Quantum Energy-Level Age Shift (QELAS): A Chrono-Dependent Extension of Quantum Mechanics
Abstract
Standard quantum mechanics assumes that the energy levels of a stationary system are strictly determined by instantaneous environmental parameters, adhering to a principle of temporal amnesia. In this paper, we propose the Quantum Energy-Level Age Shift (QELAS) framework, which postulates that quantum energy levels depend not only on present conditions but also on their duration of existence, termed state age. By formulating an extended energy functional where energy evolves with respect to state age through a characteristic shift rate parameter chi_n, we establish a theoretical foundation for chrono-dependent quantum systems. We derive the generalized differential equations governing age-dependent energy shifts, explore modifications to the Schrödinger equation, analyze relativistic proper-time covariance, and discuss fundamental implications for time-translation symmetry and long-lived quantum states.
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