Berlin 2015 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 5: Rods, Clocks, Space and Energy in General Relativity

AGPhil 5.2: Talk

Wednesday, March 18, 2015, 15:45–16:15, A 060

The Problem of Space — •Joshua Eisenthal — University of Pittsburgh, Pittsburgh, Pennsylvania, USA

I define the Problem of Space as the problem of delimiting the range of candidate physical geometries, i.e. candidate geometrical descriptions of physical space. I briefly review the nineteenth century approach to this problem, arriving at the so-called ``classical solution''. This solution centered around the claim, advanced in particular by Helmholtz and Poincaré, that candidate physical geometries were just those structures which could represent the free mobility of rigid bodies. As noted originally by Riemann, then argued for by Helmholtz and proved rigorously by Lie, congruence relations which can represent such free mobility exist only in geometries of constant curvature. Both Poincaré and Helmholtz regarded this fact as pivotal in delimiting the range of candidate physical geometries, and thus solving the Problem of Space.

However, I then review how this view was fatally undermined by the development of General Relativity. I thus turn to explore the twentieth century solution to the Problem of Space advanced by Hermann Weyl. I conclude by reflecting on the significance of this discussion for a relatively recent dispute regarding the status of the metric field in General Relativity. I suggest that this dispute has arisen partially due to a failure to properly appreciate the insights made available by the kind of analysis of geometrical concepts exemplified by Weyl's work. More generally, I argue that the nuances of Weyl's view demonstrate the importance of engaging with the Problem of Space in interpreting General Relativity today.