Abstract
This study presents wavelets-computational aspects of Sterian-realistic approach to uncertainty principle in high energy physics. According to this approach, one cannot make a device for the simultaneous measuring of the canonical conjugate variables in reciprocal Fourier spaces. However, such aspects regarding the use of conjugate Fourier spaces can be also noticed in quantum field theory, where the position representation of a quantum wave is replaced by momentum representation before computing the interaction in a certain point of space, at a certain moment of time. For this reason, certain properties regarding the switch from one representation to another in these conjugate Fourier spaces should be established. It is shown that the best results can be obtained using wavelets aspects and support macroscopic functions for computing (i) wave-train nonlinear relativistic transformation, (ii) reflection/refraction with a constant shift, (iii) diffraction considered as interaction with a null phase shift without annihilation of associated wave, (iv) deflection by external electromagnetic fields without phase loss, and (v) annihilation of associated wave-train through fast and spatially extended phenomena according to uncertainty principle.
Highlights
According to the Sterian realistic approach [1], one cannot make a device for the simultaneous measuring of the canonical conjugate variables in the conjugate Fourier spaces.Generally, Heisenberg’s uncertainty principle states that incompatible dynamic variables in relation to the measuring process satisfy the following relations: ΔxΔpx ≥ h 2 ΔyΔpy (1) ΔzΔpz ΔtΔE, where Δx, Δy, and Δz are the uncertainties in position for each spatial axis, Δpx, Δpy, and Δpz are the uncertainties in momentum, and h is the reduced Planck constant, leading to the following statement
With each wave train being described by specific frequency and wave vector, it results in that temporal and spatial correlations are involved in these relativistic transformations for part of wave trains
Considering that the wave train corresponding to the electron undergoes a set of interactions with virtual photons, it results in that a certain transient time is required by each interaction, so as physical quantities as wavelength and angular frequency to be transferred in this local phenomenon
Summary
According to the Sterian realistic approach [1], one cannot make a device for the simultaneous measuring of the canonical conjugate variables in the conjugate Fourier spaces. Further it is considered that in quantum physics simultaneous measurements of the canonical conjugate variables (as space momentum, time energy) cannot be performed, because these variables correspond to the reciprocal Fourier spaces. Uncertainty relations are considered to confirm the principle of causality due to the finite speed of propagation of interactions required by any measurement process. This approach is far from being rigorous. A rigorous analysis for coherence aspects implied by different interaction phenomena should be performed (the Fourier transformation being just a mathematical tool for analyzing this coherence for wave packets corresponding to a certain quantum particle). Aspects regarding creation annihilation of quantum particles during the measurement process should be analyzed by taking into consideration correlation aspects in quantum field theory and the change from coordinate space to momentum space (reciprocal Fourier spaces) required by the mathematical model
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