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.‎