TY - JOUR

T1 - Cosmology = Topology/Geometry: Mathematical Evidence for the Holographic Principle

AU - Alahmadi, Adel

AU - Glynn, David

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Cosmology

KW - Desargues theorem

KW - Geometrical configuration

KW - Graph

KW - History of mathematics

KW - Holographic principle

KW - Pappus theorem

KW - Projective geometry

KW - Quantum mechanics

KW - Topological surface

UR - http://www.researchgate.net/publication/296618674_Cosmology_TopologyGeometry_Mathematical_Evidence_for_the_Holographic_Principle

UR - http://www.scopus.com/inward/record.url?scp=85053293286&partnerID=8YFLogxK

U2 - 10.26749/rstpp.150.1.31

DO - 10.26749/rstpp.150.1.31

M3 - Article

VL - 150

SP - 31

EP - 38

JO - PAPERS AND PROCEEDINGS OF THE ROYAL SOCIETY OF TASMANIA

JF - PAPERS AND PROCEEDINGS OF THE ROYAL SOCIETY OF TASMANIA

SN - 0080-4703

IS - 1

ER -