THE UNRUH EFFECT

Quantum field theory can be applied to show that an observer who is uniformly accelerating through empty space will perceive a thermal bath. This means that even in the absence of any external heat sources, an accelerating observer will detect particles and experience a temperature. In contrast, an inertial observer in the same region of empty space-time would observe no temperature and no particles! [This incredible effect was first explored by Stephen Fulling in 1973, Paul Davies in 1975 and W. G. Unruh in 1976.]  The quantum vacuum is of course filled with virtual photons, but an accelerating observer will see some REAL photons.


Here is the issue: Unruh radiation is dual to Hawking radiation. It would be forever impossible to observe Hawking radiation, because of its impossibly low frequency, but Unruh radiation can (in principle anyway) be observed in a number of different experimental setups. Let's review the background. First, Einstein came up with what he called The Invariance Theory in 1905. It readily describes what an accelerating system looks like to an inertial observer, but as Einstein realized, it can't describe what things look like from the non-inertial frame of an accelerating observer. This is because of the famous Principle of Equivalence, first explored by Newton himself. NO EXPERIMENT can distinguish between the local effects of acceleration in a space with no gravity, and the local effects of gravity in an inertial frame of reference.  So Einstein fully understood that a general theory of what people were calling "Relativity" would have to be a Theory of Gravity. It took him 10 years, but he came up with his famous theory, which describes gravity in terms of space-time curvature. That's why it is often called the General Theory of Relativity. But now we come to the point. Hawking radiation is due to extreme local changes in space-time geometry, which Hawking explored by doing quantum field theory in curved space-time. The Equivalence Principle tells us that there must be a dual situation, in which radiation is observed just due to being in an accelerated frame of reference, in flat space-time! So applying quantum field theory in accelerated frames of reference is dual to applying quantum field theory in curved space-times! The derivation of the famous temperature of Hawking radiation is totally different in every way from the derivation of the temperature of Unruh radiation, but the final expressions must look formally identical! The temperature of Unruh radiation is TU = ℏa/(2πckB), where a is the acceleration and k B is Boltzmann's constant. The temperature of Hawking radiation is given by TH = ℏg/(2πckB), where g is the gravitational acceleration at the point where the radiation is emitted! The Hawking temperature of a 30 solar mass black hole is 2×10-9 Kelvin, and its Hawking luminosity a miserable 10−31 Watts. There is no hope of experimental detection of Hawking radiation. Experiments to detect Unruh radiation are very difficult, but not impossible.

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