Planck temperature

Planck temperature, denoted by TP, 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 × 10−30TP.

In SI units, the Planck temperature is about 1.417×1032 kelvins (equivalently, degrees Celsius, since the difference is trivially small at this scale), or 2.55×1032 degrees Fahrenheit or Rankine.[1]

Definition

The Planck temperature is defined as:

${\displaystyle T_{\text{P}}={\frac {m_{\text{P}}c^{2}}{k}}={\sqrt {\frac {\hbar c^{5}}{Gk^{2}}}}\approx }$ 1.416808(33) × 1032 K where:

The two digits between the parentheses are used to denote the standard error of the last two digits of the estimated value.[2]

Significance

As for most of the 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 1.42 x 1032 kelvin (TP), the radiation it would emit would have a wavelength of 1.616 x 10−35 meters (Planck length), at which point quantum gravitational effects become relevant. At temperatures greater than or equal to TP, current physical theory breaks down because we lack a theory of quantum gravity.[3]