Target Space $\neq$ Space

TL;DR

This paper explores the implications of T-duality in string theory, arguing that while dual models are physically equivalent, they disagree on the size of target space, leading to the conclusion that observed space is a higher-level phenomenon rather than fundamental.

Contribution

It provides a philosophical analysis of T-duality, clarifying the distinction between physical equivalence and the indeterminacy of target space radius in string theory.

Findings

Dual models are physically equivalent despite differing in target space radius.

The radius of target space is indeterminate between duals, but observed space has a determinate, large radius.

Phenomenal space is a higher-level phenomenon, not the fundamental target space.

Abstract

This paper investigates the significance of T-duality in string theory: the indistinguishability with respect to all observables, of models attributing radically different radii to space -- larger than the observable universe, or far smaller than the Planck length, say. Two interpretational branch points are identified and discussed. First, whether duals are physically equivalent or not: by considering a duality of the familiar simple harmonic oscillator, I argue that they are. Unlike the oscillator, there are no measurements 'outside' string theory that could distinguish the duals. Second, whether duals agree or disagree on the radius of 'target space', the space in which strings evolve according to string theory. I argue for the latter position, because the alternative leaves it unknown what the radius is. Since duals are physically equivalent yet disagree on the radius of target space, it follows that the radius is indeterminate between them. Using an analysis of Brandenberger and Vafa (1989), I explain why -- even so -- space is observed to have a determinate, large radius. The conclusion is that observed, 'phenomenal' space is not target space, since a space cannot have both a determinate and indeterminate radius: instead phenomenal space must be a higher-level phenomenon, not fundamental.