Abstract
In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated by resonance effects only and results are derived that stem from those in the quantum ground state. For an orbit with specific position and momentum at an initial time, the average energy and the average rate of energy change are evaluated, which stem with each other. Resonance effects are highlighted along the way. An outlook on the hydrogen ground state problem is provided.
Highlights
Quantum mechanics (QM) is a statistical theory, which does no less and no more than provide the Born probabilities for the outcomes of experiments
Though many interpretations have been put forward and various ontologies have been sought within the quantum theory, a deep analysis of the dynamics of a quantum measurement in a rich enough, but solvable, model has strengthened the case that QM provides no more than statistics
This approach was considered in Section 2.3.1 of [13]; the formulation in which was used as a check for our numerics
Summary
Quantum mechanics (QM) is a statistical theory, which does no less and no more than provide the Born probabilities for the outcomes of experiments. Though many interpretations have been put forward and various ontologies have been sought within the quantum theory, a deep analysis of the dynamics of a quantum measurement in a rich enough, but solvable, model has strengthened the case that QM provides no more than statistics. It is even capable of being connected to individual measurements, addressing the celebrated “measurement problem” [1,2]. One, first, has to demonstrate that SED explains various properties of QM at the statistical level This has been shown, on general grounds, within a certain flow of arguments [3,4].
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