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