Find an alternative spacetime geometry for electromagnetism

Construct or rule out a geometry independent of the charge-to-mass ratio that geometrizes electromagnetic motion while satisfying a universal spacetime criterion for local inertial frames.

Background

The manuscript constructs a charge-dependent kinematic structure and a corresponding nonlinear transport, but finds that particles with different charge-to-mass ratios do not share the same inertial motions. Consequently, the resulting structures fail the universality criterion used to identify spacetime structure.

The authors explicitly leave unresolved whether some alternative construction could geometrize electromagnetism without producing a separate effective inertial structure for each charge-to-mass ratio.

References

Whether some other construction geometrises electromagnetism is a question we neither ask nor settle.

— The kinematic structures and the inertial geometry of a moving charge  (2609.11165 - López-Monsalvo, 10 Sep 2026) in Section 5, Discussion

Whether other operationally motivated criteria, drawn from different mathematical machinery, could single out other reference geometries is a substantive question. It is not easy to `reverse-engineer' the operational criterion that would single out a given geometry, and pursuing the question would go well beyond the scope of this paper.

— $δ$-flatness and its natural extension  (2609.29823 - Gomes, 24 Sep 2026) in Introduction, final paragraph before “A word on scope”