On the Complete Understanding of Kaluza's Theory through the Exhaustion of its Given Mathematical Structur

The Kaluza-Klein theory provides a geometric unification of gravity and electromagnetism in a five-dimensional spacetime. This work shows that the Lorentz force, the Maxwell equations, and the electromagnetic energy-momentum tensor arise directly from the five-dimensional metric, confirming the consistency of the theory. A key result is that while the electromagnetic current jµ couples linearly in 5D, the associated energy density interacts nonlinearly with spacetime curvature. This is a direct consequence of the Einstein equation. This result suggests a fundamental principle: all observable forces must carry energy and act as localized deviations from flat spacetime. Consequently, electromagnetic waves cannot propagate without affecting the curvature. This supports the assumption that gravity is a universal phenomenon that accompanies all interactions. By incorporating the vector potentials into a metric, there is a direct correspondence to quantum electrodynamics. These results suggest that a fully nonlinear model could provide deeper insights into the nature of spacetime and fundamental interactions, potentially influencing future approaches to quantum gravity.