length scale in nLab

• Idea
• In physics
• Related concepts
• References

fundamental scales (fundamental/natural physical units)

• speed of light\, cc

• Planck's constant\, ℏ\hbar

• gravitational constant\, G N=κ 2/8πG_N = \kappa^2/8\pi

• Planck scale

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

  • Planck mass\, m p=ℏc/Gm_p = \sqrt{\hbar c / G}

• depending on a given mass mm

  • Compton wavelength\, λ m=ℏ/mc\lambda_m = \hbar / m c

  • Schwarzschild radius\, 2mG/c 22 m G / c^2

  • depending also on a given charge ee

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

• GUT scale

• string scale

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

  • string length scale\, ℓ s=α′\ell_s = \sqrt{\alpha'}

  • string coupling constant\, g s=e λg_s = e^\lambda