Physics: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_P is a derived, as opposed to basic, Planck unit. It is defined by:

[math]\displaystyle{ E_\mathrm{P} = \sqrt{\frac{\hbar c^5}{G}}, }[/math]

where c is the speed of light in a vacuum, ћ is the reduced Planck's constant, and G is the gravitational constant.

Substituting values for the various components in this definition gives the approximate equivalent value of this unit in terms of other units of energy:

[math]\displaystyle{ 1 \ E_\mathrm{P} \approx 1.956 \times 10^9\ \mathrm{J} \approx 1.2209 \times 10^{19}\ \mathrm{GeV} \approx 543.36\ \mathrm{kWh} }[/math]

An equivalent definition is:

[math]\displaystyle{ E_\mathrm{P} = {\frac{\hbar} {t_\mathrm{P}}}, }[/math]

where t_P is the Planck time.

Also:

[math]\displaystyle{ E_\mathrm{P} = {m_\mathrm{P}} {c^2}, }[/math]

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. Theoretically, the highest energy photon carries about 1 E_P of energy (see Ultra-high-energy gamma ray). Most Planck units are extremely small, as in the case of Planck length or Planck time, or extremely large, as in the case of Planck temperature or Planck acceleration. For comparison, the Planck energy is approximately equal to 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 (See General relativity and the Einstein Field Equations). 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:

[math]\displaystyle{ \sqrt{\frac{\hbar{}c^5}{8\pi G}} \approx 3.90 \times 10^8\ \mathrm{J} \approx 2.43 \times 10^{18} \ \mathrm{GeV} \approx 108.14\ \mathrm{kWh}. }[/math]

See also

• Max Planck
• Planck epoch
• Planck particle
• Planck units
• Quantum gravity
• Photon energy