A Logarithmic-Exponential Reformulation of Relativistic Time Dilation and Length Contraction

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Scientific Essay from the year 2026 in the subject Physics - Other, grade: 18.5, , language: English, abstract: Special Relativity, introduced by Albert Einstein in 1905, describes the dependence of time and space on relative motion through the Lorentz factor. Although the Lorentz transformation has been experimentally verified with remarkable precision, its square-root structure often obscures deeper mathematical symmetry and physical intuition. In this work, we propose an alternative exponential¿logarithmic formulation of relativistic time dilation and length contraction. A new velocity-dependent parameter, denoted by , is defined through a logarithmic function of the normalized velocity. Using this parameter, time dilation and length contraction emerge naturally as exponential laws. The proposed formulation preserves consistency with Special Relativity for all subluminal velocities while offering a smoother mathematical structure, improved interpretability, and potential relevance to information-theoretic and thermodynamic descriptions of spacetime. This paper presents the theoretical derivation, mathematical analysis, physical interpretation, and limiting behavior of the new relations.

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