Unruh effect on the Earth's surface

Question

Physics of accelerating observers can be written in Rindler's spacetime. Minkowski observers feel vacuum with 0 temperature, whereas Rindler observers feel same vacuum with non-zero temperature but some particle excitations. This is called Unruh effect. Near the black holes, the metric is approximated as Rindler metric, so observer can detect radiation from near the event horizon. This is what I understood about Unruh effect.

The question is: Via Einstein's equivalence principle, observer standing on Earth's surface could detect Unruh radiation because of gravitational field. Some guys mention this is true but others argue this is not valid on the Earth. I want to know which statement is true for Unruh effect on the Earth.

Answer 1

A concise way to reconcile the two “yes/no” viewpoints is that in principle an observer on Earth (who is indeed in non‐inertial motion) does see a “Rindler‐like” vacuum state with a tiny Unruh temperature—on the order of 10^-20 K for g~9.8 m/s^2. In practice, this is dwarfed by real thermal backgrounds and is experimentally indistinguishable from zero. Hence, the statement “the Unruh effect applies on Earth” is theoretically correct but physically unobservable at everyday accelerations.

Answer 2

The Unruh effect depends on the quantum state of the field under consideration. In a gravitational field without a horizon (for example, the Earth), the quantum state is not thermal. You do not have an analog of the Unruh effect.

It is incorrect to derive the temperature of a black hole using the equivalence principle. The equivalence principle is local, but quantum states are highly nonlocal constructions. For thermality to occur, a horizon is necessary.

It is worth pointing out that horizons are observer-dependent (although often there is a whole class of observers experiencing the same horizon, which makes it special in a sense). When we talk about an event horizon in Schwarzschild spacetime, this is a horizon for all observers that remain on the outside of the black hole. If you fall into the black hole, there is no horizon, and you see no Hawking radiation. Similarly, in Minkowski spacetime, the observers that experience Unruh radiation are precisely the accelerated observers, which also experience a Rindler horizon. In de Sitter spacetime you also have an analog of the Unruh effect (where the temperature is given by the Hubble parameter) but for inertial observers, which is due to the inertial observers experiencing a cosmological horizon.