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

Authors: Pieper, Torsten;

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

Abstract

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.

Keywords

Five-Dimensional Gravity, Electromagnetism, Unified Field Theory, Geometric Interpretation of Forces, general relativity, kaluza-klein-theory, fieldtheory, Kaluza-Klein Theory, quantumgravity, quantumelectrodynamics, differential geometry

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average