QUANTUM DETERMINISM OF RELATIVE SPACETIME COUNTING

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. INTRODUCTION To estimate the absolute parameters of the motion of various material particles at various states of the material medium, it is necessary both symbolically and numerically to describe all possible trajectories of motion of a ball of radius [e/2] inside a ball of radius [pi/2] or, which is the same, to imagine physically and to describe mathematically a spider web matrix by direct analogy with the Heisenberg uncertainty relation [P] = 2*pi*[R], where the dispersion matrix of partial perimeters [P] is direct analog of Planck's units [h] dispersion, and the dispersion matrix of partial radius-vectors [R] is direct analog of Dirac's units [h-bar] dispersion [R] = 1+2/100*(e+[A]*(1+Sqrt(2*pi*e)/10))) is spider web matrix of relative radius-vectors, [A] = (100*([R]-1)/2-e)/(1+Sqrt(2*pi*e)/10) is spider web matrix of relative eccentricity. As it turned out, [1] [14], only two of the above-mentioned interrelated equations, both of which contain the Gaussian argument of the informational entropy of the normal distribution Sqrt (2*pi*e), are sufficient to fully describe the functional relationship of the transcendental numbers "pi" and "e" with one, two, three or four decimal digits "a", "b", "c", "d" randomly selected from the full decimal alphabet [0; 1; 2; 3; 4; 5; 6; 7; 8; 9], and the following formula in symbolic notation with a numerical decimal result [73*137] is always absolutely correct for the calculation of cosmological time, with the exception of only one combination [0000] as arithmetically meaningless: abcdabcd / abcd = 73*137. In fact, this simple formula was deeply hidden in the anthropic logic of measuring and counting periods of time – in the ancient sundial and lunar clocks, in medieval mechanical and modern atomic clocks, in Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 27 November 2020 doi:10.20944/preprints202011.0699.v1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. the Julian and Gregorian calendars, and still remains hidden in the Wien’s equation of blackbody irradiation L*T = [h]/2/ pi*C/[k]/Root{X*e^X/(e^X-1) = 5}, where L, T, C – instantaneous wavelength, temperature, rotational speed and [h], [k] are the dispersion matrices of Planck and Boltzmann, respectively. The intrinsic dependence of wavelength of blackbody irradiation from transcendental number “e” was missed by S. Hawking and R. Penrose in their investigation of “black holes” of Universe. The anthropic year according to the Julian calendar is 365.25 days, but according to the Gregorian calendar it is 365.2425 days, the usual solar year is 365 days, the usual lunar year is 364 = 13*28 days, our usual calendar year has 365 days, but periodically it has 366 days. The most accurate unit of absolute cosmological time is the Gregorian one, because it gives an error of 1 day in 20 thousand years. The same calculation error (read – informational entropy) is inherent in the above formula for counting absolute time in the decimal positional system of calculation. INFORMATIONAL ENTROPY OF SPACETIME CALCULUS Any real process of measuring and calculating spatial gradients and time intervals can be carried out exclusively in numerical form, when the basis of the metric and computational systems is a finite set of rational numbers, since irrational numbers can never be completely written into the computer memory. On the other hand, the symbolic functional analysis of Euler that currently prevails in contemporary mathematical physics is based on virtual numeric symbols, such as infinite transcendental numbers "pi", "e", and the imaginary square root "j" of the number "Minus One": e^(j*pi) = j^2 or equivalently e^(j*pi)+1 = Zero – the final result of symbolic functional analysis by Euler. Any modern computer with engineering data processing can show that any finite records of irrational numbers can never give the final result “Absolute Zero”, because any finite series of recursive arithmetic operations of root extraction from any natural number N or from its inverse 1/N can never give the final result “Exactly One”, the results will always be [1.00000000 ... x] or [0.99999999 ... x] with inevitable informational entropy “x”, which, nevertheless, can be exactly calculated for any N. It was detected that the weighted average center of computational entropy of numeric functional analysis is distributed within the web matrix field [A] very near, above and under, the unique point A1 = 1/137 of the multimirror and circle center symmetry of inverse natural set: e^(j*pi) = 1/[A]/10^57 – the final result of numeric functional analysis by Gauss. A = 137 = Lim{1/Sum[729927/10*(8*N)]}, from N = 1 to N = Infinity. Ln(pi}+59*Ln(10) = 136.9972503724980956 Ln(e^137) = 137*Ln(e) = 137.0000000000000000... Ln(Sqrt(10))+59*Ln(10) = 137.0038130331457184. The "magic" properties of number 137 were first demonstrated by A. Sommerfeld. Later A. Eddington, M. Born, P. Dirac, R. Feynman and many others deeply discussed this as the so-called "mystery of 137", but in fact the only the secret here is that the relation A1 = 10^0/137 is the first hyperbolic point of the infinitely periodic and of multiple mirror symmetry of decimal fractions 10^N/137. For example: 10^64/137/10^64 = [0.0072992700729927007299270072992700729927007299270072992700729927]. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 27 November 2020 doi:10.20944/preprints202011.0699.v1


INTRODUCTION
To estimate the absolute parameters of the motion of various material particles at various states of the material medium, it is necessary both symbolically and numerically to describe all possible trajectories of motion of a ball of radius [e/2] inside a ball of radius [pi /2] or, which is the same, to imagine physically and to describe mathematically a spider web matrix by direct analogy with the Heisenberg uncertainty relation [P] = 2*pi* [R], where the dispersion matrix of partial perimeters [P] is direct analog of Planck's units [h]
As it turned out, [1] - [14], only two of the above-mentioned interrelated equations, both of which contain the Gaussian argument of the informational entropy of the normal distribution Sqrt (2*pi*e), are sufficient to fully describe the functional relationship of the transcendental numbers "pi" and "e" with one, two, three or four decimal digits "a", "b", "c", "d" randomly selected from the full decimal alphabet [0; 1; 2; 3; 4; 5; 6; 7; 8; 9], and the following formula in symbolic notation with a numerical decimal result [73*137] is always absolutely correct for the calculation of cosmological time, with the exception of only one combination [0000] as arithmetically meaningless: abcdabcd / abcd = 73*137.
In fact, this simple formula was deeply hidden in the anthropic logic of measuring and counting periods of time -in the ancient sundial and lunar clocks, in medieval mechanical and modern atomic clocks, in the Julian and Gregorian calendars, and still remains hidden in the Wien's equation of blackbody irradiation L*T = [h]/2/ pi*C/[k]/Root{X*e^X/(e^X-1) = 5}, where L, T, C -instantaneous wavelength, temperature, rotational speed and [h], [k] are the dispersion matrices of Planck and Boltzmann, respectively. The intrinsic dependence of wavelength of blackbody irradiation from transcendental number "e" was missed by S. Hawking and R. Penrose in their investigation of "black holes" of Universe.
The anthropic year according to the Julian calendar is 365.25 days, but according to the Gregorian calendar it is 365.2425 days, the usual solar year is 365 days, the usual lunar year is 364 = 13*28 days, our usual calendar year has 365 days, but periodically it has 366 days. The most accurate unit of absolute cosmological time is the Gregorian one, because it gives an error of 1 day in 20 thousand years. The same calculation error (read -informational entropy) is inherent in the above formula for counting absolute time in the decimal positional system of calculation.

INFORMATIONAL ENTROPY OF SPACETIME CALCULUS
Any real process of measuring and calculating spatial gradients and time intervals can be carried out exclusively in numerical form, when the basis of the metric and computational systems is a finite set of rational numbers, since irrational numbers can never be completely written into the computer memory. On the other hand, the symbolic functional analysis of Euler that currently prevails in contemporary mathematical physics is based on virtual numeric symbols, such as infinite transcendental numbers "pi", "e", and the imaginary square root "j" of the number "Minus One": e^(j*pi) = j^2 or equivalently e^(j*pi)+1 = Zero -the final result of symbolic functional analysis by Euler.
Any modern computer with engineering data processing can show that any finite records of irrational numbers can never give the final result "Absolute Zero", because any finite series of recursive arithmetic operations of root extraction from any natural number N or from its inverse 1/N can never give the final result "Exactly One", the results will always be [1.00000000 ... x] or [0.99999999 ... x] with inevitable informational entropy "x", which, nevertheless, can be exactly calculated for any N. It was detected that the weighted average center of computational entropy of numeric functional analysis is distributed within the web matrix field [A] very near, above and under, the unique point A1 = 1/137 of the multimirror and circle center symmetry of inverse natural set: The detection of very high informational discrepancy between symbolic and numerical functional analysis was at first view absolutely unexpected for us, because it had no precedents, but now it is a vivid illustration of the natural informational entropy caused by recursive arithmetic when decimal fractions have a short mantissa. And all this actually was the only reason for the "ultraviolet catastrophe" at the birth of quantum physics, but today it is the only reason for the "gravitational catastrophe" in modern quantum physics and in fact it is a serious logical error of standard metrology based on symbolic mathematical methods when working with very small space gradients and very short intervals of time. Well, we can not exactly measure micron length of light waves with a meter ruler!

QUANTUM ALPHABET OF MATTER LANGUAGE
We can now show that the Sommerfeld's prime A = 137 combined with the Avogadro's integer number B = 602214183 with the Maxwell's rotor speed number C = {105456978/10^8+4*pi*C/10^18)^64*10^7 and the well and long known Gaussian argument of the informational entropy of the normal distribution Sqrt(2*pi*e) allows us determine the refractive indices of material waves in various types of condensed media, and then accurately calculate the normal and anomalous dispersion of wave energy of thermal, electromagnetic and gravitational origin and, therefore, all the fundamental constants of the standard physical model with extreme accuracy, limited only by the finite bit capacity of the computing device.
Dear readers of our article, use a suitable calculator and you will be convinced that the problems and paradoxes of quantum physics were exclusively logical in nature and computational in origin!

QUANTUM ARITHMETICAL KEYS TO METRICS OF SUBATOMIC SPACE
The two basic (polynomial one C and exponential one X) quantum arithmetic keys ("quarks") to the topology and metrics of outer cosmic space and of inner subatomic space are the recently derived parametric equation The below presented partial eigenvectors R(Ai) and A(Ri) were obtained analytically using recursive (forward-back, up-down, left-right) and mutual transformations of a circle, ellipse, ring, oval, cylinder, cone, sphere, then torus, hoop, paraboloid, hyperboloid, ellipsoid, ovaloid in their functional dependence on polynomials and exponentials. As a result, we got thirteen nodes of standing waves (superposition Two space-time unitsthe rational one C and the transcendental one K = e + AS + BS determine upper and lower boundaries of translational velocity in an ideal gas environment, where any real or any virtual structural element (molecule, atom, nucleon, electron, photon) has 12 absolutely identical neighbors, symmetrically located on the surface of the sphere relative to center (like a three-dimensional star with twelve rays). The time shift of ideal infinite waves "sine" and "cosine", recursively moving along the sphere perimeter relative to 12 equidistant points, gives us the angular Boltzmann metrics. By analogy, such a metric can be transferred to cosmic space for satellites, planets, stars, constellations, galaxies.
Presented equations clearly show that there are no uniform quantum units for different aggregate states of matter. Thus, there cannot be a unified theory of the Universe, but instead there are seven interrelated mathematical "languages" of natural science: analytical chemistry (integral vector-tensor calculus), quantum physics (differential vector-tensor calculus) and five branches of mathematics: arithmetic, geometry, trigonometry, algebra, logarithms. For the logical connection of these languages, only the Gaussian informational functional of the entropy of the normal distribution Sqrt (2*pi*e) is sufficient, and now mathematical physics can be defined as the differential geometry of an arbitrarily moving sphere with a radius of e/2 inside a sphere of radius pi/2. This fact was missed by Hawking and Penrose in their equations for "black holes" of Universe. Moreover, if the above set of eigenfunctions is computed with an exponent back-compression of extremely truncated numbers PI = [3.14] and E = [2.71] into the inverse power mean space -from 1/PI^129 = 1/E^148 = 1/10^64 to 1/PI^130 = 1/E^149 = 0 then we get the natural arithmetical limits of the accuracy of root extraction. By Kolmogorov-Arnold-Moser, these hidden inverse exponent quantities are the cardinal parameters for power means but this was missed by authors of "chaos" theory.  1+[A]). One of the particular values G(NB) was not specially calculated to show that the informational entropy in SI in principle cannot be less than 1/10^8, and this is the natural arithmetic limit of accuracy for weighted average quantum metrology and computation. The previous system with the declared experimental entropy of fundamental constants was more "honest" and "fair' from the point of view of mathematical, chemical and physical logic, statistics of big data and information theory.
Three-dimensional (volume integrals and stereometry) gravitational matrix: The complete set of partial gravity matrices presented here was obtained analytically and without any experimental measurements for the first time in scientific and engineering practice.

DISCUSSION AND CONCLUSION
The web of gravity fully harmonizes classical mechanics with quantum mechanics, and Newton's theory of gravity with Einstein's general theory of relativity within the framework of objective logic of common sense, according to which the experimentally detected one-dimensional (radial) temperature field and two-dimensional (transverse ring) electromagnetic fieldthese are only part of special cases of the mathematical description of wave processes in a three-dimensional gravitational field. Gravitational waves (density waves of the translational velocity field) are primary in relation to electrical and thermal ones and cannot be described by only electrodynamics and thermodynamics, the combination with chromodynamics is requiredand this is already the relative dynamics of frequency and wavelength, showing the relationship between transcendental wave functions "pi" and "e".
The eigenvectors for the ideal gas state of matter make it possible to accurately calculate the weighted average temperature of the cosmic microwave background radiation TBG or the so-called "relic" cosmic temperature, which is measured by the COBE satellite in the interval (2.72491...2.72605) K.

TBG = Median{Median[e…(e+AS)]…Median[(e+AS)…K]},
where the operator "Median" means the arithmetic mean of the four mean valuesroot mean square, arithmetical mean, geometrical mean and harmonic mean.
This is the first in engineering practice direct calculation the cosmic background temperature without any preliminary measurements and this is a direct confirmation of the mathematical definition of gravity as the relative amplitude-phase and frequency-wavelength density of the translational velocity field.
A superposition of dynamic and infinitely long ideal wave functions "sine" and "cosine" doubles the observed frequency of oscillations when the instant translational velocity "v" tends to Cthis was first shown and stated by Nyquist, but intuitively clear for any electrical engineeras a natural result of fullwave rectification of alternative current. Thus, the canonic expression for the kinetic energy of quanta of different frequency ranges should be as follows in physical terms of chromodynamics (instant action and frequency) and of gravidynamics (instant mass and velocity): The energy of quanta tends to the Einsteinian limit m*C^2 if and only if the translational velocity tends to C, and tends to Newtonian zero if and only if the velocity tends to zero. But in a physically observable real and in mathematically described virtual Universe there can never be zero velocity, zero acceleration, zero force, zero mass, zero charge, zero energy, zero entropy and zero information. Just as there in recursive arithmetic is no absolute zero, so in natural science can be no universal field theory. World Wide Web of Gravity is therethe mathematical quintessence of the classical Newtonian physics.