Convexity and the Euclidean Metric of Space-Time
<p dir="ltr">We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches...
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2017
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| _version_ | 1864513522148311040 |
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| author | Nikolaos Kalogeropoulos (9416607) |
| author_facet | Nikolaos Kalogeropoulos (9416607) |
| author_role | author |
| dc.creator.none.fl_str_mv | Nikolaos Kalogeropoulos (9416607) |
| dc.date.none.fl_str_mv | 2017-02-08T03:00:00Z |
| dc.identifier.none.fl_str_mv | 10.3390/universe3010008 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Convexity_and_the_Euclidean_Metric_of_Space-Time/31446178 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Mathematical physics Physical sciences Quantum physics space-time metric convexity smoothness Hilbert spaces Banach spaces dualities |
| dc.title.none.fl_str_mv | Convexity and the Euclidean Metric of Space-Time |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Universe<br>License: <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3390/universe3010008" target="_blank">https://dx.doi.org/10.3390/universe3010008</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_df2c4fb6af7bbb3ca0e5650ec1fea021 |
| identifier_str_mv | 10.3390/universe3010008 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/31446178 |
| publishDate | 2017 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Convexity and the Euclidean Metric of Space-TimeNikolaos Kalogeropoulos (9416607)Mathematical sciencesMathematical physicsPhysical sciencesQuantum physicsspace-time metricconvexitysmoothnessHilbert spacesBanach spacesdualities<p dir="ltr">We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Universe<br>License: <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3390/universe3010008" target="_blank">https://dx.doi.org/10.3390/universe3010008</a></p>2017-02-08T03:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.3390/universe3010008https://figshare.com/articles/journal_contribution/Convexity_and_the_Euclidean_Metric_of_Space-Time/31446178CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/314461782017-02-08T03:00:00Z |
| spellingShingle | Convexity and the Euclidean Metric of Space-Time Nikolaos Kalogeropoulos (9416607) Mathematical sciences Mathematical physics Physical sciences Quantum physics space-time metric convexity smoothness Hilbert spaces Banach spaces dualities |
| status_str | publishedVersion |
| title | Convexity and the Euclidean Metric of Space-Time |
| title_full | Convexity and the Euclidean Metric of Space-Time |
| title_fullStr | Convexity and the Euclidean Metric of Space-Time |
| title_full_unstemmed | Convexity and the Euclidean Metric of Space-Time |
| title_short | Convexity and the Euclidean Metric of Space-Time |
| title_sort | Convexity and the Euclidean Metric of Space-Time |
| topic | Mathematical sciences Mathematical physics Physical sciences Quantum physics space-time metric convexity smoothness Hilbert spaces Banach spaces dualities |