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.

The Planck temperature in more common units of temperature is about 2.55×10³² degrees Fahrenheit, and 1.417×10³² degrees Celsius.

Definition

The Planck temperature is defined as:

$T_{\text{P}}={\frac {m_{\text{P}}c^{2}}{k}}={\sqrt {\frac {\hbar c^{5}}{Gk^{2}}}}$ = 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. In other words, the wavelength of an object can be calculated by its temperature. If an object were to reach the temperature of 1.41 x 10³² kelvin (T_P), the radiation it would emit would have a wavelength of 1.616 x 10⁻²⁶ nanometers (Planck length), at which point quantum gravitational effects become relevant. 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?