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INTRODUCTIONMax Planck’s constant qualifies the angular momentum ofthe stationary atomic state.1 The path of the transitionalquantum state has been unknown. Albert Einstein describedthe energy of a photon with Planck’s constant.2 Niels Bohrapplied these ideas to the atomic structure. Bohr’s quantumcondition states that the angular momentum carried by astationary atomic orbit is a multiple of Planck’s constant.3The quantization of angular momentum is a postulate,underivable from deeper law. Its validity depends on theagreement with experimental spectra. Werner Heisenbergand Erwin Schrödinger extended these ideas and qualifiedthe intensity of a spectral emission. These great scientistsfound that the frequency and amplitude of the emitted pho-ton is a function of the differential in energy through whichthe electron drops. The frequency and amplitude of a classi-cal wave is that of the emitter. The correspondence principlewas invented in an attempt to explain this discrepancy. Itstates that the frequency and amplitude of a classical systemis equivalent to the energy drop within a quantum system.These constructs form the foundation of modern physics.The structure built upon this foundation considers the clas-sical regime to be a subset of the quantum realm.

The Znidarsic constant Vt qualifies the velocity of thetransitional quantum state. The transitional velocity is cou-pled with a frequency and a displacement. The energy levelsof the atom are shown, in the body of this paper, to be a con-dition of the transitional frequency. The intensity of spectralemission is shown to be a function of the transitional ampli-tude. The action of the transitional quantum state replacesthe principle of quantum correspondence. An extension ofthis work would universally swap Planck’s and Znidarsic’sconstants. There would have to be a compelling reason tomake this change, as it would confound the scientific com-munity. There are two good reasons for doing so. Velocity isa classical parameter. The structure built upon this founda-tion considers the quantum regime to be a subset of the clas-sical realm. Znidarsic’s constant describes the progression ofan energy flow. An understanding of this progression may

lead to the development of many new technologies.

THE OBSERVABLESThermal energy, nuclear transmutations, and a few highenergy particles have reportedly been produced during coldfusion experiments.4,5 Transmutation of heavy elements hasalso been reported.6 The name low energy nuclear reactionsis now used to describe the process. The process wasrenamed to include the reported transmutation of heavy ele-ments. According to contemporary theory, heavy elementtransmutations can only progress at energies in the millionsof electron volts. The available energy at room temperatureis only a fraction of an electron volt. These experimentalresults do not fit within the confine of the contemporarytheoretical constructs. They have been widely criticized onthis basis. These experiments have produced very little, if no,radiation. The lack of high energy radiation is also a sourceof contention. Nuclear reactions can proceed without pro-ducing radiation under a condition where the range of thenuclear force is extended. The process of cold fusion mayrequire a radical restructuring of the range of the naturalforces. The condition of the active nuclear environment pro-vides some clues. Low energy nuclear reactions proceed in adomain of 50 nanometers.7-9 They have a positive thermalcoefficient. The product of the thermal frequency and thedomain size is 1 megahertz-meter. The units express a veloc-ity of one million meters per second.

The gravitational experiments of Eugene Podkletnovinvolved the 3 megahertz stimulation of a 1/3 of a metersuperconducting disk. These experiments reportedly pro-duced a strong gravitational anomaly.10-13 The results alsodo not appear to fit within the contemporary scientific con-struct. They have been widely criticized. It is assumed thatthe generation of a strong local gravitational field violatesthe principle of the conservation of energy. The strength ofthe electrical field can be modified with the use of a dielec-tric. The existence of a gravitational di-force-field no moreviolates the principle of the conservation of energy than

The Control of the Natural Forces

Frank Znidarsic*

Abstract — The electrical force has a convenient range and strength. This convenient range and strength has made the electromag-netic force easy to exploit. The strong nuclear force has a range measured in Fermis. The strong nuclear force has not been harnessedwith classical technology, as its range is too short. The gravitational force is very weak. This weakness has made it impossible to con-trol the gravitational force. A dielectric medium affects the range and the strength of the electrical force. It is commonly believed thatno (di-force-field) medium exists for the other forces. It is assumed that the range and strength of the nuclear and gravitational forceswill converge at high energies. These energies are beyond the reach of any conceivable technology. A low energy condition may exist inwhich the range and the strength, of all the natural forces, are affected. This condition is that of the quantum transition. This paperpresents arguments that may have exposed the path of the quantum transition. This exposure may lead to the development of tech-nologies that convert matter into energy and technologies that provide propellant-less propulsion.

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does the existence of an electrical dielectric. The geometry ofthe superconducting structure provides collaborating infor-mation.14 The product of the disk size and the stimulationfrequency expresses, as in the case with cold fusion, a veloc-ity of one million meters per second. This velocity may bethat of the quantum transition.

Electromagnetic energy flows strongly from the parent tothe daughter states during transition. This flow of energy ismediated by a strong electromagnetic interaction. It is rea-sonable to assume that the other natural forces also interactstrongly during transition. The flux of the force fields flowsstrongly, and at range, from the parent to the daughter state.The daughter is not just a displaced parent. The rearrange-ment of the force fields gives birth to an entirely new state.This process is associated with the emission of a photon. Aconvergence in the motion constants uncouples the fre-quency of the emitted photon from the frequency of theemitting electron. Znidarsic’s constant, Vt, has been refinedto a value of 1.094 megahertz-meters. Znidarsic’s theorem(“The Constants of the Motion tend toward those of theelectromagnetic in a Bose condensate that is stimulated at adimensional frequency of 1.094 megahertz-meters.”) quali-fies the strong transitional interaction. All energy flowsprogress by way of a quantum transition. This theoremdescribes the process of quantum measurement.

THE GEOMETRY OF A QUANTUM EMITTERPlanck’s constant describes the energy of an emitted photon.Znidarsic’s constant describes the geometry of the emittingstructure. Additional classical parameters are required inorder to describe quantum phenomena in terms of the emit-ting structure. They will be briefly presented. The radius rp isthat of the maximum extent of the proton. The strength ofthe electrical force equals the strength of the strong nuclearforce at this radius. The classical radius of the electron existsat 2rp. The coulombic force produced between two electricalcharges compressed to within 2rp equals 29.05 Newtons.The force produced by an amount of energy equal to the restmass of the electron confined to within 2rp is also 29.05Newtons. This confinement force Fmax was qualified inEquation (1).

Einstein’s General Theory of Relativity states that a forcecan induce a gravitational field. The gravitational field of theelectron may be coupled to the outward force of its confinedenergy. Newton’s formula of gravity was set equal toEinstein’s formula of gravitational induction in Equation (2).The dependent variable in this relationship was the mass ofthe electron.

The strength of the natural forces converges at radius rp.This convergence allows energy to flow between the naturalforce fields. The radius rp is the classical radius of energeticaccessibility.

The electrical field is usually described in terms of forceand charge. This paper describes the electrical field in terms

of an elastic displacement. The elastic displacement methodexposes the geometric conditions that are experienced byquantum emitters. The elastic constant of the electron K-ewas derived from the classical radius of energetic accessibili-ty. The force at this radius is Fmax. It was assumed that elas-tic constant of the electron varies inversely with displace-ments that exist beyond rp.

The elastic energy of the electron is given in Equation (4).

The elastic constant was tested at two radii. Radius rx wasset equal to the classical radius of the electron 2rp. The elas-tic energy contained by an elastic discontinuity of displace-ment of 2rp equals the rest energy of the electron. Radius rxwas then set equal to the radius of the hydrogen atom. Theelastic energy contained by an elastic discontinuity of dis-placement of 2rp equals the zero point kinetic energy of theground state electron. This author has suggested that thenatural force fields are pinned into the structure of matter atthis discontinuity.15 The transitional quantum state removesthe discontinuity and releases the fields. This brief introduc-tion describes the classical parameters associated with theemitting structures.

THE ENERGY LEVELS OF THE HYDROGEN ATOMMaxwell’s theory predicts that accelerating electrons willcontinuously emit electromagnetic radiation.16 Bound elec-trons experience a constant centripetal acceleration; howev-er, they do not continuously emit energy. An atom’s elec-trons emit energy at discrete quantum intervals. The quan-tum nature of these emissions cannot be accounted for byany existing classical theory. Quantum theory assumes thatthe gravitational force is always weak and ignores it. This isa fundamental mistake. During transition, electromagneticand gravitomagnetic flux quickly flows from the parent tothe daughter state. This rapid flow progresses by way of astrong electromagnetic and strong gravitomagnetic interac-tion. The energy levels of the atom are established throughthe action of this strong interaction. The velocity of the cen-tric transitional electronic state Vt was expressed as the prod-uct of its frequency ft and wavelength.

Lengths of energetic accessibility exist at rp. The velocityof the atomic transitional states are integer multiples of thisfundamental length.

A solution, Equation (7), yields the frequency of the transi-tional quantum state ft. For the isolated electron (n = 1) thefrequency ft equals the Compton frequency fc of the electron.

The transitional quantum state is a Bose ensemble of sta-

(1)

(2)

(3)

(4)

(5)

(6)

(7)

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tionary quantum states. The interaction of the fields withinthis ensemble resembles that of the electromagnetics withina superconductor. The infinite permeability of the ensembleconfines the static fields. The zero permittivity of the ensem-ble expels the dynamic fields. These effects extend to theends of the condensation. The motion constants vary direct-ly with the extent of the condensate. The frequency of theensemble is a function of its motion constants. For a Bosecondensate (n > 1) the frequency ft varies inversely with theradius of the condensate. These effects describe the di-force-field of the transitional quantum state.

The electron vibrates in simple harmonic motion. Thenatural frequency fn of the electron is a function of its elas-tic K-e constant and mass M-e.

The mass and the elastic constant of the electron were usedto formulate the electron’s natural frequency.

The frequency of the transitional state ft was set equal tothe natural frequency of the electron fn. The resultant equa-tion provided a simultaneous solution for rx.

Equation (10) was solved for rx, resulting in Equation (11).

The quantity within the brackets equals the ground stateradius of the hydrogen atom. The reduction of the termswithin the brackets produced Equation (12).

The result rx equals the radii of the hydrogen atom. A con-dition of energetic accessibility exists at points where thenatural frequency of the electron equals the frequency of thetransitional quantum state. The energy levels of the atomsexist at points of electromagnetic and gravitomagneticaccessibility.

THE INTENSITY OF SPECTRAL EMISSIONThe intensity of the spectral lines was qualified byHeisenberg. He described the position of an electron with asum of component waves. He placed these componentwaves into the formula of harmonic motion. Bohr’s quan-tum condition was then factored in as a special ingredient.Heisenberg found that the intensity of the spectral lines is afunction of the square of the amplitude of the stationaryquantum state. The great scientists knew nothing of the pathof the quantum transition. Their solutions did not incorpo-rate the probability of transition. The author claims to havediscovered the path of the quantum transition. This con-struct is centered upon the probability of transition. Theamplitude (displacement) of vibration at the dimensional

frequency of 1.094 megahertz-meters squared is proportion-ate to the probability of transition.

The transitional electron may be described in terms of itscircumferential velocity. Equation (13) describes the spin ofthe transitional quantum state.

Angular frequency n times radius of energetic accessibilityrp equals the velocity of the transitional quantum state.

Equation (14) was squared, reduced, and solved for r.Equation (15) expresses the amplitude of the transitionalquantum state squared.

The transitional frequency f of the daughter state is a har-monic multiple of the transitional frequency of the parentstate. The product of the transitional frequency, given byEquation (7), and the integer n was factored into Equation(16). Equation (16) expresses the transitional amplitude interms of the product of the amplitudes of the parent and thedaughter states.

The elastic constant of the electron was expressed in termsof lengths of energetic accessibility in Equation (17).

The numerator and denominator of Equation (16) weremultiplied by a factor of two. The elastic constant of theelectron, Equation (17), was also factored into Equation (18).

The factors within the brackets equal Planck’s constant.The reduction of the terms within the brackets producedEquation (19), Heisenberg’s formulation for the amplitude ofelectronic harmonic motion squared.

This formulation expresses the numerical intensity of theemitted photons. The intensity of a spectral line is a func-tion of the probability of transition. The probability of tran-sition is proportionate to the product of the transitionalamplitudes of the parent and daughter states. These con-structs reform the foundation of modern physics. This refor-mation is classical. It may be possible to influence these clas-sical parameters and construct devices that directly employall four of the natural forces. This control will lead to thedevelopment of many new technologies. The amplitude of anuclear state is small. The amplitude of a lattice vibration islarge. The product of these two amplitudes is great enough

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

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to allow a cold fusion reaction to proceed.

CONCLUSIONA low energy condition exists that affects the natural forces.This condition is dynamic. It consists of a vibrating Bosecondensate. The vibration of a Bose condensate at thedimensional frequency of 1.094 megahertz-meters appearsto increase the strength of the phonons that bind the con-densate. This increased strength invites nuclear participa-tion. Superconductors and proton conductors can be exter-nally vibrated to harness the effect. The process is that of thequantum transition. This new understanding may allow amulti-bodied macroscopic object to be placed into a state ofquantum transition. Trillions of atoms may be enjoinedwithin a single state of quantum transition. Strong gravita-tional and long-range nuclear effects will be produced. Thelong-range nuclear effects may be used for the production ofenergy and the reduction of nuclear waste. The strong grav-itational effects may be used for propulsion.

NOMENCLATURE

Fc = 1.236 x 1020 hertzFmax = 29.05 NewtonsM-e = 9.109 x 10-31 kgrp = 1.409 x 10-15 meters r+h = .529 x 10-10 metersVt = 1.094 x 106 hertz-meters

REFERENCES1. Planck, M. 1901. “On the Law of the Distribution ofEnergy in the Normal Spectrum,” Annalon der Physik, 4, 553.2. Einstein, A. 1909. “Development of Our Conception ofthe Nature and Constitution of Radiation,” PhysikalischeZeitschrift, 22.3. Bohr, N. 1913. “On the Constitution of Atoms andMolecules,” Philosophical Magazine, 6, 26, 1-25.4. Mosier-Boss, P., Szpak, S., Gorden, F.E., and Forsley, L.P.G.2007. “Use of CR-39 in Pd/D Co-deposition Experiments,”European Journal of Applied Physics, 40, 293-303.5. Storms, E. 1995. “Cold Fusion: A Challenge to ModernScience,” Journal of Scientific Exploration, 9, 4, 585-594.6. Miley, G.H. 1996. “Nuclear Transmutations in Thin-FilmNickel Coatings Undergoing Electrolysis,” 2nd InternationalConference on Low Energy Nuclear Reactions.7. Arata, Y., Fujita, H., and Zhang, Y. 2002. “IntenseDeuterium Nuclear Fusion of Pycnodeuterium-LumpsCoagulated Locally within Highly Deuterated AtomicClusters,” Proceedings of the Japan Academy, 78, B, 7.8. Rothwell, J., at www.lenr-canr.org.9. Rothwell, J. 1999. “The American Chemical SocietyConference Cold Fusion Sessions,” Infinite Energy, 5, 29, 23:“50 nano-meters. . .is the magic domain that produces adetectable cold fusion reaction.”10. Li, N. and Torr, D.G. 1992. “Gravitational Effects on theMagnetic Attenuation of Superconductors,” Physical ReviewB, 46, 9.11. Podkletnov, E. and Levi, A.D. 1992. “A Possibility ofGravitational Force Shielding by Bulk YBa2Cu307-xSuperconductor,” Physica C, 203, 441-444.12. Reiss, H. 2002. “Anomalies Observed During the Cool-Down of High Temperature Superconductors,” Physics

Essays, 16, 2, June.13. Tajmar, M. and deMathos, C. “Coupling of Gravitationaland Electromagnetism in the Weak Field Approximation,”http://arxiv.org/abs/gr-qc/0003011.14. Papaconstantopoulus, D.A. and Klein, B.M. 1975.“Superconductivity in Palladium-Hydrogen Systems,” Phys.Rev. Letters, July 14.15. Znidarsic, F. 2005. “A Reconciliation of Quantum Physicsand Special Relativity,” The General Journal of Physics,December, http://www.wbabin.net/science/znidarsic.pdf.16. Maxwell, J.C. 1865. “A Dynamical Theory of theElectromagnetic Field,” Philosophical Transactions of the RoyalSociety of London, Vol. 155.

About the AuthorFrank Znidarsic graduated from the University of Pittsburghwith a B.S. in Electrical Engineering in 1975. He is current-

ly a Registered Professional Engineer in thestate of Pennsylvania. In the 1980s, he wenton to obtain an A.S in BusinessAdministration at St. Francis College. Hestudied physics at the University of Indianain the 1990s. Frank has been employed as anengineer in the steel, mining, and utility

industries. Most recently he was contracted by AlstomPower to start up power plants in North Carolina.

*Email: fznidarsic@aol.com