The Philosophy of Vacuum Part 16. 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 143 wavelength exceeds the spacing of the conductors are excluded. If now the conductors are moved slightly apart new normal modes are permitted and the zero-point energy is increased. Work must be done to achieve this energy increase and so there must be an attractive force between the plates. This force has been measured and the zeropoint calculation verified. This agreement with experiment is important since it shows that calculations with the zero-point energy of a continuous field does have some correspondence with reality although the total energy associated with modes of arbitrarily high frequency is infinite. The Casimir effect show that finite differences between different configurations of infinite energy do have physical reality. Another example of this principle for zero-point effects is the Lamb shift which we shall consider shortly. 6 Zero-Point Noise and Damping We shall need to understand the properties of zero-point fluctuations when the associated density of states is large for example in a continuous field. In such a case the zero-point fluctuations can be an important source of noise and damping these two phenomena being related by a fluctuation-dissipation theorem. We shall now consider various examples of these zero-point effects. X-ray Scattering by Solids The noise associated with zero-point fluctuations was discovered in 1914 by Debye during his study of X-ray scattering by solids. His main concern was to calculate the influence of the thermal vibrations of the lattice on the X-ray scattering but he showed in addition that if one assumes with Planck that the harmonic oscillators representing these vibrations have a zero-point motion then there would be an additional scattering which would persist at the absolute zero of temperature. This additional scattering is associated with the emission of phonons by the X-rays this emission being induced by the zero-point fluctuations. Thus noise and damping are .
