nLab
Planck mass

Contents

Context

Gravity

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

The fundamental physical unit of mass.

About 10 1910^{19} GeV.

Definition

Two important physical units of length induced by a mass mm are

  1. the Compton wavelength

    m2πmc \ell_m \coloneqq \frac{2 \pi \hbar}{m c}
  2. the Schwarzschild radius

    r m2mG/c 2 r_m \coloneqq 2 m G/c^2

where

Solving the equation

m = r m 2π/mc = 2mG/c 2 \array{ & \ell_m &=& r_m \\ \Leftrightarrow & 2\pi\hbar / m c &=& 2 m G / c^2 }

for mm yields the Planck mass

m P1πm =r=cG. m_{P} \coloneqq \tfrac{1}{\sqrt{\pi}} m_{\ell = r} = \sqrt{\frac{\hbar c}{G}} \,.

The corresponding Compton wavelength m P\ell_{m_{P}} is given by the Planck length P\ell_P

P12π m P=Gc 3 \ell_{P} \coloneqq \tfrac{1}{2\pi} \ell_{m_P} = \sqrt{ \frac{\hbar G}{c^3} } \,

References

  • Max Planck, Über irreversible Strahlungsvorgänge, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin. 5: 440–480. pp. 478–80, 1899, (10.1002/andp.19003060105)

See also

Last revised on February 21, 2018 at 13:03:16. See the history of this page for a list of all contributions to it.