Cosmology = topology/geometry: mathematical evidence for the Holographic Principle

Alahmadi, AN and Glynn, DG 2016 , 'Cosmology = topology/geometry: mathematical evidence for the Holographic Principle' , Papers and Proceedings of the Royal Society of Tasmania, vol. 150, no. 1 , pp. 31-38 , doi: https://doi.org/10.26749/rstpp.150.1.31.

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In August 2015 NORDITA (Nordic Institute for Theoretical Physics) hosted a conference where Hawking strongly supported the conjectured relationship between string theory and quantum fields that was initiated with the holographic principle some 20 years ago by ’t Hooft, Maldacena, Susskind and Witten. We bring together results of several papers showing how mathematics can come to the party: the fundamentals of flat (even higher-dimensional) space can be derived very simply from topological properties on a surface. Specifically, Desargues, Pappus or other configurations do not have to be assumed a priori or as self-evident (a fundamental weakness of Hilbert’s work in 1899) to develop the foundations of geometry. Are black holes places where non-commutative (quantum) behaviour reigns while Euclidean (flat) space is where commutativity holds sway? So, we cannot hope to look inside a black hole unless we know how “deformable” topology is related to “flat” geometry.

Item Type: Article
Authors/Creators:Alahmadi, AN and Glynn, DG
Keywords: cosmology, Desargues theorem, geometrical configuration, graph, history of mathematics, holographic principle, Pappus theorem, projective geometry, quantum mechanics, topological surface, The Royal Society of Tasmania, Alexander von Humboldt, Germany, Conference, Proceedings
Journal or Publication Title: Papers and Proceedings of the Royal Society of Tasmania
ISSN: 0080-4703
DOI / ID Number: https://doi.org/10.26749/rstpp.150.1.31
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Copyright The Royal Society of Tasmania

Collections: Royal Society Collection > Papers & Proceedings of the Royal Society of Tasmania
Additional Information:

This paper was presented at GLOBAL PERSPECTIVES, LOCAL KNOWLEDGE : Proceedings of the Biennial Conference of the Australian Association of von Humboldt Fellows in association with the New Zealand Association of von Humboldt Fellows.
20–22 November 2015, Hobart, Tasmania.
Dr. Adel Alahmadi is Associate Professor of Mathematics, College of Science at King Abdulaziz University, Jeddah, Saudi Arabia and Prog. David Glynn is Distinguished Adjunct Professor at King AbdulAziz University and Adjunct Research Fellow at Flinders University of South Australia

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