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.

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:

where $t P$ is the Planck time.

Also:

where $m P$ is the Planck mass.

The ultra-high-energy cosmic ray 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). Energy of 1 $E P$ , 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 $E = m c ²$ 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 $8π G$ to 1. This normalization results in the reduced Planck energy, defined as:

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