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THE VELOCITY OF QUANTUM TRANSITION

Chapter 11 Chapter 11. A re-print of a lecture given at the University of Illinois and for the American Nuclear Society.
Note: Znidarsic's megahertz-meter constant was published in Transactions of the American Nuclear Society vol 83 TANSAO 83 1-536, 2000, ISSN: 0003-018X and in Infinite Energy Sept /Oct 2009




ABOUT ENERGY FLOWS

[This is a jpg picture of a power factor capacitor] This chapter is one of the most difficult and the most important in this text. It is important because it reveals the technologies of antigravity and low level nuclear reactions. It is difficult because it discusses concepts like energy flows and the motion constants. An everyday example may be of help. A internal combustion engine produces a certain torque and angular velocity. The torque and angular velocity qualify the mechanical motion constants of the engine. The motion constants of the road are a property of the speed of the vehicle. The automotive transmission matches the mechanical motion constants of the engine to those of the road. This process allows mechanical energy to flow smoothly from the engine to the road. For those of us who do not know how to design a transmission, the thing to know is, "set it in drive".

The natural forces have vastly different strengths and ranges. The strength and range of a force determines its motion constants. The quantum transition acts like an automotive transmission. It aligns the motion constants associated with the natural forces. This process allows matter’s energy to flow smoothly from one stationary quantum state to another. This smooth flow of energy is characterized by a match in impedance. This impedance match is similar to one billiard ball hitting directly into, all of the energy is exchanged at once, without bounce. One photon is emitted at that instant. The speed of the outgoing ball matches the speed of the incoming ball. This type of speed match was used by this author to in a classical description of the quantum condition. This author’s exposure of the path of the quantum transition provides an understanding of the process of quantum measurement.
“The quantum condition emerges at points where the electronic velocity of light equals the nuclear velocity of sound.”
Frank Znidarsic 2009

A considerable amount of mathematics was used to describe the transitional quantum state. For the readers not interested in mathematics the important point is, once understood the process of quantum transition can be employed to produce strong gravitational and long range nuclear effects.

[This is a jpg picture of a shaft]

Pick the link right to view a short introduction to impedance matching and what it means in a quantum system.

OBSERVABLES BEYOND THOSE OF THE SPECTRUM

The low level nuclear process ( cold fusion ) defies conventional wisdom. An established body of knowledge has developed over many years. According to this body of knowledge the process is improbable. The atoms in a crystal lattice are separated by a few angstroms. The range of the strong nuclear force is measured in Fermis. The atomic spacing is many orders of magnitude removed from the nuclear separation required to produce a reaction. Tens of thousands of electron volts of energy are required to overcome the electrostatic potential barrier of the nucleus. The thermal energy at room temperature is only a fraction of an electron volt. Nuclear reactions do not proceed at such low energies. The process emits almost no neutrons or gamma radiation. The lack of radiation is not indicative to a neutron activated process. Low level transmutations do not always account for the amount of energy that is liberated. It is no wonder that the established scientific community does not believe these results. This author's "Constants of the Motion" theory exposes the mechanics of the interaction. The theorem states that the constants of the motion tend toward the electromagnetic in a Bose condensate that is stimulated at a dimensional frequency of one megahertz-meter. This theorem has ramifications that extend far beyond the process of cold fusion. The theorem reveals the path of the quantum transition. This path is a classical affect of the nuclear and electrical fields. This new understanding should dispel the disbelief and guide the development of many technologies.


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FORCE CONSTANTS AND THE BOSE CONDENSATE


The electric field of the electron does not saturate. It extends to infinity. Charges are isolated by resistance. Superconductors (a type of Bose condensate) offer no resistance to electrical currents. The electrical permittivity of a superconductor is infinite. This field is confined by the infinite permittivity of the medium. No flux leaks away. The range of the electric field is limited to the dimensions of the superconductor. The electrical field is concentrated within the superconductor. This dramatic change in range and strength is reflected in the electrical motion constants.

The magnetic field normally passes around lengths as short as the diameter of a proton. A superconductor completely expels magnetic lines of flux. The shortest magnetic flux line has a dimension equal to the circumference of the superconductor. This dramatic change in range and strength is reflected in the magnetic motion constants. The phenomena illustrates that no fundamental laws fix the range and the strength of the force field. Given the proper condition the nuclear and gravitational show be subject to the same effect. The condition that adjoins all of the force fields into a state, in a like manner, is that of the quantum transition.

Scientists have discovered nuclear reaction products in cold fusion experiments. The heat of the reaction has also been detected. It appears, in cold fusion experiments, that the range of the strong nuclear force has increased to atomic dimensions.

[Lecture at UIUC]

[WAVE audio file Pick the icon to hear a quote from the lecture at the University of Illinois. File type wave. September 1999



A main point. Pick to view a chart that shows how the range of force interaction changes in a vibrationally reinforced Bose condensate.





The experiments indicate that the strong nuclear force extends beyond the Coulombic potential barrier, through the interatomic space, and to the neighboring nuclei. The Coulombic barrier no longer hinders the flow of nuclear energy. There is no change of potential at the Coulombic barrier and no radiation is produced. Compound nucleons are formed. 1 The fact that matter is not crushed by the process demonstrates that the increase in the range of the force is accompanied by a decrease in its strength. This dramatic change in range and strength is reflected in the nuclear motion constants.


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THE VIBRATION OF A BOSE CONDENSATE

Case and Arata have demonstrated that 50nm particles consistently produce low level nuclear reactions. Miley's and Patterson's processes involve thin films. These films are about 65nm thick. S. Szpak and J. Patterson have demonstrated that the reactions proceed after the particles and the thin films are stimulated thermally at a frequency of about 1x1014 hertz. 18
"50 nano-meters ..is the magic domain that produces a detectable cold fusion reaction"
Jed Rothwell, Infinite Energy, Issue 29, 1999, page 23.

Dennis Letts and Dennis Cravins have demonstrated that the vibrations produced by the laser stimulation of deuterated palladium increase the rate of reaction. 15, 16 The product of the 50nm dimension and the stimulation frequency is one megahertz-meter.

" Deuterium begins to condense when constrained in very small domains of a few tens of nanometers in dimension. It certainly can achieve a metallic deuterium state and perhaps becomes a BEC (Bose Einstein Condensate). It has been clear for some time that the reactions we work with are not a uniform bulk phenomena but rather must be produced within some unusual domain that is quite extraordinary."
Russ George   D2Fusion


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Many laboratories have investigated the phenomena of cavitational fusion. This author has worked with Yuri Potapov on a cavitational device (ref. Chapter 1). Sonofusion experiments involving cavitation appear to generate nuclear reactions and heat. According to conventional theory the energy produced in these experiments is two orders of magnitude below the energy required to trigger nuclear fusion. Sensitive experiments done by R. P. Taleyarkham at the Oak Ridge National Laboratory in 2003 have confirmed that nuclear reactions do proceed. A blue glow is observed emanating from the cavitational bubbles. The frequency of the blue light is 650 THz (650 x 1012Hz). The size of active area in the bubbles has a dimension expressed in 10's of nanometers. The product of the stimulation frequency and the bubble size is about one megahertz-meter. 2


E. Podkletnov (left ) spun a superconducting disk while stimulating it at a frequency of 3 megahertz. The disk was 1/3 of a meter in diameter. The experiment appeared to induce a strong near field gravitational anomaly. The product of the stimulation frequency and the disk diameter is one megahertz-meter. Other laboratories have now reported similar anomalies. 3, 4, 5, 6, 22 The European Space Agency reported significant results.





"Although just 100 millionths of the acceleration due to the Earth’s gravitational field, the measured field is a surprising one hundred million trillion times larger than Einstein’s General Relativity predicts."
Clovis de Matos The European Space Agency. ESA news Dec 2006
A consistent pattern of behavior is emerging. The behavior is exhibited in all of the experiments. The product of the stimulation frequency and the system's dimension is one megahertz-meter. The external stimulation of the structure excites the heavy nucleons in the material. The vibration of nucleons is associated with the velocity of sound in a material. It will be shown that the quantum transition progresses when the velocity of light in the electronic structure of a material equals the velocity of sound in the nuclear structure of the material.


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THE VELOCITY OF SOUND WITHIN A NUCLEON

Quantum interactions are currently described with Planck’s constant. Planck’s constant expresses the angular momentum of a quantum state. Angular momentum is the product of three terms. Each of these terms was produced from the observation of the atomic spectrum. They are all empirical. Current theory attempts to compensate for this lack of fundamental understanding by stating that classical universe is a subset of the quantum realm.

Znidarsic's constant consists of a single classical term. The constant Vt expresses the velocity of sound within the nuclear structure. The sonic velocity equals the velocity of light divided by twice the fine structure constant.
"All good theoretical physicists put this number (the fine structure constant) up on their wall and worry about it."
Richard Feynman
The thermal stimulation in cold fusion experiments and the radio frequency stimulation in gravitational experiments have excited the optical phonons within the nuclear structure of the atomic lattice. These phonons carry sound within the material. These affects revealed that the velocity of sound within the nuclear structure is the key to a fundamental understanding of the quantization of energy. The velocity of sound within the nucleus equals the product of the nuclear frequency of harmonic motion and the nuclear displacement. The frequency of harmonic motion was determined using the square root of the ratio of the elastic constant of the electron (29.05 / r) and mass of the nucleon (Mn). The electrical forces balance the nuclear forces within the nucleus. At the balance point the stiffness of the electrical and nuclear forces are equal. This equality in stiffness was the justification for using the electron’s elastic constant in the formulation. A nuclear spacing of 1.36 fm was used as the nuclear displacement. A nucleon has a radius of 1.25 fm. This nuclear spacing is slightly greater than the radius of a nucleon due to the packing fraction of the nucleons (ref http://hitoshi.berkeley.edu/221B-S02/nuclear.pdf).



[This equation expresses the velocity of sound in the nucleus]


[This equation expresses the velocity of sound in the nucleus]

rn = 1.36 x 10-15 meters

Mn = 1.67x10-27 KG

n = the wave number

Fmax = 29.053 Newtons

Vs = 1.094 million meters / second .




Showing Nuclear Motion



It appears, at first, that this author’s model of the velocity of sound in the nucleus is to simple. True, the formulation is simple, however, the ramifications are enormous. The nuclear density is constant at .172 kg / fm3 ( ref http://www-nsdth.lbl.gov/nnpss2005/engel_lecture1.pdf ). The consistency of the nuclear density maintains a fixed velocity of sound within the nucleus. The electrical force is expelled from the nucleus and does not impact the velocity of sound between nucleons. This insight has enabled this author to calculate the velocity of a mechanical wave (sonic wave) in the nucleus.

Right: A cryogenic cold fusion experiment. The nucleons are excited with radio frequency energy and the electronic Bose condensate is enhanced with liquid nitrogen cooling.


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THE DOWNSHIFTING OF THE FREQUENCIES


In July of 1997 Frank Znidarsic met with Dr. David Noever at NASA Marshall. Znidarsic presented his idea that the range of force interaction changes within superconductive systems. Znidarsic explained that the longer range of the nuclear spin orbit force permitted many unexpected "cold fusion" reactions to take place. In 1997, NASA was not considering the nuclear ramifications of their superconductive work. Noever explained his idea about the "Downshifting of the Frequencies" of matter. Noever had reason to believe that the Planck frequency downshifted within superconductive structures. Znidarsic understood that his ideas were intimately connected with those of Noever's. The "downshifting of the frequencies theory" should prove to be a very important scientific concept. Znidarsic joined Noever's concept with his idea of a quantum of capacitance and determined the downshifted Compton frequency of the electron. During his visit Znidarsic discovered that NASA was applying a 3.5 megahertz radio wave to an 11 inch superconductive disk. NASA was not sure of the function of the radio waves. Znidarsic believed that the radio waves were vibrating the superconductive disk at the downshifted Compton frequency of the electron. Znidarsic discovered that the product of the downshifted Compton frequency and an up shifting wavelength equals the velocity of the quantum transition. NASA continues to experiment. Znidarsic went on to developed his theorem "The gravitational and nuclear motion constants tend toward those of the electromagnetic in a Bose condensate that is stimulated at a dimensional frequency of one megahertz-meter". Znidarsic's theorem describes the velocity of the transitional quantum state.


This author conducted cryogenic zero point energy experiments.
The results were published by Hal Fox in "New Energy News vol 5 pg #19.


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THE VELOCITY OF LIGHT WITHIN THE ELECTRONIC STRUCTURE

The standard model of physics describes the stationary quantum state. This author has discovered a flaw in the standard model. The corrected model revolves around the transitional quantum state. In the standard model, the matter wave function is produced through the Fourier addition of a series of component waves. This conception is fundamentally wrong. Traveling waves consist of a series of component waves but standing waves are not localized by this process. The representation of a standing wave by a Fourier series requires an infinite number of component waves. Natural infinities do not exist within a finite universe. All standing waves, matter waves included, are held in place by restraining forces.

Force fields exist in two basic forms, local and radiational. A familiar local field is the magnetic field. A local magnetic field is always associated with a physical magnet. It moves with at group velocity of the magnet V. The radiational magnetic field of a photon does not require the physical magnet. It propagates with a phase velocity of c. What determines if a force field is local or radiational? The property of superconductivity offers a clue. The force fields within a superconductor tend to slip. Impurities are added to superconductors. The impurities produce discontinuities that pin the fields in place. A discontinuity is also produced a the point where the intensity of a force field exceeds the elastic limit of space. This discontinuity pins the force fields into the structure of matter. Local fields experience the elastic limit of space. Radiational do not. A discontinuity is produced when the displacement or intensity of a force field exceeds the ability of space to support that field. The elastic limit is a fundamental geometric property. It exists at the classical radius of the electron. Each force field experiences an elastic limit in its own way. The elastic limit of a mechanical system "K" corresponds to a quantum of reciprocal capacitance in an electrical system (K varies as 1/C). The electrical field experiences an elastic limit through a quantum of reciprocal capacitance. The quantum of capacitance, as determined in Chapter 10 , is given below. [animation]

Cq = 1.56 x 10 -25   Farads

During the quantum transition energy flows from state one to another. These states are associated with elastic discontinuities. The transitional quantum state is described by its velocity as measured with respect to an elastic discontinuity. The velocity of the quantum transition is a property of its frequency and displacement. The frequency is the Compton frequency Fc. The displacement is equal to the extent of the elastic displacement. This extent equals n times the classical radius of the electron. 2rp. For centric systems the quantum transition expresses itself through its circumferential velocity. A factor of p was incorporated to obtain circumferential velocity of the transitional state. The velocity of the quantum transition was derived, below, from this understanding.

Velocity = 2 p Fc l   million meters/second

Velocity = ( 2 p ) [Mc2/h] ( 1.409 x 10-15 )   meters/second


The result is 1.094 meters / second . The velocity is that of the transitional quantum state. The velocity of sound within the nucleus matches the velocity of sound within the electronic structure at this velocity. The match in velocities is associated with a match in characteristic impedance. The match in impedance allows energy to flow between the states of the atom. This classical effect is fundamental to the quantization of energy.

[Java Script animation.}
Animation, "The Path of the Quantum Transition. "


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[Graph] It was shown in Chapter 10 that the Compton frequency of a stationary quantum state is set by the mass of the particle and the elastic limit of space. The frequency transitional quantum state is a function of the geometry of the system. This geometry is qualified by the isotropic capacitance of a quantum system. The infinite permittivity (zero resistance) of a superconductor has the effect of connecting every point within the superconductor directly to the bulk of the superconductor. The capacitance experienced by an macroscopic electronic system equals the isotropic capacitance of a sphere. The electrical capacitance of a sphere is given by.

Cs = 4 p e0 r   Farads

The ratio of the quantum of capacitance Cq to the isotropic capacitance of a quantum system Cs was employed to determine the transitional frequency of a macroscopic quantum system. This frequency is described by the dimensional constant of one megahertz-meter. Stimulation at this dimensional frequency tends to condense the interacting states. The megahertz-meter relationship is expressed below.


Ft = [Mc2/h][Cq/Cs][2pr]   megahertz-meters


The result is 1.094 megahertz-meters. Velocity may be expressed in units of megahertz-meters. This dimensional frequency expresses a relationship between the size and frequency of the transitional quantum state. Expressing velocity in units of megahertz-meters is useful in describing the transitional state of non-centric systems.

The megahertz-meter relationship describes the process of quantum transition. The quantum transition involves a strong interaction involving all of the natural forces. Strong interactions require strong mediating forces. The strength of the electrical force, the nuclear force, and the gravitational force converge at a displacement equal to n times the classical radius of the electron 2rp.


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THE PHOTO ELECTRIC EFFECT


[This is a jpg picture of fiber optics] Classical theory reigned supreme in the 19th Century. At the beginning of the 20th Century cracks began to appear in its structure. The most notable problem arose from the study of the emission spectrum of a black body. Classical theory predicts that such a body should emit an infinite amount of high frequency energy. Such high frequency emissions would result in an “ultraviolet catastrophe“. Max Planck, following the lead of Ludwig Boltzmann, offered a solution to this problem. He proposed that thermal energy was emitted from matter in bundles called photons. The energy E of these photons is proportionate to their frequency   f.

E = hf

This solution was appealing. The higher frequency modes were simply not energetically accessible. The “ultraviolet catastrophe” was averted. Albert Einstein went on to show that the phenomena is a property of the photon.

Niels Bohr extended this idea and proposed that the electronic orbits exist at quantum intervals. Each atomic level contains a definite about of angular momentum. This angular momentum is a multiple of Planck's constant h. The great scientists discovered that the frequency of a emitted photon is inversely proportional to the level of atomic energy through which the electron falls. This frequency is not that of the orbiting electron. In a classical system the frequency and amplitude of the emitted wave match the frequency and amplitude of the emitter. The frequency and amplitude of a sound wave, for example, matches that of the loud speaker. Why don't quantum interactions obey the same rules? Bohr’s principle of complementarily highlights this mystery. It states that the energy drop within an quantum system corresponds to the frequency a classical system as would the two sides of a coin. This principle is a paradox that resolved nothing.

In 1989, Stanley Pons and Martin Fleishman discovered the process of cold fusion. They found that the reaction had a positive thermal coefficient. It was later discovered by Professor Yoshiaki Arata, and others, that the reaction took place in a domain of 50 nanometers. The product of the thermal frequency and the domain size equals a velocity of one million meters per second.

Eugene Podkletnov stimulated a one third of meter spinning superconductor with a three megahertz radio wave. This experiment was said to have produced a strong gravitational anomaly. The product of the one third of meter dimension and the three megahertz radio wave also equaled a velocity one million meters per second.

Frank Znidarsic discovered that these experiments had disclosed a hidden natural constant. The velocity of the quantum transition ( 1.094 million meters /second ) was revealed. He has applied this idea to the process of photon emission. He has shown that the process of photon emission is an affect of the transitional quantum state.

A quantity of electromagnetic energy is transferred from the stationary quantum state to the photon by the way of the transitional quantum state. This state is characterized by its velocity 1.094 million meters per second. This velocity is associated with a frequency and a wavelength. The frequency is that of the emitted photon. The wavelength, in association with an electrical charge, sets the energy of the photon. The simultaneous emergence of these two properties reconciles the duality of matter and waves.

A photon experiences capacitance through its geometry. A flat plate capacitor was used to estimate the capacitance of the transitional photon. This capacitance is that of a capacitor of a dimension of one wavelength squared is given below.

C = eo AREA / l

The area swept equals the wavelength l of the photon squared. The distance between the plates equals one wavelength. The photon has two modes of vibration that exist at right angles to each other. The geometry resembles an open ended box. The equation above was multipled by two in order to include both modes. The result was expressed below. The capacitance experienced by a photon is:

C = 2 eo l2 / l

C = 2eo l

Again energy flows at the transitional velocity as given below.

f l = 1.094 x 106 meters/second

The frequency f of the transitional quantum state is that of the emitted photon.

Substituting produced relationship between the capacitance and frequency of the transitional state. This substitution sets the velocity of the photon equal to that of the transitional quantum state.

C = 2e0 ( 1.094 x 106 / f )   farads

The energy contained by an electric charge of one at the transitional capacitance is expressed below:

E = (˝) Q2 / C   joules

This capacitance of the photon was placed into the formula for the energy of a capacitor. The resulting relationship described the energy of the emitting transitional quantum state.

E = [ Q2 / ( 4 e0 1.094 x 106 ) ] f   joules

The result within the brackets [ ] equals Planck's constant in joules-seconds. Planck's constant was substituted for the quantity within the brackets. Planck’s photoelectric relationship was produced. This relationship describes the energy of the emitted photon.

E = hf   joules

The frequency of the photon, like all other waves, is that of the emitter. This emitter is the transitional quantum state. This transition quantum state is described by a velocity of 1.094 mega meter per second.

The photon's energy is fixed by an interaction between the wavelength of the transitional quantum state and the field of an electric charge. These affects reconcile the duality of matter and waves.


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THE ATOMIC ENERGY LEVELS

Note: This is the most important section in the most important chapter.

Maxwell’s electromagnetic theory predicts that accelerating electrons should continuously emit electromagnetic radiation. Bound electrons experience a constant centripetal acceleration, however, they do not continuously emit energy. An animation has been provided below that illustrates the mechanics of a the transitional quantum state. A wave is shown propagating along through a series of masses at the transitional velocity. Given that the mass is invariant, the spring constant must be equivalent for all modes that propagate at velocity Vt. Modes of propagation are carried by the gravitomagnetic, electromagnetic, and nuclear spin orbit fields. Contemporary theory assumes that the gravitational force is always weak and ignores it. This is a fundamental mistake. During transition, gravitational flux quickly flows between the parent and daughter states. This rapid flow progresses by the way of a strong electromagnetic and strong local gravitomagnetic interaction.


ENERGY IN TRANSITION


This author’s theorem, “The constants of the motion tend toward the electromagnetic in a Bose condensate that is stimulated at a dimensional frequency of 1.094 megahertz-meters” describes the velocity of the transitional atomic state. The forces interact strongly and at range during transition. The energy levels of the atom are effects of the transitional interaction. The velocity Vt was observed in gravitational and cold fusion experiments. The velocity is associated with the phonons in these materials. The quantum condition is a classical affect of the propagation of sound through the nucleus. The observed velocity of sound in these systems is expressed below.

Vs =1,094,000   million meters per second

Just as protons couple strongly with the speed of sound electrons couple strongly with the speed of light. The characteristic impedance of the two systems is aligned at the point where these two velocities match. The points of matching impedance establish the spin of the electron and the quantum condition.

The elastic constant of the electron was found to be [ 29.053 Newtons / rx ]. The elastic constant is associated with the simple harmonic motion of the electron. The electron vibrates, in simple harmonic motion, at its Compton frequency (or a factor of n less). Simple harmonic motion is a function of the mass the elastic K constant and the M-eof the system.

The elastic constant of the electron, the mass of the electron, and the displacement at the electrons classical radius were used to express the velocity of light Vl around the elastic discontinuity of the electron (below). Harmonics n of the fundamental frequency exist.

Vl = n w rp

Vl = n[ K-e / M-e ] 1/2 rp

Vl = n [ ( 29.053 / rx ) (1 / M-e) ] 1/2 rp

[Graph]

The velocity of light in the electronic structure was set equal equal to the velocity of sound within the nuclear structure. This qualification describes channels of matching impendence. Energy is flows away from the grip of the discontinuity rp through these channels. Other modes of vibration exist, however, they are evanescent.

1,094,000 = n[ ( 29.053 / rx ) (1 / M-e) ] 1/2 rp

Solving for rx produced the radii of the hydrogen atom.

rx = ( n2 ) [ 29.053 (rp)2 / { ( 1.094 x 10 6 ) 2   M-e } ]

The quantity within the brackets [ ] equals the radius of the hydrogen atom.

rx = n2 (.529 x 10 -10) meters

The result rx equals the radii of the hydrogen atom.

Energy transits across the atomic states of the elements through channels of matching impedance. This is the a-priory principle of the quantum condition. This impedance match is characterized by matching of velocities within the hydrogen atom, the photon, and the active areas within cold fusion. States of matching impedance across systems with differing elastic constants are characterized with velocities that are square root multiples of each other. This influence determines the energy levels in elements of higher atomic number Z. Impedance is qualified by the square root of the product of the elastic constant K and the mass M. The composite electric field of higher atomic number nucleons Z have an increased elastic constant ZK. The variable elastic constant of the orbiting electron (29.05/r) compensates by decreasing its radius (29.05/(rh+/Z)). This action matches the impedance of the interacting systems and accounts for the orbits within the atoms of higher atomic number.


Z1/21,094,000 = (n) [ ( 29.053 / rx ) (1 / M-e) ] 1/2 rp


The model may be extended to the energy levels of the muonic atom, as pointed out by Lane Davis, by substituting the reduced mass of the muon for M-e.

The energy levels of the atom exist as points of electromagnetic and gravitomagnetic discontinuity. This discontinuity is effect of the pinning action of discontinuity rp. A condition of energetic continuity exists where the impedance of the interacting system align. The points were qualified by setting the velocity of light equal to the velocity of sound. This resultant continuity and impedance match conveys energy away from the grip of the elastic discontinuity. This process is known as a quantum transition.




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Some additional parameters coming out of the analysis

Leni Hue of Harvard University has shown the the velocity of light in a Bose condensate is variable. Znidarsic has shown that when this variable velocity equals the velocity of sound with the nucleus the quantum transition progresses.

Some additional terms were extracted from this understanding. They are presented below. These constants will be employed in the next chapter to produce the Fermi distribution of electrons within the atom. They are listed below.

et = 1372 eo

The magnetic constant of the transitional quantum state equals:

ut = 4uo

The velocity of the transitional state was produced from these constants.

Vt = 1 / (et ut ) .5 = 1.094 million meters per second

The velocity Vt can also be described in terms of the transitional state's index of refraction. The electrical index of refraction is a property of a maximum of force.

Vt = c/ N

N= et1/2 ≈ 3p | 29.053 |

The equalization of the velocity of light within the electronic structure and the velocity of sound within the nuclear structure is the affect to pulls the motion constants together. The quantum condition emerges as a result of this effect.


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THE WEAK NUCLEAR FORCE

This author's work involves low energy physics. A fresh look into this field has shown that the state of a quantum system can be expressed in terms of a previously hidden set of parameters. An elementary look at the weak force, with the new set of parameters in mind, can provide additional insight.

The weak nuclear force interacts with both the strong nuclear force and the electromagnetic force. The weak nuclear force is not weak. It is very strong at a dimension 1/580 the radius of the proton. It equals the strong nuclear force at a dimension 1/580 the size of the proton ( rp ). It quickly diminishes and becomes weak at the dimensions of the proton. It is 1 x 10-5 times weaker than the electromagnetic force at the surface of the proton. During the process of beta decay the electromagnetic, and nuclear forces interact strongly. How does this happen? The Weinberg-Salam theory states that an intermediary does the trick. This intermediary is the W particle. The electromagnetic and nuclear forces interact strongly with the W particle. The gravitational force is ignored. This strong interaction allows the Beta decay to proceed.

The process of beta decay is a quantum transition. This author's megahertz-meter theorem describes the process of quantum transition. According to this theorem, vibration at the dimensional frequency 1.094x106 hertz-meters places the natural forces within a reactive state. The megahertz-meter relationship for non-centric forces is expressed below.

l Fp = 1.094 x 106 hertz-meters

The megahertz-meter relationship expresses a relationship between the displacement of the weak force and its frequency of energetic accessibility.

(2 rp / 580 ) Fp = 1.094 x 106 hertz-meters

Solving the above equation for frequency yields.

Fp = 580 ( 1.094 x 106 ) / 2 rp

Fp = 2.27 x 1023 hertz

The result Fp is the Compton frequency of the proton. The weak component of the neutron vibrates naturally at its Compton frequency. This vibrational frequency is a point within the megahertz-meter relationship. The vibration of a nucleon at this dimensional frequency provides energetic access to the weak force structures within the nucleons. This point of vibration is internal to a nucleon and acts to establish the transitional velocity within the hydrogen atom. The hydrogen atom contains only a proton and the transitional velocity is not established through the interaction of adjacent nucleons. The validity of this author's low energy transitional model is eclipsed by other emergent properties at energies higher that that of these low energy weak effects.

The electromagnetic force participates in the Beta transition. The electromagnetic transition is also mediated at the dimensional frequency of one megahertz-meter. The megahertz-meter relationship for centric forces is expressed below.

2 p Fe l = 1.094 x 106 hertz-meters

The megahertz-meter relationship expresses a relationship between the displacement of the classical electron and its frequency of energetic accessibility.

(2 p rp ) Fe = 1.094 x 106 hertz-meters

Solving the above equation for frequency yields.

Fe = ( 1.094 x 106 ) / 2 p rp

Fe = 1.236 x 1020 hertz

The result Fe is the Compton frequency of the electron. The Compton frequency of a nucleon is 1836 times greater the Compton frequency of the classical electron. The transitional quantum state vibrates at a single dimensional frequency. The quantum transition cannot proceed under this condition. The energy of the W particle tends to stretch out the weak nuclear force. The displacement increases until the weak nuclear force experiences the displacement rp The weak nuclear force also experiences an elastic maximum. This maximum was determined from the Compton frequency of the nucleons and the formula of simple harmonic motion.

Fc = [ K / Mp ] 1/2 / 2p

2.27 x 1023 hertz = (1/2p) [ fmax / ( rp Mp ) ]1/2

Solving for fmax yields:

fmax = ( 2p )2 ( 2.27 x 1023 ) 2 2 rp M+p

fmax = 9.58 x 10 6 Newtons

The force applied through the diameter of the proton yields the mass of the W particle. Its mass is about 90 times that of the proton.

Mw = ( 9.58 x 10 6 Newtons ) ( 1.409 x 10-15 meters ) / c2 = 1.5 x 10 -25 Kg

The energy of the W particle stretches the weak nuclear force out the radius of the proton. The process equalizes strength of the forces at the edge of the proton. The weak nuclear, strong nuclear, and electromagnetic forces all vibrate at the Compton frequency of the the electron. The natural forces are adjoined with the megahertz-meter relationship at this frequency. The motion constants associated with the four natural forces converge. This process produces a strong reaction involving all of the natural forces. This process affects the decay of the neutron and the decay of the Muon.

The proton is stable. Its radius is locked at rp. The neutron is slightly smaller than the proton. Its geometric capacitance is not a quantum of capacitance. Its state is not solidly locked. The isolated neutron decays in about 15 minutes. Neutrons that are accompanied by protons are more stable. How does this arrangement lock the state? Is binding energy extracted from the neutron? Does the loss of binding energy increase the radius of the neutron to rp? Does the expansive electrical force of high Z elements stretch out neutrons to rp? It the stability of the muon is affected in the same way? I did an analysis of the Fermi levels in the electron in chapter 12. There must be a similar arrangement for the nucleons. I have not tried to qualify it.


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THE PROBABILITY OF ALPHA DECAY



Both this author's model and the standard model state that the height of the coulombic potential wall is determined by the isotropic capacitance of the nucleus. The standard model then backs away and implies that the height of the coulombic potential wall is fixed. According to the standard model an alpha particle escapes the nucleus by tunneling through the coulombic potential wall. This author universally embraces the idea that the height of the potential wall is determined by the isotropic capacitance of a quantum system. During a quantum transition, the isotropic capacitance of the system is determined by the state inside the nucleus and the state outside the nucleus. The individual states are condensed into a system through stimulation at a dimensional frequency of one megahertz-meter. The capacitance of the entangled quantum ensemble exceeds the capacitance of the sum of its quantums. ( ref chapter 12 Pg. 7 ) The increased capacitance lowers the height of the potential wall allowing an alpha particle to pass over it. Willian of Ockham came up with the idea that the solution with the least number of entities is correct. Both Znidarsic's and the standard model produce the same result. Znidarsic's process is simpler. It does not require the process of tunneling. Ockham would like it. 23 This author's method produces a testable result. In a macroscopic vibrationally stimulated Bose condensate the capacitance experienced at the potential wall equals the isotropic capacitance of the bulk quantum system. The stimulation of a quantum system at the dimensional frequency of one megahertz-meter greatly increases the probability of transmutations that are mediated by the strong nuclear force.


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A NOTE ON HOT FUSION

The hot fusion community understands the concept of the isotropic capacitance of the nucleus. They keep the electrostatic potential of the nucleus low by selecting nucleons with only a single electrical charge. They reduce the potential produced by this charge by selecting isotopes with the greatest size. This larger size of hydrogen's deuterium isotope increases the isotropic capacitance of the nucleus and lowers the height of the electrostatic potential barrier. At this point they abandoned the concept of capacitance and smashed deuterons together for 50 years. They failed to understand that capacitance is not a local phenomena. The height of the electrostatic potential barrier is influenced by the geometry of the system. For example, an electron within a conducting sphere experiences the isotropic capacitance of the entire sphere. The nucleons within this sphere do not experience this capacitance because they are not free to move about. The cold fusion community has shown that the mobile nucleons within proton conductors do experience the isotropic capacitance of the quantum system. They normally do not fuse because their velocity is very low. Forced diffusion experiments conducted by Mitsubishi Heavy Industries in Japan have produced anomalous nuclear reactions. 19. These experiments introduced velocity into the system. The velocity is great enough to overcome the reduced potential barrier of the mobile protons.

The stimulation of a proton conductor at a dimensional frequency of one megahertz-meter introduces superconductivity into the system. The strong, weak, electromagnetic, and gravitational forces participate in the superconductive condensate.


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THE NATURE OF THE CONDENSATE

A familiar condensate is water vapor on glass. Clouds are seeded with alum in order to condense water vapor into rain. Electrons can also condense. A condensate of electrons known as a Bose condensate. Electrons condense to form superconductors and superfluids. Electrons also condense around a bonding agent or seed. One such seed is the vibration of a crystal lattice. These vibrations are known as phonons.

"The results we found provide the first direct evidence for a significant and unconventional role of phonons in the high temperature superconductivity, meaning that all the reasons that have been used so far to disregard the importance of phonons are not valid anymore."
Prof. Alessandra Lanzara, Lawrence Berkeley National Laboratory, Nature July 8, 2004
It is also believed that electrons can be made to condense around the photons of intense light.

Electrons have a natural state of vibration known as their Compton frequency. This author has shown that this Compton frequency can downshift. The downshifted Compton frequency is described by the 1.094 megahertz-meters relationship. A pair of electrons can condense around this downshifted Compton vibration. The spins of the two condensed electrons cancel out. The resultant amplitude of vibration, at the dimensional frequency of 1.094 megahertz-meters, is zero. The amplitude of vibration at the dimensional frequency of 1.094 megahertz-meters determines the probability of transition. The probability of transition drops to zero. The electron pair no longer exchanges quantums of energy with lattice. The system enters into a state of superconductivity. The electromagnetic motion constants are strongly affected by the superconductive state.

Wolfgang Ketterle, Eric Cornell, and Carl Weiman extended the domain of the condensate at temperatures near absloute zero. This effort produced a Bose-Einstein condensate. The author takes another approach. He extends the domain of the condensate by increasing the strength of the phonons that bind the condensate. The application of an external vibration at the dimensional frequency of 1.094 megahertz-meters forces the electron pairs to strongly interact with each other. The system enters into a state of hyper-conductivity. The electromagnetic, gravitational, and nuclear motion constants are strongly affected by the hyper-conductive system.

A normal conductor conducts electrons. The hydrides of certain metals conduct protons. For example, an applied voltage will drive dissolved hydrogen and deuterium through a palladium wire. The mobile deuterons act on fixed electrons to form a condensate ( inverse Bose condensate ). The low velocity associated with thermal nucleons permits the state to condense at room temperatures. This condensation occurs at a specific frequency. It is a hyper-conductive state. The product of the cluster size and the stimulation frequency is one megahertz-meter. It helps if the plasma's natural frequency matches the frequency of the downshifted Compton wave. The nucleus participates in the condensation. Low-level nuclear reactions proceed. 11, 20


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STATISTICS

A new understanding can be gleaned through the recognition that Planck's and Znidarsic's constants represent the same phenomena. Planck's constant is expressed in units of angular momentum. Znidarsic's constant is expressed in terms of a dimensional frequency.

Znidarsic's constant of 1.094 meters / second is equivalent to a spin 1/2 state in Planck's system of units.

Angular momentum of spin 1/2 state = h/4p

The distribution of the electrons within the atom is determined from the Newtonian parameters of mass, elasticity, elastic limit, and bounce. Elastic energy is exchanged to and from kinetic energy during a bounce. Electrons (all spin ˝ particles) contain one elastic discontinuity. There is no mechanism to stretch the electric field and kinetic energy cannot be stored elastically. These particles cannot bounce and must move along paths of matching impedance. Spin two particles contain two elastic discontinuities. Kinetic energy is stored elastically as these discontinuities tug at points within the electrical field. These particles bounce and do not need to follow paths of matching impedance. Like a bouncing ball, spin two particles bounce away their energy and tend accumulate in lowest energy state of the system.




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CONCLUSION

Superconductivity affects the electromagnetic motion constants. The nuclear and gravitational forces can be strongly coupled to a superconductive system through the action of shock. The frequency of the required shock depends on the geometry of the superconducting structure. The nuclear and gravitational motion constants are strongly coupled to Bose condensate that is stimulated at a dimensional frequency of 1.094 megahertz-meters. The stimulation lowers the quantum elasticity of the condensate. The reduced elasticity is expressed in several ways. The stiffness of the leptonic and baronic fields are reduced. The Compton frequency of matter downshifts. The range of the force fields tend toward the length of the superconductor. The constants of the motion tend toward the electromagnetic. The affects are those of the transitional quantum state.




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NOTES 


 1.  G. Miley "Nuclear Transmutations in Thin-film Coating Undergoing
     Electrolysis" Second Conference on low Energy Reactions

 2.  "Additional Evidence of Nuclear Emissions During Acoustic Cavitation” 
      Physical Review E, March 2003


 3.  E. Podkletnov and A.D. Levi,  "A Possibility of Gravitational
     Force Shielding by Bulk YBa2Cu307-x  superconductor,
     "Physica C, vol 203 (1992),  pp 441-444


 4.   Dr. Harrald Reiss , "Weight Anomalies Observed During the Cool-Down of High Temperature Superconductors"
      Physics Essays, Vol 16, No. 2 June 2002       

 5.  M. Agop, C. Gh. Buzea, and P. Nica, St. Moara de Foc, Romania 
     "Local Gravitoelectromagnetic Effects on a Superconductor."
     Physica C

	
 6.  Ning Li   and D.G. Torr, 1992, 
     Physical Review B, vol 46 #9,  
     "Gravitational effects on the magnetic attenuation of superconductors"


7.  Frank Znidarsic, Infinite Energy, Issue 22, 1998,  page 60 
     "Force and Gravity"


 8.  Jed Rothwell, Infinite Energy,  Issue 29, 1999,  page 23.
     "50 nano-meters ..is the magic domain that produces a detectable cold fusion reaction"


 9.  Y. Arata, H. Fujita, Y. Zhang: Intense deuterium nuclear fusion of 
     pycnodeuterium-lumps coagulated locally within highly deuterated 
     atom clusters, Proceedings of the Japan Academy, Vol.78, Ser.B, No.7 (2002)


 10.  A. Takahashi: Drastic enhancement of deuteron-cluster fusion 
     by transient electronic quasi-particle screening, Proc. JCF4, The 4th 
     Meeting of Japan CF-Research Society, paper JCF4-21, Morioka Japan, 
     October 2002


 11.  V. A. Vdovenkow, Lanl-L preprint archinge cond-mat 003190,  
      http://xxx.lanl.gov/abs/cond-mat/003190 
      Moscow State Institute for Radio Engineering
      reports on a vibrationally reinforced Bose condensate


 12.  Carreyre, Physical Review C, 1 Sept.  2000


 13.  Kishimoto, Physical Review Letters, 28 Aug. 2000 


 14.  Znidarsic F. "The Constants of the Motion"   
      The Journal of New Energy, Vol. 5, No. 2 September 2000


 15.  Abrahamson, J., and J. Dinniss. 2000. 
      Ball lightning caused by oxidation of nanoparticle networks from normal
      lightning strikes on soil. 
      Nature 403 (Feb. 3):519. 

 16.  Dennis Letts and Dennis Cravins 
      Laser Stimulation of Deuterated Palladium
      Infinite Energy  Vol 9 Issue 50 2003 

 17.  Reifenschweiler, Otto 1994
      Reduced Radioactivity of Tritium in Small Titantum Particles"
      Phys,  Lett. A, 184, 149 1994

 18.  S. Szpak   SPWAR Systems Center San Diego 
      Thermochimica Acta 410 (2004) 101-107

 19.  http://www.newenergytimes.com/ICCF10/HigashiyamaOsakaReplicationIwamuraMHITransmutation.htm


 20.   Zackary Fisk, "Heavy Fermion Superconductivity"  FSU University
       http://www.physics.fsu.edu/PhysicsNewsletter/Spring00/Jernigan.htm 


 22.  Tajmar, M., and de Matos, C.J.
"Gravitomagnetic Field of a Rotating Superconductor and Superfluid", submitted to Physica C (also Los Alamos gr-qc/0203033)

 23.  Supersolid seen in lab.  Potential barriers are eliminated by non-local interactions.

http://physicsweb.org/articles/news/8/1/6



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Appendix sample calculation

given:
h = Planck's constant = 6.6 x 10 -16 ev/sec
g = The density of the dissolved hydrogen. = 10 28 -e/m 3 ( about 10 22 -e/cm 3 )
n = 1
L = The diameter of the condensate = 50 x 10 -9 nm
c = 3 x 10 8 m/s
Z = 1/2

Total_energy = ( g * L 3 ) n* h* Z*c / (137*L)

Total_energy = 18 kev

The kinetic energy levels, in a vibrationally stimulated Bose condensate, are partitioned. The levels are about 18 keV apart. The levels are nuclear in magnitude.



Since Nov 2005 this page has been called times.


Additional reading. Anomalous heating produced with gold nanoparticles.

http://www.physorg.com/news63003999.html

"Superconductors have no need to be negative"

http://www.newscientist.com/article/mg18624984.400-superconductors-have-no-need-to-be-negative.html



// End of chapter 11.............