Mathematical Physics

    

Quantum Oscillator Revisited: Time-of-Time Formalism and Vacuum Rigidity αU

Authors: Pedro A. Kubitschek Homem de Carvalho

The quantum harmonic oscillator is traditionally formulated under the assumption of continuous time, leading to well-known eigenstates and energy spectra. However, when extended to cosmological scales, the same formalism contributes to divergences such as the vacuum energy catastrophe (10120 discrepancy in the cosmological constant). In this paper, we propose a reinterpretation: the oscillator is reformulated using the "time-of-time" formalism, where time itself oscillates over the Planck area scale. A new constant, αU = keAP (Coulomb’s constant multiplied by Planck area), emerges as the measure of vacuum rigidity. We show how this modification regulates divergences, unifies the interpretation of vacuum tension across quantum and cosmological domains, and provides a physical ontology to the notion of time in quantum mechanics.

Comments: 4 Pages.

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[v1] 2025-08-31 20:11:56

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