Authors: A. V. Herrebrugh
A mathematical model for the slit-experiments — considered to be in the heart of quantum mechanics - is developed to gain insight in quantum theory. The proposed system-theoretical approach for the model takes a different route compared to matrix mechanics in complex vector spaces; it is based on commutative mathematics and starts with spacetime functions with cause and effect relations in the statefunction Ѱ. This approach yields: 1. Deterministic result functions and disappearance of probability in QM, 2. Information symmetry in QM causal relations , 3. Separation of causality and non-commuting (e.g. crosscorrelations of attained states) operators, 4. QM a priori fixed states after causality interactions have ended, as well in case quanta are (light-years) separated. The consequence of this model is that operators, such as cross correlations and vector cross products that cannot support information symmetry due to not being mathematically commutative,are in principal not suitable in causality descriptions on quantum level . The model predicts the exact patterns in the results of the experiments by yielding mathematical functions of the energy distributions. The quantum mechanical description of physical reality of slit experiments thus may be considered complete in the sense of [10], but requires the thought experiment of reality still, which is only seemingly contradictory with the exact results. At quantum slit-experiment energy level, assumed quantum interference in double slit experimentsis an effect of energy (amplitude-) modulation. For one-slit, a modulated function is shown to giveidentical results of a double-slit extended experiment, by yielding two distributions as result of theconvolution in the (k-space) frequency domain. This rules out interference due to the absence of multiple slits. In principle it may be possible to experimentally verify the effect with a modulated result function of a one slit experiment.The system-theoretical method uses generic properties of quanta and evolves into determinism in quantum mechanics slit experiments, be it with the restriction of a direct observation/measurementor direct description with variables of the individual quanta at the heart of the state-function Ѱ. The mathematics handles beables [9,10] and allows the proposed description by avoiding directly addressing of the individual quanta through variables. The mathematical treatment yields exact, non-probabilistic results.
Comments: 14 Pages. HyperScience International Journal (HSIJ) September issue 2022.
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