Geometric Interpretation of Mass-Energy Equivalence in Weyl Spacetime

This paper presents a novel interpretation of the mass-energy equivalence E = mc2 within the framework of Weyl geometry, a generalization of Riemannian geometry that incorporates local conformal invariance. By introducing a scalar field to break this invariance, we derive particle masses and recover the standard relativistic energy relation in a specific gauge. The model is formulated in natural units (h¯ = c = 1), ensuring dimensional consistency across all equations, and offers testable predictions, including deviations in particle trajectories and potential cosmological effects. This approach provides a geometric perspective on mass generation without requiring additional fields beyond the metric and a scalar field, bridging classical relativity with conformal gauge theories.