The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none, that is, the accelerating observer will find themselves in a warm background. The quantum state which is seen as ground state for observers in inertial systems is seen as a thermodynamic equilibrum for the uniformly accelerated observer.

Unruh demonstrated that the very notion of vacuum depends on the path of the observer through spacetime. From the viewpoint of the accelerating observer, the vacuum of the inertial observer will look like a state containing many particles in thermal equilibrium -- a warm gas. Although the Unruh effect came as a shock, it makes intuitive sense if the word vacuum is interpreted appropriately, as below.

In modern terms, the concept of "vacuum" is not the same as "empty space", as all of space is filled with the quantized fields that make up a universe and the vacuum is simply the lowest possible energy state of these fields, a very different concept than "empty". The energy states of any quantized field are defined by the Hamiltonian, based on local conditions, including the time coordinate. According to special relativity, two observers moving relative to each other must use different time coordinates. If those observers are accelerating, there may be no shared coordinate system and, due to this, the observers will see different quantum states and thus different vacua.

In some cases the vacuum of one observer is not even in the space of quantum states of the other. In technical terms, this comes about because the two vacua lead to unitarily inequivalent representations of the quantum field canonical commutation relations. This is because two mutually accelerating observers may not be able to find a globally defined coordinate transformation relating their coordinate choices. In fact, an accelerating observer will perceive an apparent event horizon forming (see Rindler spacetime ). The existence of Unruh radiation can be linked to this apparent event horizon, putting it in the same conceptual framework as Hawking radiation. On the other hand, the Unruh effect shows that the definition of what constitutes a "particle" depends on the state of motion of the observer.

This is because we need to decompose the (free) field into positive and negative frequency components before we can define the creation and annihilation operators. This can only be done in spacetimes with a timelike Killing vector field. This decomposition happens to be different in Cartesian and Rindler coordinates (although they are related by a Bogoliubov transformation) which explains why the "particle numbers", which are defined in terms of the creation and annihilation operators are different in both coordinates.

Just as the Rindler spacetime can be seen as a toy model for black holes and cosmological horizons , the Unruh effect provides a toy model to explain Hawking radiation.

The equivalent energy kT of a uniformly accelerating particle is:

So the temperature seen by a particle accelerated by the Earth's gravitational acceleration of g=9.81 m/s² is only 4*10^-20K. For an experimental test of the Unruh effect it is planned to use accelerations up to 10²⁶m/s², which would give a temperature of about 400,000K.

See also Rindler coordinates