ENTANGLED ANTIPODAL POINTS ON BLACK HOLE SURFACES: THE BORSUK-ULAM THEOREM COMES INTO PLAY

Arturo Tozzi
Center for Nonlinear Science, University of North Texas
1155 Union Circle, #311427
Denton, TX 76203-5017 USA
tozziarturo@libero.it
 
James F. Peters
Department of Electrical and Computer Engineering, University of Manitoba
75A Chancellor’s Circle
Winnipeg, MB R3T 5V6 CANADA
James.Peters3@umanitoba.ca
 
 
 
The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship
with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum
entanglement takes place on the antipodal points of a S3 hypersphere, a novel framework can be developed, based on
algebraic topological issues: a feature encompassed in an S2 unentangled state gives rise, when projected one dimension
higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle
occurring in S2. Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a
negative mass might exist on the surface of a black hole.
 

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negative mass might exist on the surface of a black hole.Arturo Tozzi (Corresponding Author)
Center for Nonlinear Science, University of North Texas
1155 Union Circle, #311427
Denton, TX 76203-5017 USA
tozziarturo@libero.it
James F. Peters
Department of Electrical and Computer Engineering, University of Manitoba
75A Chancellor’s Circle
Winnipeg, MB R3T 5V6 CANADA
James.Peters3@umanitoba.ca
The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship
with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum
entanglement takes place on the antipodal points of a S3 hypersphere, a novel framework can be developed, based on
algebraic topological issues: a feature encompassed in an S2 unentangled state gives rise, when projected one dimension
higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle
occurring in S2. Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a fourdimensional
spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a
negative mass might exist on the surface of a black hole.