# What do we know about the geometry of space?

## TL;DR

This paper questions the assumption of infinite, flat space in physics by examining observational bounds and explores implications for relativity and Yang-Mills theory through the Telescope Principle.

## Contribution

It introduces the Telescope Principle as a framework to understand the geometry of space based on observable bounds, linking it to relativity and gauge theories.

## Key findings

- Space geometry is bounded by observations, challenging the assumption of flatness at infinity.
- The Telescope Principle offers new insights into the structure of space in relativity.
- Connections between space geometry and Yang-Mills theory are explored through projective equivalences.

## Abstract

The belief that three dimensional space is infinite and flat in the absence of matter is a canon of physics that has been in place since the time of Newton. The assumption that space is flat at infinity has guided several modern physical theories. But what do we actually know to support this belief? A simple argument, called the "Telescope Principle", asserts that all that we can know about space is bounded by observations. Physical theories are best when they can be verified by observations, and that should also apply to the geometry of space. The Telescope Principle is simple to state, but it leads to very interesting insights into relativity and Yang-Mills theory via projective equivalences of their respective spaces.