Rationalized system of units

Rationalized systems of units are systems of units in which factors of occur in the denominator of the force equations. This is made possible by defining the coupling constants of the corresponding force differently in the unit systems. Including the factor in the force equations testifies to the fact that a force is inversely proportional to the surface of a sphere . ${\displaystyle 4\pi r^{2}}$

The International System of Units is a rationalized system of units for electrodynamics , but not for gravity . The force equation for two charges reads in it ${\displaystyle q,Q}$

${\displaystyle F={\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ}{r^{2}}}}$

with the electric field constant , but the force equation for two masses ${\displaystyle \varepsilon _{0}}$ ${\displaystyle m,M}$

${\displaystyle F=G{\frac {mM}{r^{2}}}}$

with the gravitational constant . ${\displaystyle G}$

Another property of rationalized systems of units in electrodynamics is that the -factors are omitted in Maxwell's equations (see here ). For rationalized systems of units with regard to gravitation, Einstein's field equations are simplified insofar as the factor becomes a factor . ${\displaystyle 4\pi }$ ${\displaystyle 8\pi }$ ${\displaystyle 2}$

history

For Oliver Heaviside , the Gaussian system of units used in particle physics at the time was irrational and he fought for the implementation of a rationalized system of units.

Executions

• International system of units (electrodynamics)
• Heaviside-Lorentz unit system (electrodynamics)
• Rationalized Planck units (electrodynamics and gravitation)

Individual evidence

1. ^ Neal J. Carron: Babel of Units. The Evolution of Units Systems in Classical Electromagnetism . In: arXiv - physics.hist-ph . June 3, 2015, arxiv : 1506.01951 (English).