Length Matters: The History and the Philosophy of the Notion of a Fundamental Length in Modern Physics

Indiana University, Bloomington IN

Investigators

Abstract

This project will develop a history of the notion a fundamental length in modern physics and it will explore the philosophical problems associated with that notion. The eventual aim is to produce an extended monograph. Currently, there is no comprehensive study of this notion. The proposed study will consider the diverse scientific and philosophical motivations for introducing this notion into modern physical theories this notion, including epistemic grounds for a finite spatial resolution or ontological grounds for spatial discreteness. The discussion will focus on the instantiations of this notion in the 20th century, and it will characterize and then analyze its philosophical and the phenomenological consequences of this notion, which are currently at the center of heated debates in the high energy physics community in struggling to unify the theories of relativity with quantum mechanics. The PI has already published two chapter-length journal articles on the subject, and aims to produce six more chapters for the monograph in a period of three years. These chapters will discus the history of the idea of fundamental length, the rationale for introducing it into modern theoretical physics, and both the methodological and philosophical problems this notion generates (particularly within quantum field theory and quantum gravity). The project offers an outlook on the notion of fundamental length that spans two different research programs, namely the unification of quantum theory with each of the two theories of relativity. Based on written and oral sources, it builds on earlier historical studies of the notion of fundamental length in quantum field theory. It will draw methodological conclusions from the (partly-documented) historical episode, and applying them to the current attempts to construct quantum theories of gravity that introduce finite resolution or spatial discreteness. By combining the methodological analysis with an analysis of the philosophical issues that surround the notion of fundamental length, the project will bring to light some of the most pressing methodological problems in modern theoretical physics, first and foremost of which is the attempt to distinguish itself from pure mathematics at a time when empirical tests in the regimes it purports to describe are almost nonexistent.