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.^[1]

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 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). 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 $E = m c ²$ 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:

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

References

↑ "Planck Energy". Cosmos, The SAO Encyclopedia, Swinburne University of Technology. Retrieved 18 September 2015.

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Planck's natural units

Planck's constant Planck units

Base Planck units	Planck time Planck length Planck mass Planck charge Planck temperature

Derived Planck units	Planck energy Planck force Planck power Planck density Planck angular frequency Planck pressure Planck current Planck voltage Planck impedance Planck momentum Planck area Planck volume Planck acceleration

Planck energy

See also

References