Planck temperature

Planck temperature (T_P) is the unit of temperature in the system of natural units known as Planck units.

It serves as the defining unit of the Planck temperature scale. In this scale the Planck temperature = 1, absolute zero = 0, and all other temperatures are some decimal of T_P. For example, 0°C = 1.928 × 10^-30T_P.

Definition

The Planck temperature is defined as:

$T_P = \frac{m_P c^2}{k} = \sqrt{\frac{\hbar c^5}{G k^2}}$ = 1.416833(85) × 10³² K

where:

• m_P = the Planck mass
• c = speed of light in a vacuum
• $\hbar$ is the reduced Planck constant defined as $\hbar\ = \frac{h}{2\pi}$
• k = Boltzmann constant
• G = Gravitational constant

The two digits between the parentheses denote the standard error of the last two digits of the estimated value.

Significance

As for most of Planck units, a Planck temperature of 1 (unity) is a fundamental limit of quantum theory, in combination with gravitation, as presently understood. At temperatures greater than or equal to T_P, current physical theory breaks down because we lack a theory of quantum gravity.

See also

• Absolute hot
• Hagedorn temperature
• Orders of magnitude (temperature)
• Planck constant
• Planck units

External links

• NIST reference: Planck temperature
• What is the opposite of absolute zero?