A brief study of time

TL;DR

This paper explores the geometric and topological origins of time using Clifford algebra, proposing a unification of space and time that offers new insights beyond traditional relativistic frameworks.

Contribution

It introduces a Clifford algebra-based geometric model that distinguishes time as a point-like quantity and unifies it with space in a Minkowski-like formalism.

Findings

Time is modeled as a point-like quantity separate from space.

A Clifford algebra multivector provides a new geometric foundation for space-time.

The approach offers a topological distinction between space and time.

Abstract

Understanding the nature of time remains a key unsolved problem in science. Newton in the Principia asserted an absolute universal time that {\it `flows equably'}. Hamilton then proposed a mathematical unification of space and time within the framework of the quaternions that ultimately lead to the famous Minkowski formulation in 1908 using four-vectors. The Minkowski framework is found to provide a versatile formalism for describing the relationship between space and time in accordance with relativistic principles, but nevertheless fails to provide deeper insights into the physical origin of time and its properties. In this paper we begin with a recognition of the fundamental role played by three-dimensional space in physics that we model using the Clifford algebra multivector. From this geometrical foundation we are then able to identify a plausible origin for our concept of time. This geometrical perspective also allows us to make a key topological distinction between time and space, with time being a point-like quantity. The multivector then allows a generalized unification of time and space within a Minkowski-like description.