Mass–Energy–Momentum: Only there Because of Spacetime?

I describe how relativistic field theory generalizes the paradigm property of material systems, the possession of mass, to the requirement that they have a mass–energy–momentum density tensor Tμν associated with them. I argue that Tμν does not represent an intrinsic property of matter. For it will become evident that the definition of Tμν depends on the metric field gμν in a variety of ways. Accordingly, since gμν represents the geometry of spacetime itself, the properties of mass, stress, energy, and momentum should not be seen as intrinsic properties of matter, but as relational properties that material systems have only in virtue of their relation to spacetime structure. 1 Introduction 2 The Concept of Matter in Relativistic Field Theory 2.1 A short history of energy–momentum tensors 2.2 Metaphysical matters 3 Explicit Dependence of Energy Tensors on the Metric Field 4 Metric Dependence in Lagrangian Theories 4.1 The basic ideas of Lagrangian field theory 4.2 Enter the energy tensor 4.3 Different kinds of coupling 5 Metric Dependence in General 5.1 Definitional dependence at the level of the matter fields 5.2 Definitional dependence at the level of conditions on the energy tensor 5.3 Abstract definitional dependence 5.4 Interpretational dependence 6 What Kind of Property is Mass–Energy–Momentum Density? 6.1 A relational property? 6.2 Relational and essential? 7 Conclusion