The origin of the difference between space and time

TL;DR

This paper proposes principles explaining the fundamental differences between space and time by treating spacetime as a fixed manifold with boundary conditions determining its properties, including the metric signature and arrow of time.

Contribution

It introduces a novel approach where boundary conditions in a fixed spacetime manifold explain key features of nature, such as metric signature and time arrow, without assuming a priori special roles for coordinates.

Findings

The metric signature (1,D-1) arises from boundary conditions.

Energy is bounded from below due to finiteness of solutions.

The arrow of time is explained by ordered boundary conditions.

Abstract

All differences between the role of space and time in nature are explained by proposing the principles in which none of the spacetime coordinates has an {\it a priori} special role. Spacetime is treated as a non-dynamical manifold, with a fixed global $\mathbb{R}^D$ topology. Dynamical theory of gravity determines only the metric tensor on a fixed manifold. All dynamics is treated as a Cauchy problem, so it {\em follows} that one coordinate takes a special role. It is proposed that {\em any} boundary condition that is finite everywhere leads to a solution which is also finite everywhere. This explains the $(1,D-1)$ signature of the metric, the boundedness of energy from below, the absence of tachyons, and other related properties of nature. The time arrow is explained by proposing that the boundary condition should be ordered. The quantization is considered as a boundary condition for field operators. Only the physical degrees of freedom are quantized.