Planck mass

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The Planck mass is the natural unit of mass, denoted by m_P. 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 = 21.76 µ g

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 21.7645 µg ± 0.0016 µg.

Particle physicists and cosmologists often use the reduced Planck mass, which is

<math>\sqrt{\frac{\hbar{}c}{8\pi G}}</math> ≈ 4.340 µg.

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 it is roughly the mass of some fleas.

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Significance

The Planck mass is the mass of a black hole whose Schwarzschild radius multiplied by π equals its Compton wavelength. 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.

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