UC Irvine

How should we understand gravitational influence? In traditional formulations of Newtonian Gravity, gravitational influence is understood through forces; massive bodies attract one another through gravitational force. Our current best theory of gravity, General Relativity (GR), presents a different understanding of gravitational influence. GR is thought to have taught us that gravitational influence should be properly understood as a manifestation of spacetime curvature. This lesson, however, is complicated by the existence of a gravitational theory that is empirically equivalent to General Relativity and represents gravitational influence again through forces: Teleparallel Gravity (TPG). In contrast to Newtonian Gravity, the forces of TPG feature torsion (or, twisting). TPG raises both questions regarding underdetermination and more fundamental conceptual questions: Which theory, General Relativity or Teleparallel Gravity, describes our world? And how should we understand the torsional forces posited by Teleparallel Gravity?

The first question mentioned above has been the subject of philosophical study (see, e.g., Knox 2011). Addressing the second question mentioned above will be the main goal of this dissertation. Since we are familiar with how forces operate in the non-relativistic context, Chapter 1 begins by formulating a novel non-relativistic theory of gravity that features torsional forces. To build this theory, we discuss how to incorporate torsion in the non-relativistic context and what we would expect of such a theory. We state and prove a theorem that establishes the relation between models of Newton-Cartan theory and torsional models.

With a non-relativistic, torsional theory in hand, in Chapter 2, I turn to consider the non-relativistic limit of Teleparallel Gravity. I show how to take the classical limit using the tetrad formalism of Teleparallel gravity. I prove that Teleparallel gravity reduces not to the previously outlined non-relativistic, torsional theory but, rather, to standard Newtonian Gravity.

In Chapter 3, I discuss and contextualize these results. I first present the similarities between my results and those derived in the torsion-free context. Malament (1986) shows that taking the classical limit of General Relativity results in Newton-Cartan theory, a theory that is spatially flat. In other words, taking the classical limit “squeezes out” the spatial curvature of General Relativity. I discuss how my results similarly show that taking the classical limit of TPG “squeezes out” the torsion.

Next, I consider recent efforts by physicists to develop classical, torsional theories of gravity. It is commonly claimed in this literature that one cannot have both non-vanishing torsion and a closed temporal metric. Having formulated a classical theory with both non-vanishing torsion and a closed temporal metric, I reflect on why this claim is made and where the argument went awry.

Finally, I discuss projects that use other methods of relating relativistic theories to classical, torsional ones. Some argue that torsional gravity is the correct framework to describe the non-relativistic limit of General Relativity while others claim it is the non-relativistic limit of Teleparallel Gravity. I show how we might understand these projects so that their claims are not inconsistent with one another or with the results presented here.