Abstract
The arithmetic limits of natural bit calculations are strictly established. The natural quantum metric system has been developed. Only seven scaling units that generate thirteen invariant values are necessary and sufficient for an accurate estimation and a mutual coordination of the fundamental constants of quantum physics. For the first time, the calibration constants of quantum physics were obtained, calculated and identified analytically with almost an absolute accuracy, which is limited only by a bit capacity of a computer. The basic constants of quantum physics are, in fact, the dynamic parameters of the functional relationships of the transcendental numbers PI and E with natural numbers, which draw a holographic picture of the motion of spherical wave fronts.
Highlights
The first attempt to develop the absolute metric system was made by Gauss in the early nineteenth century
The first derivative of PI by E can be considered as a unit of speed, and the second derivative is the unit of acceleration
E/2 is the radius, 4*PI*(E/2)^2 is the surface of the sphere, and 4/3*PI*(E/2)^3 is the volume of the sphere, PI*(E/2)^2 is the surface of a circle, N*(PI*E^2)/4 is a discrete set of the cylinder volumes
Summary
The first attempt to develop the absolute metric system was made by Gauss in the early nineteenth century. The inverse logarithmic relationships of the transcendental numbers PI and E resolve this problem and create the absolute metric without any artifacts and without measurements at all. It suffices to postulate the number PI as the universal unit of space and the number E as the universal unit of time. An inverse natural set generates a universal spatial unit PI = (1+1)*Sum{d(1/N)/Sqrt(11/N^2)} as a circle perimeter. It will be shown below that K and C are essentially fundamental mathematical units of the inverse natural calculus, such as PI and E of the standard analysis, and they can be obtained analytically from the mutual functional relations of the transcendental numbers PI and E. All other constants of quantum physics can be obtained analytically, and their physical meanings can be explained geometrically
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