Renormalization for Philosophers

TL;DR

This paper explains the concept of renormalization in quantum field theory, its philosophical significance, and contrasts historical and modern approaches, highlighting its impact on understanding physical theories and reductionism.

Contribution

It provides an accessible exposition of renormalization, relates it to philosophical ideas of reduction, and clarifies the shift from old to new approaches in physics.

Findings

Renormalization is a key idea and success in 20th-century physics.

The old approach viewed renormalizability as necessary for acceptable theories.

The new approach explains renormalizability as an emergent feature at accessible energies.

Abstract

We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites (Sections 2 and 3). Our motivation is that renormalization is undoubtedly one of the great ideas, and great successes, of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction (Section 4). One theme will be a contrast between two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization (from 1970 onwards) explains why the phenomena we see, at the energies we can access in our particle accelerators, are described by a renormalizable quantum field theory. For whatever non-renormalizable interactions may occur at yet higher energies, they are insignificant at accessible energies. Thus the new approach explains why our best fundamental theories have a feature, viz. renormalizability, which the old approach treated as a selection principle for theories. We also maintain that universality, a concept stressed in renormalization theory, is essentially the familiar philosophical idea of multiple realizability; and that it causes no problems for reductions of a Nagelian kind.