Unruh Effect - The Equation

The Equation

The Unruh temperature, derived by William Unruh in 1976, is the effective temperature experienced by a uniformly accelerating detector in a vacuum field. It is given by:

where:

is the local acceleration
is the Boltzmann constant
is the reduced Planck's constant
is the speed of light

Thus, for example, an acceleration of corresponds to a temperature of 1 K. The Unruh temperature has the same form as the Hawking temperature of a black hole, which was derived (by Stephen Hawking) independently around the same time. It is, therefore, sometimes called the Hawking–Unruh temperature.

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