Planck energy

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

$E_{p}={\sqrt {\frac {\hbar c^{5}}{G}}}\approx$ 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. E_P is a derived, as opposed to basic, Planck unit.

Equivalently,

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

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

The Planck energy approximately equals the electricity consumed by an average person in a developed country in two weeks (data for the United States in 2001). The ultra-high-energy cosmic rays observed in 1991 had a measured energy of about 50 joules, equivalent to about 2.5 x 10^-8 Planck energy units.

When mass, energy, length, and time are all measured in Planck units, c=1. Hence the mass-energy equivalence E = mc² simplifies to E = m, and the Planck energy and mass are numerically identical.

Even though one unit of Planck energy is a "macroscopic" amount of energy, E_p is nevertheless a meaningful quantity in particle physics when gravitation is taken into account. The Planck energy is not only the energy needed (in principle) to probe the Planck length, but is probably also the maximum possible energy that can fit into a region of that scale. A sphere 1 Planck length in diameter, containing 1 unit of Planck energy, will result in a tiny (and very hot) black hole.

Planck units are designed to normalize certain basic physical constants, including G, to 1. In many equations of general relativity, G is multiplied by 8π. Hence particle physicists and cosmologists often prefer to normalize 8πG to 1. This normalization results in the reduced Planck energy, namely:

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

See also

• Planck units
• Planck's constant
• Holographic principle