Planck energy

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

$E_{\mathrm {P} }={\sqrt {\frac {\hbar c^{5}}{G}}}\approx 1.956\times 10^{9}\ \mathrm {J} \approx 1.22\times 10^{28}\ \mathrm {eV} \approx 0.5433\ \mathrm {MWh}$

where c is the speed of light in a vacuum, ћ 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:

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

where t_P is the Planck time.

Also:

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

where m_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).

Planck units are designed to normalize the physical constants , 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:

${\sqrt {\frac {\hbar {}c^{5}}{8\pi G}}}\approx 0.390\times 10^{9}\ \mathrm {J} \approx 2.43\times 10^{18}\ \mathrm {GeV} .$

See also

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