Materials Science and Nanotechnology

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Short Communication - Materials Science and Nanotechnology (2018) Volume 2, Issue 1

Quantum nano-arithmetics for nanotechnology.

Eugene Machusky*


National Technical University of Ukraine, Ukraine

*Corresponding Author:
Eugene Machusky
National Technical University of Ukraine

Accepted date: February 15, 2018

Citation: Machusky E. Quantum nano-arithmetics for nanotechnology. Mater Sci Nanotechnol. 2018;2(1):10-12.


Quantum physics is a matrix calculation system that creates a two-dimensional holographic Picture of the three-dimensional harmonic motion of wave fronts. To estimate the fundamental constants of quantum physics with almost unlimited accuracy, only the functional relationships of two transcendental numbers Pi and E are sufficient with three unique integers A=137 (Sommerfeld), B=602214183 (Avogadro), R=105456978 (Dirac). In fact, quantum physics can be interpreted as a digital computational bridge between continuous and discrete mathematics. In general, quantum physics is the ultimate metric system of the pulsating universe.


The first attempt to develop an absolute metric system was made by Gauss in the early nineteenth century. The attempt was unsuccessful due to the inconsistency of parabolic, elliptic and hyperbolic geometry. Using the inverse logarithmic relations of the transcendental numbers PI and E, one can solve this problem if to postulate the number PI as the universal unit of space and the number E as the universal unit of time [1,2]. Then the first derivative of PI by E is the unit of speed and the second derivative is the unit of acceleration. Geometrically, PI is a universal relative perimeter, E is the universal relative diameter of relative space-time. E/2 is the universal radius, 4*PI*(E/2)^2 is the universal surface, 4/3*PI*(E/2)^3 is the universal volume of the sphere, PI*(E/2)^2 - the surface of the universal circle, and N*(PI*E^2)/4 - a discrete set of volumes of universal cylinders. The functional relations between these space-time parameters and an infinite set of integers N determine the computational accuracy of projective geometry in calculation systems with dynamic differential base. The keys to quantum differential calculus are following expressions and the corresponding decimal digital sequences:

[Sqrt((PI^2+E^2)/2) + (PI+E)/2 + Sqrt(PI*E) + 2*PI*E/ (PI+E)]^2 = 136.9938985020083597

Ln(PI) + 59*Ln(10) = 136.9972503724980956

For any four (a, b, c, d) decimal digits A = [abcdabcd]/ [abcd]/[73] = 137.0000000000000000 = A

Ln(Sqrt(10)) + 59*Ln(10) = 137.0038130331457184

It is an initial self-information (or information entropy) Alpha-matrix that connect decimal and natural calculation systems. Complete inverse alpha-matrix [Ai] and inverse radial matrix [Ri] are derived from the equations of the projective differential geometry. Geometrical parameters of pulsating spiral in inverse polar coordinates [3,4] are identified as following:

Ri = 1+2/100*(E+Ai*(1+Sqrt(2*PI*E/100))) is relative inverse radii (points of Dirac)

Ai = (100*(Ri-1)/2-E)/(1+Sqrt(2*PI*E/100))) is relative inverse eccentricities (points of Sommerfeld)

Pi = 2*PI*Ri is relative inverse perimeters (points of Planck)

Gi = Pi*(1+Ai) is relative densities of perimeters (points of Newton)

MMi = 12-[Ai]/10 is relative amplitudes of pulsations (points of Amagat)

KBi = Cos[MMi]-Sin[MMi] is relative phases of pulsations (points of Boltzmann)

Ni={Sqrt(8*PI*E/(8*PI*E+A^2))/(1+2*[Ai]/1000)- 5/10^8}/10 is entropy of eccentricity (points of Avogadro)

0.0073189621138002 = (PI*E/100)^2+4*(1/A- (PI*E/100)^2) = A4 is upper parabolic point of eccentricity

0.0073187289405399 = 1/(16*PI*E) = AH is upper hyperbolic point of eccentricity

0.0060221410732354 = B/(1+4*PI/(10^8))/10^11 = NB is upper point of entropy of eccentricity

0.0073071361524362 = 1/(Ln(E)+59*Ln(10)) = AL is upper logarithmic point of eccentricity

0.0072992700729927 = 1/A = A1 is point of periodical mirror symmetry of eccentricity

0.0072973525205056 = 1000/Integer{1000*Sqrt(A^2+PI^2)} = AF is point of fine symmetry of eccentricity

0.0072927060593902 = (PI*E/100)^2 = A0 is parabolic point of symmetry of eccentricity

0.0072900000000000 = 1/100/Sum{[A+(A- 100)*N]/10^(3*N+2)} = AS is bit-symmetry point of eccentricity

1.0545697837673031 = (R+4*PI*C/(10^10))/(10^8) = RC is upper point of rotational radius

1.0545697836787944 = (R+1/E)/(10^8) = RE is upper point of vibrational radius

1.0545697836689549 = [R+1/(E+AS)]/(10^8) = RA is qubit-point of vibrational radius

1.0545697836608581 = [R+1/(E+AS+Sum{B/10^(3*N+11)}]/(10^8) = RK is lower vibrational radius

0.0070261763632109 = 5/Root{X*E^X/(E^X-1)=5}-1 = AX is lower bound of inverse eccentricity

Unified matrix of standing and travelling waves consists of orbital (A4...AS) and nuclear (AS...AX) parts:

A4 = 0.0073189621138002

NH4 = 0.0060221410039861 = Median{NH...N4}

AH = 0.0073187289405399

NB = 0.0060221410732354 = B/(1+4*PI/10^8)/10^11 is upper bound of entropy

NA = 0.0060221410564149 = Median{NE...NB} is median point of entropy

NE = 0.0060221410395944 = Median{NLH...NH4} is lower bound of entropy

NHL = 0.0060221410752027 = Median{NH...NL}

AL = 0.0073071361524362

A1 = 0.0072992700729927

R01 = 1.0545718610477836 = Median{R0...R1}

AF = 0.0072973525205056 is fine structure point

RQ = 1.0545718475783874 = Median{RP...R(AF)} is upper bound of gravitational radius

RP = 1.0545717955420578 = Median{R0S...R01} is harmonic orbital radius (reduced Planck's)

A0 = 0.0072927060593902

R0S = 1.0545717300363340 = Median{R0...RS}

AS = 0.0072900000000000 = 1/100/(1.1111111>)^3 is point of qubit symmetry of eccentricity

RVS = 1.0545707377551176 = Median{RV...RS}

RG = 1.0545703605282681 = Median{RM...RQ} is harmonic center of gravitational radius

RC = 1.0545697837673031

RV = 1.0545697837183468 = Median{RT...RC}

RE = 1.0545697836787944

RAE = 1.0545697836738746 = Median{RA...RE}

RA = 1.0545697836689549

RT = 1.0545697836693905 = Median{RAK...RAE}

RAK = 1.0545697836649065 = Median{RA...RK}

RK = 1.0545697836608581

RM = 1.0545688734791973 = Median{RVX...RVS} is lower bound of gravitational radius

RVX = 1.0545670092049249 = Median{RV...RX}

AX = 0.0070261763632109 is self-information lower point of inverse eccentricity

Fundamental Units of Quantum Metric

Decimal orders of normalized quantum constants are easily extracting from the Wien wavelength displacement law and the approximate exponential expression E^137 = 100*PI*10^57.

C = [RC^64/10]*10^8 = 2.9979245786759104(30)*10^8 is rotational speed of light

V = [RV^64/10]*10^8 = 2.9979245697688564*10^8 is translational speed of light

T = [RT^64/10]*10^8 = 2.9979245608618054*10^8 is vibrational speed of light

K = [E+AS+BS] = 2.7315999984590452 is Kelvin's limit of background temperature

AF = [1000/Integer{1000*Sqrt(A^2+PI^2)}] = 0.0072973525205056 is fine structure constant

PP = 2*(RP)/(10^34) = 6.6260700111158524*(10^-34) is Planck's constant (harmonic orbital perimeter)

MM = 12-[AV]/10 = 11.9992777505492 is molar mass constant (relative amplitude)

KB = Cos[MM]-Sin[MM]/(10^23) = 1.380648450231*(10^-23) is Boltzmann's constant (relative phase)

NA = 1000*Median{NE...NB}*(10^23) = 6.0221410564149*(10^23) is Avogadro's constant (entropy)

G = Median{GM...GQ}/(10^11) = 6.6740528968519343*(10^-11) is Newtonian gravitational constant

The problem of the mutual coordination of constants was not physical, it was not metrological, it was a computational problem. Insufficiently correct conventional CODATA values of the speed of light, of the triple point of water and the relative molar mass led to the weak coordination of other fundamental constants and caused ultraviolet and infrasound "catastrophes" of quantum physics.


Absolute quantum metric system has been created.

Basic formula of quantum metric is E^(j*PI) + 1 = [Ai]/10^57>0.


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