Physical quantities and dimensional analysis: from mechanics to quantum gravity

TL;DR

This paper provides a pedagogical overview of physical quantities and dimensional analysis, exploring their applications across physics from mechanics to quantum gravity, including fundamental constants and units.

Contribution

It offers a comprehensive review connecting dimensional analysis to advanced physics topics, emphasizing educational insights and the role of fundamental constants.

Findings

Dimensional analysis aids understanding across physics disciplines

Fundamental constants are key to unifying physical theories

Natural units simplify complex physical relationships

Abstract

Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional analysis, I will embark in a journey through various branches of physics, from basic mechanics to quantum gravity. I will also discuss a little bit about the fundamental constants of Nature, the so-called "cube of Physics", and the natural system of units.