An Engineering Approach

This chapter begins with a discussion of Julian Schwinger’s “engineering approach” to particle physics. Schwinger argued from a number of perspectives that the very theory (Quantum Electrodynamics, for which he won a Nobel prize) was inadequate. Further, he claimed that an intermediate theory between the fundamental and the phenomenological was superior. Such a theory focuses on a few parameters at intermediate or mesoscales that we employ to organize the world. Schwinger’s motivations were avowedly pragmatic, although he did offer nonpragmatic reasons for preferring such a mesoscale approach. This engineering approach fits well with the idea that the introduction of order parameters in condensed matter physics introduced a natural foliation of the world into microscopic, mesoscopic, and macroscopic levels. It further suggests that a middle-out approach to many-body systems is superior to a bottom-up reductionist approach. The chapter also discusses a middle out approach to multiscale modeling in biology.

Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety

Considering the scale-dependent effective spacetimes implied by the functional renormalization group in d-dimensional quantum Einstein gravity, we discuss the representation of entire evolution histories by means of a single, (d+1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian structure. This “scale-spacetime” carries a natural foliation whose leaves are the ordinary spacetimes seen at a given resolution. We propose a universal form of the higher dimensional metric and discuss its properties. We show that, under precise conditions, this metric is always Ricci flat and admits a homothetic Killing vector field; if the evolving spacetimes are maximally symmetric, their (d+1)-dimensional representative has a vanishing Riemann tensor even. The non-degeneracy of the higher dimensional metric that “geometrizes” a given RG trajectory is linked to a monotonicity requirement for the running of the cosmological constant, which we test in the case of asymptotic safety.