nLab natural units

Idea

In physics, by natural units one means physical units of measurements formed from combinations of fundamental physical constants, such as

• $c$ – the speed of light

• $G$ – gravitational constant,

• $\hbar$ – Planck's constant,

• $\epsilon_0$ – permittivity of the vacuum,

etc.

Examples

Examples of natural units used in physics include

• Planck units (Planck mass, Planck length, …)

• Stoney units,

• Hartree units,

• particle physics natural units,

• QCD units,

• Schrödinger units.

Related concepts

• physical unit

fundamental scales (fundamental/natural physical units)

• speed of light$\,$ $c$

• Planck's constant$\,$ $\hbar$

• gravitational constant$\,$ $G_N = \kappa^2/8\pi$

• Planck scale

  • Planck length$\,$ $\ell_p = \sqrt{ \hbar G / c^3 }$

  • Planck mass$\,$ $m_p = \sqrt{\hbar c / G}$

• depending on a given mass $m$

  • Compton wavelength$\,$ $\lambda_m = \hbar / m c$

  • Schwarzschild radius$\,$ $2 m G / c^2$

  • depending also on a given charge $e$

    • Schwinger limit$\,$ $E_{crit} = m^2 c^3 / e \hbar$

• GUT scale

• string scale

  • string tension$\,$ $T = 1/(2\pi \alpha^\prime)$

  • string length scale$\,$ $\ell_s = \sqrt{\alpha'}$

  • string coupling constant$\,$ $g_s = e^\lambda$

References

• Robert Loren Jaffe, Natural Units and the Scales of Fundamental Physics, Course Notes 2007 (pdf, pdf)

See also:

• Wikipedia, Natural units