The Philosophy of Vacuum Part 17. Physicists will find it extremely interesting, covering, as it does, technical subjects in an accessible way. For those with the necessary expertise, this book will provide an illuminating and authoritative exposition of a many-sided subject." -John D. Barrow, Times Literary Supplement. | The Vacuum State of a Quantum Field 153 frequency variable conjugate to the proper-time of the oscillator. However this is no longer true for the noise power in the field. This noise power must now be evaluated along the accelerated world-line of the oscillator which deviates from a geodesic. By the Wiener-Khinchine theorem this noise power is the Fourier transform of the autocorrelation function of the field evaluated along the accelerated world-line. Now we would expect such an autocorrelation function to be the same along all timelike geodesics in a vacuum electromagnetic field since the vacuum state is Lorentz-invariant and we can transform any timelike geodesic in Minkowski space-time into any other by a Lorentz transformation. But there is no reason to expect the autocorrelation function to be the same along a non-geodesic that is accelerating world-line which of course would take us outside the Lorentz group. We now come to the most remarkable feature of this situation. If the world-line is that of a uniformly accelerated observer in the sense of special relativity then the additional noise power in the field has a precisely thermal spectrum with the temperature T given by where a is the observer s proper acceleration. This result was discovered only in 1976 by W. G. Unruh although a closely similar result was obtained by P. C. W. Davies in 1975 . It should not be regarded as a casual algebraic coincidence because as we shall see the quantum fluctuations about this mean state are also precisely those derived by Einstein for thermal radiation at temperature T. Uniform acceleration can be defined by reference to an instantaneous inertial frame relative to which the accelerated observer has zero velocity. At any instant we may define the proper acceleration as the acceleration relative to such an inertial frame. If this proper acceleration is independent of time then we say that the acceleration is uniform. An example of such motion is provided by a classical .
