Stability Principle and the Nature of Quantization

This book presents a novel approach to the foundations of quantum mechanics, demonstrating that quantization, phase coherence, and correlation phenomena can emerge from classical variational principles when extended to non-inertial reference frames. Central to the work is the Stability Principle, which refines the principle of stationary action by requiring dynamical stability—a criterion that selects physically realizable regimes from mathematically admissible solutions. By incorporating higher-order time derivatives and treating them as stochastic hidden variables common to all subsystems, the author shows that the operator formalism of quantum mechanics arises as an effective representation of stable phase dynamics. The hydrogen atom is analyzed as a test case, where stationary states are shown to result from a dynamic energy balance between classical radiation and non-inertial energy supply, rather than from the absence of radiation. The book further reinterprets Bell inequalities within this framework, arguing that their violation reflects the non-factorizable statistical structure inherent in non-inertial reference frames, not fundamental dynamical non-locality. Intended for researchers and graduate students in theoretical physics, this work offers a unified perspective on classical and quantum descriptions grounded in well-defined dynamical principles.