Space-time is doomed! Introducing Planck scale physics in the classroom

Abstract

This article provides an overview of some tentative ideas relating to Planck scale physics at a level suitable for advanced high school students, beginning undergraduate students, and teachers. After discussing the ratio of the electric and gravitational forces, Heisenberg’s uncertainty principle is combined with Einstein’s theory of special relativity to estimate the scale at which the strength of gravity becomes comparable to the electrostatic force. It is shown that the energy required to probe a region of space smaller than the Planck length may lead to the formation of a black hole, placing a fundamental lower limit on the distances that can be meaningfully probed in Nature. The Planck length, mass and time are then obtained using a combination of dimensional analysis and the fundamental constants appearing in theories of quantum mechanics, relativity and gravity. Finally, a heuristic derivation of the generalised uncertainty principle is provided.