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| {{Unreferenced|date=December 2009}}
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| In [[physics]], '''Planck energy''', denoted by ''E''<sub>P</sub>, is the unit of [[energy]] in the system of [[natural units]] known as [[Planck units]].
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| :<math>E_\text{P} = \sqrt{\frac{\hbar c^5}{G}} \approx</math> 1.956 × 10<sup>9</sup> [[Joule|J]] <math>\approx</math> 1.22 × 10<sup>28</sup> [[Electronvolt|eV]] <math>\approx</math> 0.5433 [[MWh]] | |
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| where ''c'' is the [[speed of light]] in a vacuum, <math>\hbar</math> is the reduced [[Planck's constant]], and ''G'' is the [[gravitational constant]]. ''E''<sub>P</sub> is a ''derived'', as opposed to ''basic'', Planck unit.
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| An equivalent definition is:
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| :<math>E_\text{P} = {\frac{\hbar} {t_\text{P}}},</math>
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| where <math>\ t_\text{P}</math> is the [[Planck time]].
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| Also:
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| :<math>E_\text{P} = {m_\text{P}} {c^2},</math>
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| where <math>\ m_\text{P}</math> is the [[Planck mass]].
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| The [[ultra-high-energy cosmic ray]]s observed in 1991 had a measured energy of about 50 [[joule]]s, equivalent to about 2.5×10<sup>−8</sup> ''E''<sub>P</sub>. 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''<sub>P</sub>, 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).
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| Planck units are designed to normalize the [[physical constant]]s <math>\hbar</math>, ''G'', and ''c'' to 1. Hence given Planck units, the [[mass-energy equivalence]] ''E'' = ''mc''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 [[Normalisable wave function|normalization]] results in the '''reduced Planck energy''', defined as:
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| :<math>\sqrt{\frac{\hbar{}c^5}{8\pi G}}</math> <math>\approx</math> 0.390 × 10<sup>9</sup> J <math>\approx</math> 2.43 × 10<sup>18</sup> GeV. | |
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| == Notes and references==
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| {{Reflist|2}}
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| ==See also==
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| * [[Max Planck]]
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| * [[Planck epoch]]
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| * [[Planck particle]]
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| * [[Planck units]]
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| * [[Quantum gravity]]
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| {{Planck's natural units}}
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| {{Portal bar|Physics}}
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| {{DEFAULTSORT:Planck Energy}}
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| [[Category:Units of energy]]
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| [[Category:Natural units|Energy]] | |
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