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The Philosophy of Vacuum Part 4. 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 Mass of the Classical Vacuum 23 intimately involved in the forces that bind particles together to form atoms. There must be a substantial contribution to any body s mass from the electromagnetic fields within it. Though unfortunately this contribution is incalculable on present theory which gives infinity as its provisional but unhelpful answer The energy in an electromagnetic field can be described as an energy density i.e. as energy per unit volume which is the normal way of describing the energy for a continuous medium. It is the spatial integral of this density that provides the total energy of the system. The energy density is a component not of a 4-vector but of a valence-2 tensor. If there are many continuous media present e.g. quantum field descriptions of particles then we have an energy density and hence a corresponding tensor for each one. We add all these tensors together to obtain a quantity Tab referred to as the energy momentum tensor of the system. What about Einstein s gravitational field In many ways it resembles Maxwell s. As with Maxwell s theory bodies in motion can emit waves and like electromagnetic waves they travel with the speed of light and carry energy. Yet this energy is not measured in the standard way which would be by the above energy momentum tensor. In Einstein s equation ab n ab where G is Newton s gravitational constant Rah is the Ricci tensor gab the metric tensor and R the scalar curvature the Tab on the right is supposed to be describing the entire non-gravitational energy. In vacuum which in Einstein s theory means in the absence of all physical fields except gravity the energy-momentum tensor is zero whence Rab 0 but there can still be a gravitational field present. This gravitational tidal distortion field is described by the full Riemann curvature tensor Rabcd which has a total of 20 components. The Ricci tensor has just ten components and the remaining ten collect together in the form of another tensor Cabcd called .
