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

Abstract

I describe how relativistic field theory generalises the paradigm property of material systems, the possession of mass, to the requirement that they have a mass-energy-momentum density tensor T µν associated with them. I argue that T µν does not represent an intrinsic property of matter. For it will become evident that the definition of T µν depends on the metric field g µν in a variety of ways. Accordingly, since g µν 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.

The Metaphysics of Super‐Substantivalism

“…So if one takes the metric field (or the pair of manifold M and metric field ) to represent spacetime, then according to GR the theory can be seen as ontologically prior to matter in the sense that it allows for spacetime to exist without matter, but not for matter to exist without spacetime. Furthermore, as argued in Lehmkuhl (), in GR it is in general not possible to assign the property of possessing mass‐energy, essential for a field to be a matter field, without reference to the spacetime metric.…”

“…Of course, taking such a position does not mean that the properties of material systems do not depend on spacetime. In Lehmkuhl (), I argued that mass‐energy‐momentum density is a property material systems have only in virtue of their relationship to spacetime structure. However, such a dependence of important properties of material systems on spacetime structure is not the same as a reduction of these properties to spacetime structure.…”

“…If I had to choose among only different variants of the identity view rather than also being allowed to choose from (what I think are) more attractive variants of super‐substantivalism, I would choose a variant where only spacetime regions that possess mass‐energy are identified with material objects. The reason is that, I think, there are strong reasons to regard mass‐energy as an essential (or, if you want, necessary) property of matter, as argued in Lehmkuhl ().…”

The metaphysics of emergent spacetime theories

“…They would only be relational theories if relationalism were to be redefined as the claim that the relata of spatioremporal relations are not spacetime points-which would conflate my narrower definition of relationalism with emergent spacetime. 5 But see Lehmkuhl (2011) for a large variety of ways in which matter does depend on the metric in general relativity. It is outside the scope of this paper to discuss to what extent those dependencies are forms of ontological dependence.…”

“…But see Lehmkuhl () for a large variety of ways in which matter does depend on the metric in general relativity. It is outside the scope of this paper to discuss to what extent those dependencies are forms of ontological dependence.…”