Classical Approximations vs. Relativistic Realities: A Theoretical Analysis of Kinetic Energy
- 1Indian Institute of Technology Kharagpur
Abstract
This paper presents a rigorous theoretical examination of kinetic energy across classical and relativistic domains. While Newtonian mechanics model’s kinetic energy as a straightforward function of mass and velocity squared, special relativity introduces Lorentz transformations that account for mass-energy equivalence and velocity limits near the speed of light. Utilizing a binomial series expansion of the Lorentz factor, this study demonstrates that Newtonian kinetic energy represents a valid first-order approximation at low velocities. However, as velocity approaches the speed of light, the higher-order relativistic terms become dominant, creating a substantial divergence between classical predictions and physical reality. The findings highlight the boundaries of classical mechanics and reinforce the necessity of relativistic models in high-energy physics applications
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BibTeX
@misc{annamalai2026classical,
title = {{Classical Approximations vs. Relativistic Realities: A Theoretical Analysis of Kinetic Energy}},
author = {Chinnaraji Annamalai},
year = {2026},
month = jul,
doi = {10.33774/coe-2026-vzlr0},
url = {https://doi.org/10.33774/coe-2026-vzlr0},
note = {CC BY},
}
RIS
TY - UNPB
TI - Classical Approximations vs. Relativistic Realities: A Theoretical Analysis of Kinetic Energy
AU - Chinnaraji Annamalai
PY - 2026
DA - 2026/07/31
DO - 10.33774/coe-2026-vzlr0
UR - https://doi.org/10.33774/coe-2026-vzlr0
AB - This paper presents a rigorous theoretical examination of kinetic energy across classical and relativistic domains. While Newtonian mechanics model’s kinetic energy as a straightforward function of mass and velocity squared, special relativity introduces Lorentz transformations that account for mass-energy equivalence and velocity limits near the speed of light. Utilizing a binomial series expansion of the Lorentz factor, this study demonstrates that Newtonian kinetic energy represents a valid first-order approximation at low velocities. However, as velocity approaches the speed of light, the higher-order relativistic terms become dominant, creating a substantial divergence between classical predictions and physical reality. The findings highlight the boundaries of classical mechanics and reinforce the necessity of relativistic models in high-energy physics applications
ER -