Planck energy: Difference between revisions
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:<math>E_p = \sqrt{\frac{\hbar c^5}{G}} \approx</math> [[1 E9 J|1.956 × 10<sup>9</sup>]] [[Joule|J]] <math>\approx</math> [[1 E9 J|1.22 × 10<sup>19</sup>]] [[GeV]] <math>\approx</math> 0.5433 [[MWh]] |
:<math>E_p = \sqrt{\frac{\hbar c^5}{G}} \approx</math> [[1 E9 J|1.956 × 10<sup>9</sup>]] [[Joule|J]] <math>\approx</math> [[1 E9 J|1.22 × 10<sup>19</sup>]] [[GeV]] <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]]. |
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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Equivalently, |
Equivalently, |
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where <math>\ t_P</math> is the [[Planck time]]. |
where <math>\ t_P</math> is the [[Planck time]]. |
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The Planck energy approximately equals the electricity consumed by an average person in a [[developed country]] in two weeks ( |
The Planck energy approximately equals the electricity consumed by an average person in a [[developed country]] in two weeks (data for the [[United States]] in 2001). The [[ultra-high-energy cosmic ray]]s observed in [[1991]] had a measured energy of about 50 [[joule]]s, equivalent to about 2.5 x 10<sup>-8</sup> Planck energy units. |
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When mass, energy, length, and time are all measured in Planck units, ''c''=1. Hence the [[mass-energy equivalence |
When mass, energy, length, and time are all measured in Planck units, ''c''=1. Hence the [[mass-energy equivalence]] ''E'' = ''mc''² simplifies to ''E'' = ''m'', and the Planck energy and mass are numerically identical. |
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Even though one unit of Planck energy is a "macroscopic" amount of energy, ''E''<sub>p</sub> is nevertheless a meaningful quantity in particle physics when [[gravitation]] is taken into account. The Planck energy is not only the energy needed (in principle) to probe the [[Planck length]], but is probably also the maximum possible energy that can fit into a region of that scale. A sphere 1 [[Planck length]] in diameter, containing 1 unit of Planck energy, will result in a tiny (and very hot) [[black hole]]. |
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Planck units are designed to normalize certain basic physical constants, including ''G'', to 1. In many equations of [[general relativity]], ''G'' is multiplied by 8π. Hence [[Particle physics|particle physicists]] and [[physical cosmology|cosmologists]] often prefer to normalize 8π''G'' to 1. This [[normalization]] results in the '''reduced Planck energy''', namely: |
Planck units are designed to normalize certain basic physical constants, including ''G'', to 1. In many equations of [[general relativity]], ''G'' is multiplied by 8π. Hence [[Particle physics|particle physicists]] and [[physical cosmology|cosmologists]] often prefer to normalize 8π''G'' to 1. This [[normalization]] results in the '''reduced Planck energy''', namely: |
Revision as of 05:11, 19 May 2008
In physics, the unit of energy in the system of natural units known as Planck units is called the Planck energy, denoted by EP.
- 1.956 × 109 J 1.22 × 1019 GeV 0.5433 MWh
where c is the speed of light in a vacuum, is the reduced Planck's constant, and G is the gravitational constant. EP is a derived, as opposed to basic, Planck unit.
Equivalently,
where is the Planck time.
The Planck energy approximately equals the electricity consumed by an average person in a developed country in two weeks (data for the United States in 2001). The ultra-high-energy cosmic rays observed in 1991 had a measured energy of about 50 joules, equivalent to about 2.5 x 10-8 Planck energy units.
When mass, energy, length, and time are all measured in Planck units, c=1. Hence the mass-energy equivalence E = mc² simplifies to E = m, and the Planck energy and mass are numerically identical.
Even though one unit of Planck energy is a "macroscopic" amount of energy, Ep is nevertheless a meaningful quantity in particle physics when gravitation is taken into account. The Planck energy is not only the energy needed (in principle) to probe the Planck length, but is probably also the maximum possible energy that can fit into a region of that scale. A sphere 1 Planck length in diameter, containing 1 unit of Planck energy, will result in a tiny (and very hot) black hole.
Planck units are designed to normalize certain basic physical constants, including G, to 1. In many equations of general relativity, G is multiplied by 8π. Hence particle physicists and cosmologists often prefer to normalize 8πG to 1. This normalization results in the reduced Planck energy, namely:
- 0.390 × 109 J 2.43 × 1018 GeV.