Unruh effect

The Unruh effect (also known as the Fulling–Davies–Unruh effect) is a theoretical prediction in quantum field theory that an observer who is uniformly accelerating through empty space will perceive a thermal bath. This means that even in the absence of any external heat sources, an accelerating observer will detect particles and experience a temperature. In contrast, an inertial observer in the same region of spacetime would observe no temperature.

In other words, the background appears to be warm from an accelerating reference frame. In layman's terms, an accelerating thermometer in empty space (like one being waved around), without any other contribution to its temperature, will record a non-zero temperature, just from its acceleration. Heuristically, for a uniformly accelerating observer, the ground state of an inertial observer is seen as a mixed state in thermodynamic equilibrium with a non-zero temperature bath.

The Unruh effect was first described by Stephen Fulling in 1973, Paul Davies in 1975 and W. G. Unruh in 1976. It is currently not clear whether the Unruh effect has actually been observed, since the claimed observations are disputed. There is also some doubt about whether the Unruh effect implies the existence of Unruh radiation.

The Unruh temperature, sometimes called the Davies–Unruh temperature, was derived separately by Paul Davies and William Unruh and is the effective temperature experienced by a uniformly accelerating detector in a vacuum field. It is given by

where ħ is the reduced Planck constant, a is the proper uniform acceleration, c is the speed of light, and k_B is the Boltzmann constant. Thus, for example, a proper acceleration of 2.47×10²⁰ m⋅s⁻² corresponds approximately to a temperature of 1 K. Conversely, an acceleration of 1 m⋅s⁻² corresponds to a temperature of 4.06×10⁻²¹ K.

The Unruh temperature has the same form as the Hawking temperature T_H = ⁠ħg/2πck_B⁠ with g denoting the surface gravity of a black hole, which was derived by Stephen Hawking in 1974. In the light of the equivalence principle, it is, therefore, sometimes called the Hawking–Unruh temperature.

Solving the Unruh temperature for the uniform acceleration, it can be expressed as

where ${\displaystyle a_{\mathrm {P} }}$ is Planck acceleration and ${\displaystyle T_{\mathrm {P} }}$ is Planck temperature.