Falsifiability of Newton’s Laws of Motion and Special Theory of Relativity – An Analytical Approach based Solution in Physics

Abstract

Newton’s laws of motion (NLM) and Einstein’s Special Theory of Relativity (STR) form the conceptual backbone of classical and modern physics, respectively. Despite their extensive empirical success, both frameworks are typically formulated without explicit consideration of thermodynamic constraints such as temperature evolution, system openness, and energy dissipation. This work investigates the thermodynamic consistency of NLM and STR by analytically examining their foundational equations under closed, open, and adiabatic system conditions using established principles from classical mechanics, kinetic theory of gases, and thermodynamics. The analysis demonstrates that Newton’s equations of motion implicitly assume constant acceleration and unbounded time evolution, which, when applied to open systems, violate energy conservation and imply behaviour akin to perpetual motion. By explicitly incorporating temperature as a dynamical variable and recognising its intrinsic coupling to time, modified equations of motion are derived for closed thermodynamic systems. These equations retain the functional form of Newtonian relations but introduce a bounded temperature increment, ΔT, thereby ensuring compliance with the first and second laws of thermodynamics and preventing divergence in velocity, displacement, or work. A similar thermodynamic examination of STR is conducted, focusing on relativistic length contraction, time dilation, and the mass–energy relation E = mc2 . When interpreted in terms of macroscopic or open systems, these relations imply the simultaneous divergence of mass and energy at high velocities, thereby contradicting conservation principles. However, when reformulated for isolated or adiabatic ideal-gas systems, analogous relativistic relationships emerge naturally from mechanical compression and temperature variation, without requiring inertial-frame abstractions or unphysical infinities. The study further demonstrates that the traditional interpretation of E = mc2 as unrestricted mass–energy interconvertibility is thermodynamically inconsistent. Instead, the equation is shown to represent the mechanical work required to accelerate a mass toward relativistic speeds within a finite time, thereby highlighting the physical impossibility of reaching the speed of light for finite-energy systems. Overall, this work establishes that both NLM and STR remain conditionally valid only within restricted thermodynamic domains. By explicitly incorporating temperature, system boundaries, and energy conservation, the analysis clarifies the physical limits of these foundational theories and provides a thermodynamically consistent reinterpretation of classical and relativistic dynamics.