The local validity of special relativity from a scale-relative perspective

TL;DR

This paper clarifies the mathematical and conceptual foundations of how special relativity's local validity is modeled within general relativity, emphasizing the nuanced role of coordinate systems and symmetries.

Contribution

It provides a detailed analysis of the mathematical concepts used to model SR's local validity within GR, defending the standard approach against recent philosophical critiques.

Findings

Clarifies the role of normal coordinate systems in modeling SR within GR

Highlights the subtlety of using approximate Killing symmetries in the modeling process

Defends the standard mathematical framework against recent philosophical concerns

Abstract

Most contemporary physicists hold that the local validity of special relativity (SR) within general relativity (GR) is expressed by means of an interdependent cluster of mathematical concepts, one of which is the existence of normal coordinate systems. Nonetheless, there remains conceptual work to be done with regard to this `standard story' on the local validity of SR in (a) clarifying how a network of mathematical concepts is recruited in a particular modelling context in order to account for the local validity of SR within GR, and (b) highlighting the richness and subtlety of this mode of modelling, as well as the way in which it interacts with the concept of `approximate Killing symmetry'. With this paper, we carry out this work, thereby also defending the standard story from concerns recently voiced in the philosophy of physics literature.