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Physics in Higher Education

The balance equation in quantum physics

Pavel Pavlovich Rymkevich, Vladimir Anatolyevich Lyashenko, Антифеева Елизавета Львовна, А. С. Горшков

Published Jan 1, 2023• 0 citations
Publisher
DOI
10.54965/16093143_2023_29_2_20

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This short theoretical note formally codifies the concentration–dispersion balance equation as the Record Stability Equation within the Trinity / Scalar–Tensor–Observable framework. The equation, first developed operationally in Trinity Diagnostic Tool work as an S-balance metric, is here elevated into a proposed ontological stability principle. Within the Trinity/STO ontology, stable observable records are proposed to arise through a balance between concentration and dispersion under awareness-tensor registration. The note does not claim complete proof that the equation is a universal physical law; rather, it establishes a formal discovery claim and defines the equation’s role as a candidate record-stability condition across physical, informational, and experiential domains. Version note: This version clarifies the relationship between the Record Stability Equation and prior Trinity work on quantum uncertainty. The earlier text referred to future work “connecting” the equation to quantum uncertainty. This has been revised to state that prior Trinity work has already explored that connection, while future work may further formalize and extend it toward field theory, spinor geometry, and proper-time dynamics. No change is made to the central equation or the main discovery claim.
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrodinger equation. The knowledge of such properties in the case of Rabi Hamiltonian is exploit to provide arguments to make easier the variational engineering of the ground state of this model.
This work presents a new method called Dimensionless Fluctuation Balance (DFB), which makes it possible to obtain distributions as solutions of Partial Differential Equations (PDEs). In the first case study, DFB was applied to obtain the Boltzmann PDE, whose solution is a distribution for Boltzmann gas. Following, the Planck photon gas in the Radiation Law, Fermi-Dirac, and Bose-Einstein distributions were also verified as solutions to the Boltzmann PDE. The first case study demonstrates the importance of the Boltzmann PDE and the DFB method, both introduced in this paper. In the second case study, DFB is applied to thermal and entropy energies, naturally resulting in a PDE of Boltzmann's entropy law. Finally, in the third case study, quantum effects were considered. So, when applying DFB with Heisenberg uncertainty relations, a Schrödinger case PDE for free particles and its solution were obtained. This allows for the determination of operators linked to Hamiltonian formalism, which is one way to obtain the Schrödinger equation. These results suggest a wide range of applications for this methodology, including Statistical Physics, Schrödinger's Quantum Mechanics, Thin Films, New Materials Modeling, and Theoretical Physics.