tom.stoer said:
The Unruh effect claims that a quantum state which can be defined as an "empty vacuum state" by an inertial observer will become a "thermal state containing particles" for an observer with constant acceleration a; the temperature observed is T ~ a.
In contrast to other oberver dependent effects this is not just a different interpretation of one frame-independent reality but seems to be a challange for physical reality at all. Let me explain why.
Suppose we are detecting particles in different references frames, i.e. with different detectors. Each time we are detecting a particle we agree that there is a particle, but we are not in agreement regarding its energy. We are not worried about this fact b/c we can use a Lorentz transformation to get the relation between energy and momentum.
For the Unruh effect it becomes much more disturbing b/c we cannot even agree whether there there is a particle or not. So it seems that we are no longer talking about one unique quantum state with frame dependent interpretations but that we have two truly different quantum states, two different "realities". There is not one event "a particle" with different interpretations like "energies E, E', E'', ...", but there are different realities some with an event "a particle", some with "no particle".
Suppose an accelerating observer and a goup of stationary observers at rest collect the information regarding "their quantum states" over a couple minutes. Once the accelerating observer passes a stationary one they make a simultaneous measurement whether there is a particle or not. After a while the obervers at rest will not have counted any particle, but the accelerating observer will have counted many. So they disagree on the fact "whether there are particles at all".
b/c every particle can be detected only once one could get rid of the problem via the idea that the particles detected by the accelerated observer cannot be detected by the obsevers at rest, so there is no logical contradiction. This is OK, but of course the accelerating observer "knows" that there are other particles that he could detect in principle, but that they escape from his detector by whatever reason. These particles are not detected by the observers at rest, not even in principle.
So the particles detected by the accelerated observer are not and cannot be detected by the observers at rest (b/c they can be detected only once). And the particles not detected by the accelerated observer are not and need not be detected by the observers at rest. So it really seems that there is no logical contradiction - but you may understand that when talking about "reality" one may be bothered by these ideas.
Any thoughts?
The following is a conjecture. I am speculating on the importance of the event horizon in the accelerated observers frame.
The observer in the accelerating frame vehicle sees an "event horizon" in the direction opposite the direction of the acceleration vector. The event horizon is analogous to a very big black hole. The observer in an inertial frame does not see this event horizon. However, he sees that light emitted from behind the accelerated observer vehicle can never catch up to the accelerated observer vehicle. I think that it is the event horizon that resolves the Unruh conundrum.
In order to emit Bremstrahlung radiation, there has to be a charged particle that is being accelerated. An observer traveling with this charged particle sees a stationary electric charge, and an event horizon.
The accelerated observer sees a sky emitting thermal radiation. In the eyes of the accelerated observer, the electric charge is an antennae for electromagnetic radiation. Some of the thermal radiation is absorbed by the electric charge antennae. All thermal radiation not absorbed by the antennae is swallowed by the event horizon that is a finite distance from the antennae. The energy swallowed by the event horizon is lost forever to both observers.
The inertial observer does not see the thermal photons as thermal photons. He sees the thermal photons as virtual photons. In other words, the thermal distribution of photons in the accelerated frame is seen as a Lorentz invariant distribution of photons in the inertial frame. Because the Lorentz invariant distribution is a zero point radiation, it is not seen in the inertial frame. The Lorentz invariant distribution is sometimes called the virtual photons.
The photons that are absorbed by the "antennae" in the accelerated reference frame reappear as photons in the inertial reference frame. The gravitational gradient seen in the accelerated frame provides enough energy to the virtual photons to become real photons in the inertial frame.
Thus, the electric charge is an emitting antennae in the inertial frame. The accelerating electric charge emits Bremstrahlung radiation in the inertial frame.
Thus, one can look at it this way. A virtual photon falls down in the accelerating frame, acquiring enough energy to become a real photon. If it is absorbed by an electric charge, then it appears to the inertial observer as an emitted photon. If the virtual photon misses the electric charge, it is absorbed by the event horizon and never seen again by either observer.
