Planck energy

The Planck energy is the unit of energy, denoted by E_P, in the system of natural units known as Planck units.

$E_{p}={\sqrt {\frac {\hbar c^{5}}{G}}}\approx$ 1.956 × 10⁹ J $\approx$ 1.22 × 10¹⁹ GeV $\approx$ 0.5433 MWh

where $c$ is the speed of light in a vacuum, $\hbar$ is the reduced Planck's constant and $G$ is the gravitational constant.

Or equivalently,

$E_{p}={\frac {\hbar }{t_{P}}}$

where $t_{P}$ is the Planck time.

The Planck energy is equivalent with the Planck mass according to E = mc². The Planck energy equals approximately the electricity consumed by an average person in a developed country in two weeks (2001 figures for US citizens). The Oh-My-God particle observed in 1991 with some 50 joules contained about 25 billionths of the Planck energy.

While the Planck energy equals an already macroscopic amount of energy, it is nevertheless thought to be an important quantity in particle physics - as soon as gravitation is taken into account. The Planck energy is not only the energy (in principle) necessary to probe the Planck length, but it is probably also the maximum energy that can fit into a region of that scale - which in this case will immediately collapse to a (very hot) Black Hole.

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

${\sqrt {\frac {\hbar {}c^{5}}{8\pi G}}}$ $\approx$ 0.390 × 10⁹ J $\approx$ 2.43 × 10¹⁸ GeV

Including the additional factor of 8π simplifies several equations in gravity.

See also

• Planck's constant
• Holographic principle