Planck mass

The Planck mass is the unit of mass, denoted by m_P, in the system of natural units known as Planck units. Named after Max Planck, it is the mass for which the Schwarzschild radius is equal to the Compton length divided by π.

<math>m_P = \sqrt\frac{\hbar c}{G}</math> ≈ 1.2209 × 10¹⁹ GeV/c² = 2.176 × 10^-8 kg

The 2002 CODATA-recommended value for the Planck mass is 2.176 45(16) × 10^-8 kg, where the part in parentheses indicates the uncertainty in the last digits shown — that is, a value of 2.17645 × 10^-8 kg ± 0.00016 × 10^-8 kg. Particle physicists and cosmologists often use the reduced Planck mass, which is

<math>\sqrt\frac{\hbar{}c}{8\pi G}</math> ≈ 4.340 µg = 2.43 × 10¹⁸ GeV/c².

Adding the 8π simplifies several equations in gravity. Unlike most of the other Planck units, the Planck mass is on a scale more or less conceivable to humans, as the body mass of a flea is roughly 4000 to 5000 m_P.

Significance

The Planck mass is the mass of a black hole whose Schwarzschild radius multiplied by π equals its Compton wavelength. This can be thought of as the mass at which a particle has the same energy (<math>E = mc^2 </math>) as a photon of wavelength λ <math>(\mbox{E}\ = \frac{h c}{\lambda}), </math> where λ divided by π is also the radius within which the escape velocity becomes greater than the speed of light <math>(\frac {\lambda}{\pi} = \frac{2Gm}{c^2})</math>, causing the particle to continually collapse into itself. The radius of such a black hole is roughly the Planck length, which is believed to be the length scale at which both general relativity and quantum mechanics simultaneously become important.

See also

• Planck unit
• Planck length
• Planck particle
• Orders of magnitude (mass)

External links

• The NIST Reference on Constants, Units, and Uncertainty