Determinism in Quantum Slit-Experiments
Abstract
A mathematical model for the slit experiments in the heart of quantum mechanics is developed to gain insight into quantum theory. The proposed system-theoretical model is entirely based on commutative mathematics, i.e. convolution, and integral transformations, and starts with spacetime functions with inherent energy-based cause and effect relations of the state-function Ѱ in the complex Hilbert space. The benefits of his approach are as 1-Invariance in time reversal. 2-Deterministic result functions in the model in line with the outcome of slit experiments. 3- Separation of causality and cross-correlations of attained states. 4- Disappearance of a posteriori probability of quantum states. 5- Quantum a priori fixed states after causality interactions have ended, (even) when quanta are (light-years) separated. The model predicts the patterns in the experiments with mathematical functions of the energy distributions. The quantum mechanical counterpart description of the physical reality of slit experiments thus may be considered complete in A. Einstein’s definition. The patterns in double slit experiments are found to be an effect of energy (amplitude-) modulation. An equivalent double-slit pattern can be retrieved from an input modulated 1-slit experiment excluding interference interpretations. The system-theoretical model uses generic properties of quanta and evolves into determinism in quantum mechanics slit experiments. The mathematics in the model handles beables by treatment of momentum p in system theoretical I/O relations of the transformed functions and allows the proposed description by the avoidance of a direct addressing of the individual quanta through variables. The following method yields exact, non-probabilistic results.