convex cones of order-preserving functions. In this paper we will consider the case of isocones inside almost-commutative algebras of the form C ( M ) ⊗ A f , with M a compact metrizable space. We will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family. We conjecture that this family is in fact a complete classification, a hypothesis related with the noncommutative Stone-Weierstrass conjecture. We also obtain that every isocone in C ( M ) ⊗ A f , with A f noncommutative, induces an order relation on M with the property that every point in M lies in a neighbourhood of incomparable points. Thus, if the causal order relation on spacetime is induced by an isocone in an almost-commutative (but not commutative) algebra, then causality must disappear at small scale. The usual Lorentzian causality would then only arise as an approximation of this noncommutative causality.
doi_str_mv 10.1063/1.4985929
format Article
fullrecord <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_proquest_journals_2116063922</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1970634368</sourcerecordid><originalsourceid>FETCH-LOGICAL-c354t-b4f624f0435c2c67d6224585ccb4f04375ee1b31d71ac2df663a59d5eedcd8c43</originalsourceid><addsrcrecordid>eNp9kFFLwzAUhYMoOKcP_oOATwqduWmSpo9jqBMmvszncJemLKNtZtMO9u_t3NC3PV04fJxz-Qi5BzYBptJnmIhcy5znF2QETOdJpqS-JCPGOE-40Pqa3MS4YQxACzEiH8u1o4WPuN06bLGxjoaSWuwjVr7bU-xorLGqaLRYOeobilUdYpfYUNd9h53fOVpj48tQFfGWXJVYRXd3umPy9fqynM2Txefb-2y6SGwqRZesRKm4KJlIpeVWZYXiXEgtrV39ppl0DlYpFBmg5UWpVIoyL4a0sIW2Ih2Tx2PvGiuzbX2N7d4E9GY-XZhDxkAJCRnbwcA-HNltG757FzuzCX3bDO8ZDqAGaTnn5yjIswESqdL_u7YNMbau_BsHZg7-DZiT_4F9OrLR-oOn0JyBfwCpSoMT</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1970634368</pqid></control><display><type>article</type><title>The disappearance of causality at small scale in almost-commutative manifolds</title><source>AIP Journals Complete</source><source>Alma/SFX Local Collection</source><creator>Bizi, Nadir ; Besnard, Fabien</creator><creatorcontrib>Bizi, Nadir ; Besnard, Fabien</creatorcontrib><description>This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by the so-called isocones which generalize to the noncommutative setting the convex cones of order-preserving functions. In this paper we will consider the case of isocones inside almost-commutative algebras of the form C ( M ) ⊗ A f , with M a compact metrizable space. We will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family. We conjecture that this family is in fact a complete classification, a hypothesis related with the noncommutative Stone-Weierstrass conjecture. We also obtain that every isocone in C ( M ) ⊗ A f , with A f noncommutative, induces an order relation on M with the property that every point in M lies in a neighbourhood of incomparable points. Thus, if the causal order relation on spacetime is induced by an isocone in an almost-commutative (but not commutative) algebra, then causality must disappear at small scale. The usual Lorentzian causality would then only arise as an approximation of this noncommutative causality.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.4985929</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>New York: American Institute of Physics</publisher><subject>Algebra ; Approximation ; Causality ; Cones ; General Relativity and Quantum Cosmology ; Mathematical analysis ; Mathematical Physics ; Physics ; Topological manifolds</subject><ispartof>Journal of mathematical physics, 2017-09, Vol.58 (9), p.1</ispartof><rights>Author(s)</rights><rights>Copyright American Institute of Physics Sep 2017</rights><rights>2017 Author(s). Published by AIP Publishing.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c354t-b4f624f0435c2c67d6224585ccb4f04375ee1b31d71ac2df663a59d5eedcd8c43</citedby><cites>FETCH-LOGICAL-c354t-b4f624f0435c2c67d6224585ccb4f04375ee1b31d71ac2df663a59d5eedcd8c43</cites><orcidid>0000-0003-4038-2640 ; 0000-0003-2643-6980</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.4985929$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,780,784,794,885,4512,27924,27925,76384</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01645170$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bizi, Nadir</creatorcontrib><creatorcontrib>Besnard, Fabien</creatorcontrib><title>The disappearance of causality at small scale in almost-commutative manifolds</title><title>Journal of mathematical physics</title><description>This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by the so-called isocones which generalize to the noncommutative setting the convex cones of order-preserving functions. In this paper we will consider the case of isocones inside almost-commutative algebras of the form C ( M ) ⊗ A f , with M a compact metrizable space. We will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family. We conjecture that this family is in fact a complete classification, a hypothesis related with the noncommutative Stone-Weierstrass conjecture. We also obtain that every isocone in C ( M ) ⊗ A f , with A f noncommutative, induces an order relation on M with the property that every point in M lies in a neighbourhood of incomparable points. Thus, if the causal order relation on spacetime is induced by an isocone in an almost-commutative (but not commutative) algebra, then causality must disappear at small scale. The usual Lorentzian causality would then only arise as an approximation of this noncommutative causality.</description><subject>Algebra</subject><subject>Approximation</subject><subject>Causality</subject><subject>Cones</subject><subject>General Relativity and Quantum Cosmology</subject><subject>Mathematical analysis</subject><subject>Mathematical Physics</subject><subject>Physics</subject><subject>Topological manifolds</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kFFLwzAUhYMoOKcP_oOATwqduWmSpo9jqBMmvszncJemLKNtZtMO9u_t3NC3PV04fJxz-Qi5BzYBptJnmIhcy5znF2QETOdJpqS-JCPGOE-40Pqa3MS4YQxACzEiH8u1o4WPuN06bLGxjoaSWuwjVr7bU-xorLGqaLRYOeobilUdYpfYUNd9h53fOVpj48tQFfGWXJVYRXd3umPy9fqynM2Txefb-2y6SGwqRZesRKm4KJlIpeVWZYXiXEgtrV39ppl0DlYpFBmg5UWpVIoyL4a0sIW2Ih2Tx2PvGiuzbX2N7d4E9GY-XZhDxkAJCRnbwcA-HNltG757FzuzCX3bDO8ZDqAGaTnn5yjIswESqdL_u7YNMbau_BsHZg7-DZiT_4F9OrLR-oOn0JyBfwCpSoMT</recordid><startdate>20170901</startdate><enddate>20170901</enddate><creator>Bizi, Nadir</creator><creator>Besnard, Fabien</creator><general>American Institute of Physics</general><general>American Institute of Physics (AIP)</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-4038-2640</orcidid><orcidid>https://orcid.org/0000-0003-2643-6980</orcidid></search><sort><creationdate>20170901</creationdate><title>The disappearance of causality at small scale in almost-commutative manifolds</title><author>Bizi, Nadir ; Besnard, Fabien</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-b4f624f0435c2c67d6224585ccb4f04375ee1b31d71ac2df663a59d5eedcd8c43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Approximation</topic><topic>Causality</topic><topic>Cones</topic><topic>General Relativity and Quantum Cosmology</topic><topic>Mathematical analysis</topic><topic>Mathematical Physics</topic><topic>Physics</topic><topic>Topological manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bizi, Nadir</creatorcontrib><creatorcontrib>Besnard, Fabien</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bizi, Nadir</au><au>Besnard, Fabien</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The disappearance of causality at small scale in almost-commutative manifolds</atitle><jtitle>Journal of mathematical physics</jtitle><date>2017-09-01</date><risdate>2017</risdate><volume>58</volume><issue>9</issue><spage>1</spage><pages>1-</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by the so-called isocones which generalize to the noncommutative setting the convex cones of order-preserving functions. In this paper we will consider the case of isocones inside almost-commutative algebras of the form C ( M ) ⊗ A f , with M a compact metrizable space. We will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family. We conjecture that this family is in fact a complete classification, a hypothesis related with the noncommutative Stone-Weierstrass conjecture. We also obtain that every isocone in C ( M ) ⊗ A f , with A f noncommutative, induces an order relation on M with the property that every point in M lies in a neighbourhood of incomparable points. Thus, if the causal order relation on spacetime is induced by an isocone in an almost-commutative (but not commutative) algebra, then causality must disappear at small scale. The usual Lorentzian causality would then only arise as an approximation of this noncommutative causality.</abstract><cop>New York</cop><pub>American Institute of Physics</pub><doi>10.1063/1.4985929</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0003-4038-2640</orcidid><orcidid>https://orcid.org/0000-0003-2643-6980</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0022-2488
ispartof Journal of mathematical physics, 2017-09, Vol.58 (9), p.1
issn 0022-2488
1089-7658
language eng
recordid cdi_proquest_journals_2116063922
source AIP Journals Complete; Alma/SFX Local Collection
subjects Algebra
Approximation
Causality
Cones
General Relativity and Quantum Cosmology
Mathematical analysis
Mathematical Physics
Physics
Topological manifolds
title The disappearance of causality at small scale in almost-commutative manifolds
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T12%3A10%3A25IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20disappearance%20of%20causality%20at%20small%20scale%20in%20almost-commutative%20manifolds&rft.jtitle=Journal%20of%20mathematical%20physics&rft.au=Bizi,%20Nadir&rft.date=2017-09-01&rft.volume=58&rft.issue=9&rft.spage=1&rft.pages=1-&rft.issn=0022-2488&rft.eissn=1089-7658&rft.coden=JMAPAQ&rft_id=info:doi/10.1063/1.4985929&rft_dat=%3Cproquest_hal_p%3E1970634368%3C/proquest_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1970634368&rft_id=info:pmid/&rfr_iscdi=true