A GROUPOID FOR COMMUTATIVE AND NONCOMMUTATIVE OPERATIONS: A STEP TOWARDS QUANTUM/RELATIVITY UNIFICATION

Arturo Tozzi (Corresponding Author)

Center for Nonlinear Science, University of North Texas

1155 Union Circle, #311427Denton, TX 76203-5017 USA

Computational Intelligence Laboratory, University of Manitoba, Winnipeg, Canada

Winnipeg R3T 5V6 Manitoba

tozziarturo@libero.it

 

James F. Peters

Department of Electrical and Computer Engineering, University of Manitoba

75A Chancellor’s CircleWinnipeg, MB R3T 5V6 CANADA and

Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey

James.Peters3@umanitoba.ca

 

 

The unexploited unification of general relativity and quantum physics is a painstaking issue that prevents physicists to properly understanding the whole of Nature. Here we propose a pure mathematical approach that introduces the problem in terms of group theory.  Indeed, we build a cyclic groupoid (a nonemptyset with a binary operation defined on it) that encompasses both the theories as subsets, making it possible to join together two of their most dissimilar experimental results, i.e., the commutativity detectable in our macroscopic relativistic world and the non-commutativity detectable in the quantum, microscopic world.  Further, we provide a feasible physical counterpart able to throw a bridge between relativity and quantum mechanics, namely, the gravitational force.  The latter stands for an operator able to reduce the countless orthonormal bases required by quantum mechanics to just one, i.e., the relativistic basis of an observer located in a single cosmic area. 

 

Tozzi, A.; Peters, J.F.. Unification of Commutative Relativity and Noncommutative Quantum Dynamics Via Cyclic Groupoids and Spacetime Fusion Categories. Preprints 2018, 2018090021 (doi: 10.20944/preprints201809.0021.v1).