International Society for the Advanced Study of Spacetime

What is the Significance of Relational Localization?

Dean Rickles

The hole argument for general relativity is often taken by physicists, and some philosophers, to imply that localization must be based on relations between physical fields, rather than based on relations to the points of a spacetime manifold. The reason is that fields and quantities defined at manifold points are not diffeomorphism-invariant. Thus, the value of a field at a point is not measurable, but the value of a field where a thing is, or where a field takes on a certain value is measurable. The idea that there is no background (metric) spacetime available to localize fields is known as background independence (it is grounded in active diffeomorphism-invariance). Lately, background independence has been taken to imply that a relational conception of spacetime is the only tenable position available. The argument proceeds by way of an entailment between background independence and relational localization (along the lines of the hole argument: see Rovelli, 1992: 3). Diffeomorphisms change the localization of fields on spacetime; GR is diffeomorphism-invariant; so localization *cannot* be relative to spacetime. It must be relative to other fields. Rovelli (2000: 108) then draws an explicit relationalism from this: since fields and quantities are independent from the manifold, the manifold can (and should) be dispensed with. My question is then: do these implications and entailments hold? And, if not, what *is* the significance of relational localization vis-a-vis the ontological status of space(time)?


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