Abstract
My talk will revisit the foundations of Teleparallel Gravity (TPG), an alternative theory of gravity, observationally indistinguishable from General Relativity (GR). In contrast to the latter, gravity in TPG isn’t conceptualised as a manifestation of spacetime curvature. Instead, TPG’s gravitational degrees of freedom appear to be encoded in a suitable--the so-called Weitzenbock--connection’s torsion (a salient feature of non-Riemannian geometries in virtue of which parallelograms formed by parallel-transported vectors do fail to close). In the first part of my talk I shall try to carefully reconstruct TPG’s conceptual structure and interpretation.
For this, it will prove useful to articulate the sense in which TPG--but arguably not GR--can be said to be a gauge theory, akin to (yet not exactly the same as) classical Yang-Mills theories. This will clarify the status of TPG’s spacetime structure in particular. On one common view, TPG’s spacetime structure is that of a Weitzenbock spacetime: the spacetime’s structure is supposed to be that of a manifold, endowed with a Weitzenbock connection. Does this position do justice to TPG? A related, and often simultaneously endorsed, claim purports that whereas GR geometrises gravity, TPG does not: the latter is a force theory; that is, in TPG gravity remains a force. How do these two views go together? Does the failure to geometrise gravity in the manner exemplified by GR indeed imply, as seems to be typically assumed in the literature, that in TPG gravity is force? More fine-grained taxonomies of degrees of geometrisation render this questionable. Or should we--yet another position one finds in the literature--regard merely as a notational variant of GR, an alternative representation of the same theory, with all differences solely pertaining to means of mathematical form, not to physical content?
In the second part of my talk, I shall critically examine conceptual advantages (both inherent ones and advantages over GR) with which TPG tends to be touted, such as its separation of gravity and inertia, or the fact that it admits of a well-defined status of a gravitational energy-stress tensor. While I urge that TPG be taken seriously, my analysis regarding its alleged superiority over GR will be largely deflationary. An exception is the coherence of principles that TPG achieves via its gauge theoretical structure.
The third and final part of my talk will draw some broader philosophical lessons from my results. In particular, I shall draw attention to the relevance of TPG to the standing of conventionalism about (spacetime) geometry--a philosophical stance that, to my mind, deserves a place at the table of the Modified Gravity/Dark Energy debate
