Planck temperature

Planck temperature, denoted by 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 magnitude of the Planck temperature is equal to 1, while that of absolute zero is 0. Other temperatures can be converted to Planck temperature units. For example, 0 °C = 273.15 K = 1.9279 × 10⁻³⁰T_P.

Definition

The Planck temperature is defined as:

$T_\text{P} = \frac{m_\text{P} c^2}{k} = \sqrt{\frac{\hbar c^5}{G k^2}}$ = 1.416833(85) × 10³² K / - where:

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

The two digits between the parentheses are used to 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?