This means that even in the absence of any external heat sources, an accelerating observer will detect particles and experience a temperature.
Unruh demonstrated theoretically that the notion of vacuum depends on the path of the observer through spacetime.
And although the Unruh effect would initially be perceived as counter-intuitive, it makes sense if the word vacuum is interpreted in the following specific way.
The energy states of any quantized field are defined by the Hamiltonian, based on local conditions, including the time coordinate.
In technical terms, this comes about because the two vacua lead to unitarily inequivalent representations of the quantum field canonical commutation relations.
An accelerating observer will perceive an apparent event horizon forming (see Rindler spacetime).
On the other hand, the theory of the Unruh effect explains that the definition of what constitutes a "particle" depends on the state of motion of the observer.
The free field needs to be decomposed into positive and negative frequency components before defining the creation and annihilation operators.
This decomposition happens to be different in Cartesian and Rindler coordinates (although the two are related by a Bogoliubov transformation).
This explains why the "particle numbers", which are defined in terms of the creation and annihilation operators, are different in both coordinates.
So the Rindler spacetime gives the local properties of black holes and cosmological horizons.
Different thermal states or baths at the same temperature need not be equal, for they depend on the Hamiltonian describing the system.
This makes the Unruh temperature spatially inhomogeneous across the uniformly accelerated frame.
[12] In special relativity, an observer moving with uniform proper acceleration a through Minkowski spacetime is conveniently described with Rindler coordinates, which are related to the standard (Cartesian) Minkowski coordinates by The line element in Rindler coordinates, i.e. Rindler space is where ρ = 1/a, and where σ is related to the observer's proper time τ by σ = aτ (here c = 1).
by the relation[13] An observer moving along a path of constant ρ is uniformly accelerating, and is coupled to field modes which have a definite steady frequency as a function of σ.
Translation in σ is a symmetry of Minkowski space: it can be shown that it corresponds to a boost in x, t coordinate around the origin.
So A path integral with real time coordinate is dual to a thermal partition function, related by a Wick rotation.
[22] Theoretical work in 2011 suggests that accelerating detectors could be used for the direct detection of the Unruh effect with current technology.
[23] The Unruh effect may have been observed for the first time in 2019 in the high energy channeling radiation explored by the NA63 experiment at CERN.