Even in a weird version of space where "distance" isn't a thing, everything still takes the path of least resistance.
March 13, 2026
Original Paper
Autoparallels and the Inverse Problem of the Calculus of Variations
arXiv · 2603.11581
The Takeaway
Usually, physics assumes we can measure the distance between points to find the shortest path. This discovery shows that the universal law of 'least action' is so fundamental that it still works in 'broken' mathematical universes where standard distance is inconsistent, providing a new foundation for theories of gravity beyond Einstein's.
From the abstract
We prove that autoparallel curves associated with a torsion-free but not necessarily metric-compatible affine connection can be derived from an action principle. We explicitly construct the action functional and show by standard variational techniques that it produces the desired equations. Our analysis is based on systematically solving the inverse problem of the calculus of variation and the associated Helmholtz conditions. This demonstrates that the dynamics of autoparallels admit a consisten