Minimum Length from First Principles

TL;DR

This paper argues that fundamental physical principles prevent any device or thought experiment from measuring distances smaller than the Planck length, implying a fundamental minimal length scale in nature.

Contribution

It provides a first-principles derivation showing the impossibility of measuring sub-Planckian distances based on causality, quantum uncertainty, and classical gravity.

Findings

No device can resolve distances below the Planck length.

The minimal length arises from fundamental physical principles.

Supports the concept of a minimal length scale in quantum gravity.

Abstract

We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the eigenvalues of the position operator to within that accuracy. The only assumptions in our argument are causality, the uncertainty principle from quantum mechanics and a dynamical criteria for gravitational collapse from classical general relativity called the hoop conjecture. The inability of any gedanken experiment to measure a sub-Planckian distance suggests the existence of a minimal length.