# Accelerated detector

1. Nov 24, 2004

### hellfire

In a Minkowski vacuum virtual particles with electric charge (electrons, positrons,…) create and annihilate. If a detector is accelerated within the Minkowski spacetime, will it detect a radiation from the charged virtual particles? How to quantify this effect? Is this effect related to the Unruh radiation?

2. Nov 28, 2004

### Creator

Yes, hellfire; Unruh & Davies showed that an accelerated detector will act as if it is being bathed in a thermal bath at a temperature given by:

T = ah/(2pi)ck

where h is h(bar), k = Boltzmann's k, a is acceleration, and the rest are the usual constants.

Creator

3. Nov 29, 2004

### hellfire

It seams to me that these are two different phenomena.

The Unruh effect is due to different ground states of vacua in a Minkowski and a Rindler spacetime. This is a general effect: it arises also if one considers e.g. only the ground state(s) of an uncharged scalar field.

The other phenomenon would depend only on the ground state of charged fields. A Rindler observer, i.e. an accelerated observer in a Minkowski spacetime, would be accelerated wrt to the virtual particles of the Minkowki vacuum. This means that the virtual particles would be accelerated with respect to him. The question is whether this charged virtual particles would radiate.

4. Nov 29, 2004

### Creator

I believe I gave that answer in the last post; namely, a detector (or person) would see a thermal radiation at a temperature given by the formula in my 1st post. [This is similar to thermal radiation discovered by Hawking (Hawking radiation) emitted by black holes, which result in their eventual evaporation.] Let me expand a bit.

Thermal radiation is simply photons that are a mix of frequencies near the thermal frequecy, w, which is strictly a function of temperature defined by:

w = KT
where T is Temp., and K = 3.67x10^11/sec.-*K

According to Unruh & Davies (see ref.#1), observers in an accelerating frame would see thermal radiation at a temperature given by the equation in my 1st post. This eqn. quantifies the fullness of the effect, (I've never heard of two effects). The distribution is apparently Planckian. The mechanism responsible for this radiation is basically that the quantum (zero point) vacuum fluctuations are being transformed into real photons by the acceleration.

However, if you solve for a (acceleration) in the former equation you will realize the extremely high accel. required to achieve any realistically measureable temperature, over 10^20 m/sec^2 or so. (Or conversely, g =9.8 m/sec^2 results in an infinitesmal 10^-20*K. temp.)

Creator

#1). P.C. Davies, J.Physics A, vol.8, p.609 (1975).
Also see W.G. Unruh, Phys. Rev.D, vol14.p.870, (1976).

Last edited: Nov 29, 2004
5. Nov 30, 2004

### hellfire

The Unruh radiation arises indeed due to the mechanism you explained. This happens for every field, also in case of uncharged scalar fields. E.g. if you consider a Rindler spacetime with only a scalar field in it, then the Unruh radiation would appear. This is actually the scenario (accelerated observer in a Minkowski spacetime + scalar field) used for the usual derivation of the Unruh radiation.

In such a scenario there would be no charged fields, and therefore this other radiation I am postulating here would not appear. This radiation would appear only in case of an observer accelerating wrt to charged fields (and thus virtual particles accelerating wrt to him) and should depend on the charge of the field. Of course, in case of charged fields, the Unruh radiation does also appear.