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.

$E_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{G}}}\approx$ 1.956 × 10⁹ J $\approx$ 1.22 × 10²⁸ eV $\approx$ 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.

An equivalent definition is:

$E_{\text{P}}={\frac {\hbar }{t_{\text{P}}}},$

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

Also:

$E_{\text{P}}={m_{\text{P}}}{c^{2}},$

where $\ m_{\text{P}}$ is the Planck mass.

The ultra-high-energy cosmic rays observed in 1991 had a measured energy of about 50 joules, equivalent to about 2.5×10⁻⁸ E_P. Most Planck units are fantastically small and thus are unrelated to "macroscopic" phenomena (or fantastically large, as in the case of Planck density). One E_P, on the other hand, is definitely macroscopic, approximately equaling the energy stored in an automobile gas tank (57.2 L of gasoline at 34.2 MJ/L of chemical energy).

Even so, E_P is 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 the physical constants $\hbar$, G, and c to 1. Hence given Planck units, the mass-energy equivalence E = mc² simplifies to E = m, so that the Planck energy and mass are numerically identical. In the equations of general relativity, G is often multiplied by 8π. Hence writings in particle physics and physical cosmology often normalize 8πG to 1. This normalization results in the reduced Planck energy, defined as:

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

See also

• Max Planck
• Planck epoch
• Planck particle
• Planck units
• Quantum gravity