Time discretization from noncommutativity

We show that a particular noncommutative geometry, sometimes called angular or rho-Minkowski, requires that the spectrum of time be discrete. In this noncommutative space the time variable is not commuting with the angular variable in cylindrical coordinates. The possible values that the variable can take go from minus infinity to plus infinity, equally spaced by the scale of noncommutativity. Possible self-adjoint extensions of the time operator are discussed. They give that a measurement of time can be any real value, but time intervals are still quantized. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

This passage discusses a specific noncommutative geometry known as angular or rho-Minkowski, which requires the spectrum of time to be discrete. In this space, the time variable does not commute with the angular variable in cylindrical coordinates, with possible values ranging from minus infinity to plus infinity equally spaced by the noncommutativity scale. The possible self-adjoint extensions of the time operator allow for time measurements to be any real value, but time intervals remain quantized.