Heaviside–Lorentz units

Lore & Background

In the mid-late 19th century, electromagnetic measurements used electrostatic (ESU) or electromagnetic (EMU) systems, leading to many factors of 4π in formulas. Lorentz noted in the opening section, crediting Heaviside, that they would use 'the clearer and more condensed form' given by Heaviside and Hertz, introducing units that get rid of factors like 4π and √4π. Lorentz stated that their unit of electricity would be √4π times smaller than the usual electrostatic unit, and the unit of magnetic force similarly scaled.

Reader's Guide

Heaviside–Lorentz units are significant because they rationalize electromagnetic equations, removing factors of 4π that appear in CGS-Gaussian and other systems. This rationalization partly explains their appeal in quantum field theory, where the Lagrangian underlying the theory does not have any factors of 4π when this system is used. The system is often used in relativistic calculations and particle physics, and is particularly convenient when performing calculations in spatial dimensions greater than three, such as in string theory. In the Heaviside–Lorentz system, electromagnetic quantities differ by factors of √4π in the definitions of electric and magnetic fields and of electric charge compared to Gaussian units. For example, the HL unit of charge is √4π times larger than the corresponding Gaussian quantity. The system uses length–mass–time dimensions, with Coulomb's equation given as F = q₁q₂/(4πr²). Conversion to SI units involves the vacuum permittivity ε₀ and permeability μ₀, with SI charge expressed as √(ε₀L³M/T²). The system's legacy lies in providing a cleaner mathematical framework for theoretical physics, particularly in contexts where spherical symmetry is not inherent.

Did You Know?

• Heaviside–Lorentz units normalize ε₀ = 1 and μ₀ = 1 while revising Maxwell's equations to use the speed of light c.
• The system is rationalized, so no factors of 4π appear explicitly in Maxwell's equations.