On Knots and Temporality

Abstract

In a class of quantum gravity approaches it is indicated that our observable world emerges out of a fundamental structure that appears highly resistant to any clear spatial or temporal interpretation. In this work we are examining an analogue quantum system that appears to simulate such an unintuitive structure: the emergence of the so called topolgoical phase of matter depicted by the Chern-Simons gauge theory. By investigating the proposed analogy from the lens of category theory, we offer a clear interpretation of the way in which space and time act at the fundamental level. In this way, we put forward an analogical argument in support of a relational view of space and time.