A New Lorentz Transformation with Geometry Satisfying the Principle of Relativity and Evaluating the Application of Field Theory to Special Relativity

The classical Lorentz transformation provides the mathematical framework for Minkowski spacetime symmetries; however, its operational derivation implicitly assumes that space and time exhibit identical symmetric projections. This paper proposes a comprehensive, dual-pathway formulation to address the structural paradoxes within special relativity. First, by analyzing the impact of signal propagation latency on measurements across distinct inertial frames, time is decomposed into four separate operational parameters. Based on this temporal distinction, we reconstruct a new Lorentz transformation characterized by a spatial scaling factor of $k=1$, thereby fully preserving the principle of relativity and the invariant constancy of the speed of light $c$. This formulation is geometrized through a novel, localized ``time cone'' architecture that moves alongside the observers, demonstrating how equiangular coordinate axis rotation structurally ensures exact reciprocity. Second, to address the principle of relativity within a broader context, this framework is extended by relaxing its absolute validity at extreme scales. This alternative pathway introduces a static four-dimensional spacetime background field to account for the physical origins of length contraction and time dilation. Within this field-theoretic approach, the traditional Lorentz transformation is recovered not as an invariant kinematic symmetry, but as a dynamical consequence of vacuum field resistance acting upon moving excitations. Ultimately, evaluating the application of field theory to explain the operational principles of special relativity requires a rigorous, case-by-case analysis to achieve an objective theoretical conclusion.