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Concept# Unruh effect

Summary

The Unruh effect (also known as the Fulling–Davies–Unruh effect) is a kinematic prediction of quantum field theory that a uniformly accelerating observer will observe a thermal bath, like blackbody radiation, whereas an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame; in layperson's terms, an accelerating thermometer (like one being waved around) in empty space, removing 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 local acceleration, c is the speed of light, and kB is the Boltzmann constant. Thus, for example, a proper acceleration of 2.47e20m.s-2 corresponds approximately to a temperature of 1K. Conversely, an acceleration of 1m.s-2 corresponds to a temperature of 4.06e-21K.
The Unruh temperature has the same form as the Hawking temperature TH = ħg/2πckB 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 acceleration, it can be expressed as
where is Planck acceleration and is Planck temperature.

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