Re-examining the law of energy conservation-A Euclidean geometric proof

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The law of energy conservation is a cornerstone of physics, limiting energy use and dictating the efficiency of thermodynamic processes. The primary objective of this paper is to challenge the traditional acceptance of the law of energy conservation as an unprovable axiom by presenting a novel, provable, and purely geometric approach within the framework of Euclidean geometry, thereby re-evaluating its theoretical and empirical foundations. Driven by the ongoing pursuit of solutions to energy crises, the paper critically examines attempts to disprove the law and the search for alternative energy sources. Contrary to prevailing beliefs, it posits two key viewpoints: the lack of rigorous proof establishing the law’s validity and the obscured motivations driving the invention of new energy sources. Highlighting the gap between theoretical acceptance and empirical evidence, the paper introduces a geometric framework to elucidate the empirical limitations and precision of energy conservation. Through this lens, it challenges the law’s universal applicability, particularly debunking the notion of perpetual motion machines as proof of its validity. The findings include a geometric and practical redefinition of isolated systems, a proof of Newton’s laws of motion, a geometric derivation of the Newtonian kinetic energy equation, and the demonstration of these geometric concepts’ practicality independent of experiments. These insights call for a re-evaluation of the traditional understanding of energy conservation and offer transformative implications for future energy exploration and innovation.