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 temperature). 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, ћ 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
• Photon energy