Physics Paradigm Challenge

Physics just settled an old debate: even when gravity gets weird and warps space-time, things still take the ultimate shortcut.

March 20, 2026

Original Paper

On the Finsler variational nature of autoparallels in metric-affine geometry

Lehel Csillag, Nicoleta Voicu, Salah Elgendi, Christian Pfeifer

arXiv · 2603.18416

The Takeaway

In standard gravity, objects follow the shortest possible routes (geodesics), but in more complex theories, the math suggested these paths were lawless and couldn't be described by a simple rule. This paper proves these paths aren't chaotic; they obey a hidden, efficient geometry known as a Finsler Lagrangian.

From the abstract

In metric-affine geometry, autoparallels are generically non-variational, i.e., they are not extremals of any action integral. The existence of a parameter-invariant action principle for autoparallels is a longstanding open problem, which is equivalent to the so-called Finsler metrizability of the connection, i.e., to the fact that these autoparallels can be interpreted as Finsler geodesics. In this article, we address this problem for the class of torsion-free affine connections with vectorial