Can Light Tell Whether Spacetime Is Complex?

This paper investigates whether real light-cone measurements can distinguish a complex spacetime metric from an ordinary Lorentzian metric within the framework of Complex Relativity. It demonstrates that nine suitably chosen null directions constrain the imaginary part of the metric to a single scalar multiple of the real metric. While this scalar remains undetermined by pointwise light-cone tests and the free-particle mass shell, its gradients can contribute to gravitational focusing under a specified gravitational action. The paper further examines angular-diameter distances in a scalar-filled cosmological model and compares gravitational effects with a parameter-dependent matter interaction, highlighting both potential observational consequences and limitations of their distinguishability. This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). License: https://creativecommons.org/licenses/by-nc/4.0/