The phenomenal mathematical efficiency of quantum field theories in modern high-speed information and communication systems has a very simple explanation from the point of view of common sense and higher mathematical logic: all of them – quantum cosmology, quantum physics, quantum metrics and quantum calculus – are the self-informational mathematical systems based on symbolic and numerical functional analysis and elementary recursive calculations of interrelated space and time parameters of matter motion in various states of the material environment.For the first time in scientific and engineering practice, it was clearly shown that the information entropy of both standard symbolic and non-standard numerical functional analysis has absolute exact limits of computational accuracy – 1/10^16 and 1/10^64, respectively. Moreover, the second limit determines the maximum level of accuracy of practical quantum metrics and calculations and fully coordinates four branches of classical physics – thermodynamics, electrodynamics, gravidynamics, chromodynamics with special and general relativity.
Quantum physics and quantum cosmology were originated and remain today self-informational metric systems based on long-term multiple experiments with subsequent statistical averaging of results and spectral description of motion of material bodies and waves in subatomic and cosmic space. For the first time in scientific and engineering practice, it is logically and mathematically substantiated, experimentally, metrically and arithmetically confirmed that for the absolute assessment of the hidden parameters of the motion of matter, it is sufficient evaluate the vibrational, rotational and translational speed, as well as the amplitudes and phases of spatial displacement of a sphere with a diameter of "e" inside a sphere with a diameter of "pi", but if and only if the length of mantissa of decimally normalized fractions is at least 64 bits – to frequency 10^64 Hz, well above the Planck barrier
For the first time in scientific and engineering practice, it is logically and mathematically substantiated, computationally verified and metrologically confirmed that classic and quantum physics, analytical and quantum chemistry, as well as continuous symbolic and discrete digital mathematical analysis, all have computational limits of information entropy, upper 1/10^16 and lower 1/10^64. Mutual displacement of these limits relatively center of Euclidean three-dimensional and of Cartesian two-dimensional space generate sets of quantum dots of mesh topology and weighted average harmonic units of quantum metrics of internal atomic and outer cosmic space, as well as determines limits of communication speed, clock frequency, calculation power and accuracy for any computing machine with subatomic elements of memory. The matrices of functional density and entropy of energy and information fields reconciles classic and quantum physics with continuous and discrete mathematics of special and general relativity.
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