##**Znidarsic, Franck P.E, PART 3**:

# **CHAPTER 9, THE STRUCTURE OF THE UNIVERSE**, http://www.angelfire.com/scifi2/zpt/chapter9.html

**INTRODUCTION **

Aristotle’s believed that the earth lay motionless at the center of the universe and that the heavens revolved around this center. Aristotle’s system could explain some of the motions observed in the night sky, however, it could not explain them all. In the second century A.D., Claudius Ptolemy tried to explain the observed anomalies by placing additional eccentrics and epicycles into Aristotle’s model. This refined system is known as the Ptolemaic system.

http://www.angelfire.com/scifi2/zpt/PtolJav.html, (Java annimation) Pick the link to view the Earth centered Ptolemaic Universe.

The Ptolemaic system, in spite of these modifications, still could not explain every observed phenomena. In 1543 a new perspective of the universe was proposed by Nicolas Copernicus (1473-1543). 1 Copernicus proposed that the sun lies at the center of the universe. This idea was opposed by the Roman Church authorities. These authorities believed that man was the centerpiece of the creation and as such he resides at the center of the creation. 2

Galileo invented the telescope in 1609. With his telescope, Galileo provided strong evidence that the earth revolved around the sun. Galileo proclaimed that Copernicus was correct and that the sun did lie at the center of the universe. This greatly angered Church authorities. These authorities sentenced to Galileo to house imprisonment and forced him to;

** “Abjure, curse, and detest the said heresies and errors!” **

It was too late. The evidence was out, and even the Church authorities could not prevent the spread of the information. By the 18 Century it became generally accepted that the sun, not man, lies at the center of the universe.

In 1785 German-born English astronomer William Herchel (1738-1822) suggested that the stars were arranged into the shape of a lens. This collection of stars is known as the Milky Way Galaxy. Herchel discovered that the sun did not lie at the center of this collection of stars. It became clear to all but the most naive that man held no special position in the cosmos.

In the 1920’s astronomers Herber Doust Curtis and Edwin Powell Hubble discovered that the Milky Way galaxy was just one of an immense collection of galaxies. Using the 100 inch telescope at Mount Wilson Observatory in California, Hubble discovered that the Milky Way Galaxy seemed to lie at the center of this collection of Galaxies. Were the early church authorities correct and did man reside at the center of the cosmos? Earlier observations revealed that man held no special position in the universe. Observations made on the largest scale, however, seemed to indicate that the earth was at the center of the universe. How can this be?

**THE FOUR DIMENSIONAL STRUCTURE OF THE UNIVERSE **

To make some sense out of this paradox, the cosmological principle was invented. This principle states that there are no special positions in the universe. According to this principle all positions in the universe are equivalent. The view from any location in the universe is one from the center.3For example, if you traversed great distances in a space ship, you would always appear, from your vantage point, to be at the exact center of the universe. You would never venture from the exact center no matter how far you traveled. The edge of the universe would always be out of reach.

Some illumination about the nature of this paradox can be gleaned from the study of dimensions. Victorian schoolmaster Edwin Abbott Abbott published Flatland in 1884. Flatland is the story of a square who takes a trip into higher dimensions. This story is very instructive. A brief review is in order. A point has zero dimensions A line has one dimension. A slice through a line produces a a point. A line has one dimension and a circle has two. A slice through a circle forms a line. A sphere has three dimensions and a circle has two. A slice through a sphere forms a circle. Continuing with this logic, a hypersphere has four dimensions. Any slice through a hypersphere forms a sphere.4

http://www.angelfire.com/scifi2/zpt/images/dimen.gif Pick the link to view slices through structures of various dimensions.

Any slice through an object of n dimensions produces an object of n-1 dimensions. The earth is a three dimensional object. Its surface is a two dimensional slice of a three dimensional object. A sailor on the ocean gets a two dimensional view of the three dimensional earth. He sees water all around. No matter where he travels, his view is always one from the center of the ocean (when there is no land in sight). The sailor has a lot in common with the space traveler. They both have a view from the center. The universe is a four dimensional hypersphere. Three of these dimensions are of space, the fourth is of time. We live on the surface of this hypersphere or, in other words, we live in the present. Like the sailor, no matter how far we travel we stay on the surface (the sailor remains on the surface of the ocean and we remain in the present) and our view remains one from the center. Look up in the night sky. You will see stars many light years away. You are viewing the stars as they were. You are looking though a hypersphere into the past. A view from a telescope reveals the edge of the universe is equally distant (15 billion light years away) in all directions. Many scientists believe this central view results from the four dimensional construction of the universe. To me its amazing.

**THE GRAVITATIONAL LINKAGES CONNECTING THE UNIVERSE AND ACCELERATING MATTER **

Electrons are very much smaller than common electrical circuits. Induced electrical fields exchange energy and momentum between electrons and the vastly larger electrical circuits in which they flow. The momentum of a moving charge is carried by the magnetic field that surrounds the charge “I”. The kinetic energy imparted to an accelerating charge is carried by an induced electrical field “E2”. The induced electrical fields determine how electrons interact with the larger electrical circuit.

http://www.angelfire.com/scifi2/zpt/images/fields.gif

Similar gravitational linkages exchange energy between the universe and accelerating matter. The momentum of moving matter is carried by the gravitomagnetic field “Ig” The kinetic energy imparted to accelerating matter generates an induced gravitational field “E2g”. This gravitational field induced by acceleration carries a momentum opposite to that of the accelerated matter. This field propagates outward and eventually transfers this momentum to every bit of matter in the universe. An equal and opposite force is eventually imposed upon the universe.

**Force _{universe} = – Force _{local}**

Equation #1 The universe reacts to local acceleration.

The relationship between force and gravity is given by General Relativity and was derived in Chapter 6 of this text. This relationships has yielded many answers. Substituting the general formula of gravitational induction into Equation #1 yields Equation #2. The right side of Equation #2 represents a local force. The left side of Equation #2 represents the force that is imparted to the universe by the induced gravitational field. This field (shown on the left side of Equation #2) is produced by the acceleration of a local mass. The local acceleration force is expressed as the change in momentum with respect to time (dp/dt).

**G / (c ^{2}r) (M_{u}) (dp/dt) = (dp/dt)**

Equation #2 The gravitational linkages that couple local events to the universe

If Equation #2 is correct then Equation #3 must equal one.

**G / (c ^{2}r) (M_{u}) = 1**

Equation #3 Does it equal one?

Given:G = 6.67 x 10^{-11} new-m^{2} / kg^{2}

M_{u} = 2.0 x 10^{53} kg

The radius of the universe “r” = 1.42 x 10^{26} meters ; c = 3 x 108 meters/ second

Against all odds, given the tremendous magnitude of the numbers involved, Equation #3 does equal one. The relationship between force and gravity has once again revealed another secret of the universe. It has been demonstrated that gravitational linkages couple local events to remote regions of the universe. This coupling is accomplished through the introduction of additional forces. These additional forces act as a reservoir of momentum and energy. This reservoir stores energy and momentum until it can be transferred to distant regions of the universe. Local positive energy is linked to the negative gravitational potential of the universe through an interplay of transient interactions. These interactions enable a week long range force, like gravity, to immediately exchange a significant amount of energy.

**CONCLUSION **

On the largest scale the universe has a four dimensional structure. Gravitational linkages exchange energy and momentum within this this structure. This exchange of energy and momentum links local events to the whole of the universe. Energy, momentum, and changes in entropy are coupled to the universe through gravitational linkages. The four dimensional structure of the universe itself is a manifestation of the gravity that binds it together. Time itself flows as a result of energy passing through the structure of the universe.

**NOTES **

**1.** De Revolutionibus Orbium 1543

**2.** The concept that the universe requires man in order to exist is called the antropic principle.

**3.** The isotropy of the universe was first discovered by Edwin Hubble

**4.** The Fourth Dimension Rudy Rucker 1984 Houghton Mifflin Company Boston Mass

// end of chapter 9 …………………………………………………………………

# **CHAPTER 10, THE ELASTIC LIMIT OF SPACE ** http://www.angelfire.com/scifi2/zpt/chaptera.html

**INTRODUCTION **

The idea that a force that imparts structure to the material world has been around since antiquity. Some of the earliest references to this idea are found in the Hindu scriptures. These scriptures were originated by the ancient Indus Valley civilization at about 3,000 BC. The concept of the Brahman is described in these scriptures. The Brahman is the basis of the material world, the force that holds all things together, and the hidden power that is latent in all things.

Later references to this concept were developed in ancient Greece at about 500 BC. The Greek philosopher Heraclitus spoke of the concept of the Logos. According to Heraclitus the Logos is the source of all order. This source of order is hidden in a deeper reality. Heraclitus believed that seeing this deeper reality is reserved only for the Gods and for those few humans who can escape conventional modes of understanding.

The concept of the Logos was taken up by Philo, a central figure in Judaism, at about 10 AD. Philo concluded that the Logos was the divine power that mediated the universe. To Philo the Logos was the mind of the universe.

In the 19th century Thomas Young, who discovered the wave nature of light, described an ether. Young’s ether is the medium in which light travels and matter rests. This ether fixes the speed of light and sets the elementary constants.

Throughout recorded history the concept of a force that gives form and function to the material world has been described by philosophers, theologians, and scientists.

In 1887 the Michelson Morley experiment failed to detect Young’s ether. Since that time the concept of an ether has been abandoned by the scientific community. The abandonment of the concept of an ether has resulted in an atomic information crisis. All atomic and sub-atomic particles are identical to other particles of the same type. For example each elementary particle “knows” how much to weigh, how fast to vibrate, and how fast to spin. Without a force that exchanges information, how do elementary particles “know” what to be? If elementary particles are not restricted to definite states of being (quantum states) the universe would be without order.

Present quantum theory does not embrace the idea that an external source of information determines the quantum states. Claude E. Shannon developed the science of information in 1948. Shannon showed that information is a measurable commodity. 1 As a commodity, information can only be obtained through a communications channel. Hans Christian Von Baeyter writes, 2

** ” ..in the last two decades physicists have finally realized what they should have understood long ago – that classical mechanics is almost always chaotic…Indeed, it has been proved quite generally that chaos cannot exist in a quantum mechanical system…” **

Astronomers reading spectral lines with the help of telescopes have found that all elementary particles (of like types) in the universe are identical. A long range communications channel or exchange force eliminates chaos (the natural tendency of a system) from quantum systems. This communication channel sets the standard of being for every elementary particle within the universe. A mathematical analysis will now be presented. This analysis develops the concept of the elastic limit of space. It will be shown that a limit of elasticity acts as a quantum communications channel.

**Reflections **

Reflections take place when the impedance, of the medium through which the wave travels, changes. For example, on the rear of many television sets there is a matching transformer. (It looks like a little barrel.) This transformer matches the coaxial cable’s 75 ohms impedance to the 300 ohm impedance of the television’s twin lead antenna wire. This matching transformer prevents the television signal from being reflected at the point at which the two cables, each with a different impedance, connect. All reflections, including the one of yourself in a mirror, result from a change in impedance. The reflection of mass energy at the surface of matter is also due to a drastic change in impedance.

Reflections occur when the impedance of the medium, through which the wave travels, changes. Impedance is expressed in units of ohms. The impedance of a mechanical wave is given by equation #1.

**Impedance = (MK) ^{1/2}
Equation #1 the impedance of a mechanical system **

M = mass ; K = The spring constant

The same laws of simple harmonic motion apply to all waves. Transmitters send out electromagnetic signals. These signals are traveling waves of energy. These waves have an impedance associated with them. The electrical impedance in ohms is given by Equation #2.

**Impedance = (L/C) ^{1/2}
Equation #2 The impedance of an electrical system**

L = inductance ; C = capacitance

A variation in the ratio of inductance to capacitance results in a change in characteristic impedance. This variation reflects waves.

Mediums convey waves of many different frequencies. For example, a coaxial cable can pass many different channels. The inner and outer conductors of a transmission line form a continuous capacitor. Electromagnetic waves passing through the line will intersect a certain segment of this continuous capacitor. The wavelength of the energy passing through the line determines the length of the segment intersected. A segment of a certain length will have a specific value of capacitance and inductance. The values of inductance and capacitance that determine the impedance of a transmission both vary inversely with the frequency of the wave passing through the line.

http://www.angelfire.com/scifi2/zpt/images/coax.gif Pick the link to view an example of wave motion. Shows a wave traveling down a coaxial cable

This effect also holds the ratio of capacitance to inductance constant. No reflections take place in this constant impedance environment.

Stray capacitance is a phenomena familiar to electrical engineers. The first radios were limited to low frequency operation because of the high value of stray capacitance inherent to the large vacuum tubes and components of the day.

http://www.angelfire.com/scifi2/zpt/radio.html Pick the link to view an example of the frequency of a technology.

As components were miniaturized, the stray circuit capacitance was reduced. The reduction of stray circuit capacitance allowed electronic circuits to operate at increasingly higher frequencies. Today’s miniature chips compute at frequencies which are higher than the frequency at which circuits, of just a few years ago, could oscillate at. Stray capacitance is not a phenomena which is limited to the components of electrical circuits. Everything in the universe is capacitively coupled to everything else in the universe. This coupling manifests itself as the minimum capacitance of a point. Electrical capacitance is equivalent to the reciprocal mechanical elasticity. The capacitance of a point expresses the elastic limit of free space.

The characteristic impedance of free space varies when the energy density of a field exceeds the ability of space to support the field. At higher energy densities space breaks down like a spring stretched beyond its limit. Matter forms when the intensity of field exeeds the elastic limit of space.

The displacement x in a mechanical system is conceptually equivalent to the reciprocal of the capacitance “1/C” of an electrical system. This relationship is exhibited by the following two equations.

force = -K x ; voltage = -(q)(1/capacitance)

The spring can be stretched until its material elastic limit is exceeded. The voltage associated with an electrial charge q can increase until space can no longer support the field. This author refers to this breakdown voltage as the elastic limit of space.

Capacitance expresses the aspects of geometry that are experienced by the electromagnetic field. All of the natural forces experience geometry. They do it in their own unique way. Capacitance expresses the effective geometry of a quantum system as measured by the electromagnetic force and experienced by the other forces.

**The quantum of capacitance and the rest energy of the electron **

The relationship between energy E, voltage V, and capacitance C is given by equation number 1.

E = (1/2) C V^{2}

Substituting the rest energy of the electron for E yields equation 2.

M_{-e}c^{2} = (1/2) C V^{2}

The relationship between capacitance and charge Q is given by equation number 4.

Q = C V

Substituting equation number 4 into equation number 2 yields equation number 5.

M_{-e}c^{2} = (1/2) q^{2}/C

Solving for C

C = (1/2) q^{2} / [M_{-e}c^{2} ]

Inserting the known value of the rest mass of an election, and setting the electric charge “Q” to one “q” yields the quantum of capacitance C_{q}. The electromagnetic force experiences the quantum of capacitance through a maximum of intensity.

———————

**C _{q} = 1.568 x 10 ^{-25} Farads : The quantum of capacitance **

———————

This equation was placed in a box. This was done to emphasize the importance of the equation.

**The quantum of capacitance and the nuclear radius **

The geometry of the proton determines the isotropic capacitance of the proton. The electromagnetic and the nuclear forces experience the geometry of the proton. The quantum of capacitance is a universal property. It is experienced by all of the natural forces. In particular, the geometry of the proton determines the isotropic capacitance experienced by the nuclear and electromagnetic forces. The quantum of capacitance and the electromagnetic force were employed to qualify this geometry.

The capacitance of a sphere = the quantum of capacitance

4pi e_{o}r = 1.568 x 10^{-25} Farads

Solving for r yields the classical radius of the electron. It is also the maximum radius of the proton. The strengths of electric and strong nuclear forces are equal at this displacement. The equalization of the strength of the forces makes this geometry accessable to both the electromagnetic and the strong nuclear forces.

r_{p} = 1.409 x 10^{-15} meters

The strong nuclear force experiences the quantum of capacitance through a maximun of displacement.

**THE GRAVITAIONOAL FIELD **

Energy flows through a series of cascading quantum transitions. The birth of the universe was a flow of energy. This flow of energy progressed through the process of quantum transition. Energy was conserved during the moment of creation. The positive energy of the universe was balanced by its negative gravitational potential. All quantum transitions conserve energy, however, the first transitions were different from the later ones. The first transitions established the positive energy of the universe. All subsequent quantum transitions have conserved this quantity of positive energy. Why did the principle of the conservation of energy change the way in which it is expressed? The gravitational field is weak. No gravitational discontinuities have been found within matter. The gravitational field flows freely between the various classes of matter. It is, however, bound to the positive energy of this matter. The negative gravitational potential of the universe is bound to the positive energy of the universe. This coupling expresses itself through a conservation of positive energy. This was not always the case. In the early universe the positive energy of the universe was in a state of transition. This transitional state, as other transitional states, was established through an equalization in the strength of the forces. The first transitional states were unique in that the strength of the gravitational force equaled the strength of the other forces. The gravitational coupling constant g expresses the ratio of the strength of the gravitational to the electric force. This force is measured between and electron and a proton.

Y = 2.27 x 10^{39}

The universe extends for 13.3 billion light years. This extent is expressed in meters.

E_{u} = 1.26 x 10^{26} meters

A relationship exists between the strength of forces, the classical diameter of the electron, and the extent of the universe. This relationship is expressed below. An explanation of the factor of 4p2 will be presented. A factor of 2p may an effect of the hyperspheric geometry of the universe. For example, the view of the earth is from the circumference of a sphere. The diameter of the earth is a factor of 2p less than the observed circumference. The view of the universe is from the circumference of a hypersurface. The diameter of the universe is a factor of 2p less than its observed extent. A second adjustment factor of 2p results from the fact the gravitational forces of the universe are non-centric and the electrical force of the atom is centric. The idea will be developed in Chapter 11.

Y = E_{u} / ( 2p)^{2} r_{p}

In the early universe the strengths of nuclear, electric, and gravitational forces were equal at a surface with a radius near the radius of the proton. The equalization of the strengths of the forces unlocked the negative gravitational potential of the early universe. The positive energy of the early universe fluctuated with its negative gravitational potential. The strength of the gravitational force diminished as the universe expanded. The negative gravitational potential of the present universe was crystallized by a disparity in the strength of the forces. The positive energy of the present universe was pinned to its negative gravitational potential by a change in boundary. This pining action affects the flow of energy within the universe. It establishes the conditions of energetic accessibility. The classical radius of the electron is also a condition of energetic accessibility. These geometries are related by a geometric factor (2p)2 and the ratio of the strength of the forces. Adjusted for these factors, each natural force experiences a similar elastic discontinuity. The displacement of the discontinuity establishes the geometry of energetic accessibility.

**The quantum of capacitance and the electronic Compton frequency **

The quantum of capacitance determines the Compton frequency the electron.

The force exerted by an electric charge at the elastic limit of space is:

Force = Q^{2} / ( 4pi e_{o}d_{p}^{2} ) = 29.05 newtons

d_{p} = the diameter of the proton = 2 (1.409 x 10^{-15} ) meters

The compressive forces exerted by the electric field are balanced by the tensile forces exerted by the leptonic field. These forces balance at an expansive displacement equal to the ground state radius of the hydrogen atom. The stiffness “K” of the electron was determined from this force and displacement length.

K = (max_force) / (radius_of_hydorgen) = 29.05 newtons / .529 x 10^{-10}meters = 5.48 x 10^{11} newton/meter

The Compton frequency of the electron was then determined from the elastic constant K and the mass of the electron.

Frequency = (1/2pi ) (K / mass_of_electron)^{1/2} = (1/2 pi ) [ 5.489 x 10^{11} newton/meter / 9.1 x 10 ^{-31}kg ]^{1/2}

Frequency = 1.236 x 10 ^{20} Hertz

The stiffness of the single electron is determined by the elastic limit of space and the electromagnetic force. The electron rings like a bell at its Compton frequency.

**THE ELASTIC LIMIT OF SPACE AND THE GRAVITY OF AN ELECTRON **

The general formula of gravitational induction as given by General Relativity and derived in Chapter 6 is given below.

Field = (G/c^{2}r)(dp/dt)

The gravitational field of matter is is given below.

Field = GM/r^{2}

The above two equations were set equal and solved for mass. The result is given below.

M = (r/c^{2})(dp/dt)

Substituting twice the nuclear diameter (1.409 x 10^{-15} meters) for r and the 29.05 newton force limit for (dp/dt) yields the gravitational mass of the electron. The mass of the electron is determined by the electrical force produced at the elastic limit of space.

M_{-e} = 9.1 x 10 ^{-31} kg

**THE ELASTIC LIMIT OF SPACE AND BETA DECAY **

The electron is to large to fit inside a neutron. During beta decay an electron and a anti-neutrino are ejected from a neutron. These particles are created from the available energy at the instant of decay. According to this author’s model the electron and the anti-neutrino are crushed by forces beyond their their elastic limit while inside the neutron. The force required to crush an electron beyond its elastic limit is 29 newtons. During beta decay the crushing force is released.

Mass = Energy / c^{2}

Mass = Force * Distance / c^{2}

A force is 29.05 newtons is applied through the diameter of the neutron [2 (1.409 x 10^{-15} meters) ].

M_{-e} = (29.05)(2) (1.409 x 10^{-15} meters) / c^{2}

M_{-e} = 9.1 x 10 ^{-31} kg

The mass of the beta electron is produced by the force exerted at the elastic limit of space.

**THE ELASTIC LIMIT OF SPACE AND ALPHA DECAY **

Current models of alpha decay describe an electrostatic potential wall around the nucleus. This potential wall has a limited height. The height of the nuclear potential wall as currently described in the texts is given below.

E = 1 / (4 pi e_{0}) ( Z^{2} / r )

For a single proton the height of the coulombic barrier is.

E = 1 / (4 pi e_{0}) ( e^{2} / 1.409 x 10^{-15} meters)

E = 1.64 x 10 ^{-13} joules

Expressed in electron volts.

E = 1.64 x 10 ^{-14} joules / ( 1.6 x 10^{-19}joules per ev) = 1.02 x 10^{+6} ev

This author contends that the height of the nuclear potential wall is determined by the elastic limit of space. The elastic limit gives the height in volts.

Volts = q / C

For a single nucleon the electric charge is q and C is the quantum of capacitance.

E = q / 1.568 x 10 ^{-25}

**E = 1.02 x 10 ^{+6} ev **

The agreement of the two results demonstrates that the height of the coulombic nuclear potential wall is determined by the elastic limit of space. The analysis my be extended to nucleons of higher atomic number by factoring in the charge and isotropic capacitance of the nucleus.

**CONCLUSION **

Each natural force is affected by the elastic limit of space. The gravitational force experiences it through the geometry of space and its weakness. The electrical force experiences it through a maximum in intensity. The strong and the weak nuclear force experience it through the geometry of the proton. The elastic limit of space is expressed by a quantum of reciprocal capacitance. The natural forces have vastly differing strengths, ranges, and motion constants. The elastic limit of space pins each of the natural forces into the structure of matter. The elastic limit of space determines many of the zero point properties of stable matter.

Conventional science looks to higher energies to find interesting phenomena. Many new phenomena are observed as fixed parameters thaw (become variable) at higher energies. This author has introduced a new parameter, the quantum of capacitance. The quantum of capacitance thaws at low energies. Understanding the affects produced by a changing quantum of capacitance will allow man to control all of the natural forces. This knowledge will produce a revolution in technology.

**NOTES **

-1- ” **A Mathematical Theory of Communication** “, Claude E. Shannon, Bell System Technical Journal #27, July 1948,

-2- Discover, November 1995, Page 109

-3- ” **Cosmological Antigravity** ” Lawrence M. Kruss, Scientific American, December 31, 2002, Pg 36, “The most recent analysis by our group puts the best-fit age of the universe at 13.4 billion years.”

-4- ” **Elementary Antigravity** “, Frank Znidarsic, Vantage Press, 1989, Pg 50 “13.5 billion light years”.

-5- ” **New Measurements of Ancient Deuterium Boosts the Baryon Density of the Universe** “, Songala and Tytler, Physics Today, August 1996

-6- Hal Puthoff, PHYSICAL REVIEW A, March 1989

Hal Puthoff, D.C. Cole, PHYSICAL REVIEW E, August 1993.

Hal Puthoff, OMNI, “Squeezing Energy From a Vacuum” 2/91

# **Chapter 11, THE PATH OF THE QUANTUM TRANSITION **, http://www.angelfire.com/scifi2/zpt/chapterb.html

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

**ABSTRACT **

The low level nuclear process 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 new understanding should dispel the disbelief and guide the development of many technologies.

**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.

Low level nuclear reactions have been identified through the measurement of their reaction products. The heat of the reaction has also been detected. It appears that the range of the strong nuclear force has increased to atomic dimensions.

http://www.angelfire.com/scifi2/zpt/sounds/constant.wav Pick the link to hear a quote from the lecture at the University of Illinois. File type wave. September 1999

http://www.angelfire.com/scifi2/zpt/images/zpe.gif A main point. Pick to view a chart that shows how the range of force interaction changes in a vibrationally reinforced Bose condensate.

The strong nuclear force extends beyond the Coulombic potential barrier, through the interatomic space, and to the neighboring nuclei. The Coumbic 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.

**THE VIBRATION OF A BOSE CONDENSATE **

Case and Arata have demonstrated that 50nm particles consistently produce 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 1×10^{14} 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

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 625 THz (.625 x 10^{15}Hz). The size of active area in the bubbles has a dimension expressed in nanometers. The product of the stimulation frequency and the bubble size is 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, 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 stimulation of a Bose condensate at the dimensional frequency of one megahertz-meter invites nuclear participation. The process is that of the quantum transition. The motion constants associated with the natural forces converge and the quantum transition proceeds.

**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. 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”.

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

**THE VELOCITY OF QUANTUM TRANSITION **

The standard model of physics does not describe the transitional 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 infinites 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. 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.

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 displacment. This extent equals the classical radius of the electron rp. For centric systems the quantum transition expresses itself through its circumferential velocity. A factor of 2 pi was incorporated to obtain circumferential velocity of the transitional state. The velocity of the quantum transition was derived, below, from this understanding.

Velocity = 2 pi F_{c} l meters/second

**Velocity = ( 2 pi ) [Mc ^{2}/h] ( 1.409 x 10^{-15} ) meters/second **

The result is **1.094 meters / second **. The velocity is that of the transitional quantum state.

http://www.angelfire.com/scifi2/zpt/stim.html Java Animation, “The Path of the Quantum Transition. ”

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 a mobile charge in a superconducting sphere equals the isotropic capacitance of the entire sphere. The electrical capacitance of a sphere is given by.

Cs = 4 pi e_{0} r Farads

The capacitance of a sphere one meter in diameter is:Cs = 1.113 x 10^{-10} Farads

The transitional quantum state expresses itself through the capacitance of a quantum system. The downshifted Compton frequency of the electron ‘Fc’ plays a central role in this expression. It was shown in Chapter 10that the Compton frequency of the electron is set by the elastic limit of space. The downshifted Compton frequency is determined by the isotropic capacitance of a quantum system. The downshifted Compton frequency of a quantum system is described by the dimensional constant of one megahertz-meter. Stimulation at this dimensional frequency tends to condense the interacting states. This condensed state is one of transition. The megahertz-meter relationship was derived, below, from this understanding.

**Fc = [Mc ^{2}/h][Cq/Cs][2pi r] 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-meteres 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 equals the strength of the nuclear force at a displacement equal to the classical radius of the electron r_{p}. Adjusted for strength the gravitational force also experiences a similar elastic displacement. This vibrational mode is an expression of the ground state energy of a Bose condensate. This vibrational mode may be externally reinforced in a macroscopic Bose condensate. The nucleus participates in the reinforced Bose condensation. The Compton frequency of the nucleus downshifts and the nuclear wavefunction spreads out. These affects induce unexpected low level nuclear reactions. 8

**THE PHOTO ELECTRIC EFFECT **

Light has amplitude associated with it. This amplitude is related to the frequency of the light. This amplitude is associated with the energy of a photon.

E = hf

This mechanics of this amplitude are a central mystery in modern physics. This author’s understanding of the process of the quantum transition has enabled him to unravel this mystery.

Local flux is pinned at a discontinuity. A discontinuity forms when the intensity of a field exceeds the elastic limit of space. The elastic limit of space is expressed in units of reciprocal capacitance. A photon is not pinned down. It does not experience the quantum of capacitance. It experiences capacitance through its non-divergent geometry. A flat plate capacitor was used to estimate the capacitance “C” experienced by a photon.

C = e_{o} AREA / D

The area swept equals the wavelength l of the photon squared. The distance between the plates equals the distance between the positive and negative peak of a sin wave. This distance is (Â½) wavelength. The capacitance experienced by a photon is:

The process of quantum transition is described by the dimensional frequency of 1.093 megahertz-meters. The relationship between the frequency and wavelength of the non-centric quantum transition is given by:

Substituting yields a relationship between the capacitance and frequency of a photon.

C = 2 e0 ( 1.094 x 10^{6} / f ) farads

The energy contained by a capacitor with a charge of one is given by:

E = (Â½) q^{2} / C joules

The capacitance of a photon was placed into the formula for the energy of a capacitor. The energy of a photon is expressed in terms of the geometry of the emitter.

E = [ q^{2} / ( 4 e_{0} 1.094 x 10^{6} ) ] 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. The energy of a photon is expressed in terms of the frequency of the emitted.

E = hf

The energy of a photon is set by the mechanics of the quantum transition.

Local fields are pinned at discontinuities. Discontinuities are produced when the intensity of a field exceeds the elastic limit of space. Photons are formed when bits of the local field break away. The motion constants converge during the breakaway interval. The breakaway interval is a quantum transition. The transition is described by a dimensional frequency of one megahertz-meter. The author was able to compute the energy of the photon from this understanding.

**THE ATOMIC ENERGY LEVELS **

MaxwellÂ’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 atomÂ’s electrons emit energy at discrete quantum intervals. The emission of such quanta can not be explained with any existing classical theory. 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 interaction. 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. The spring must be stiff enough to push the masses. The spring constant is equivalent to the strength of a force field. During the quantum transition gravitational flux, electromagnetic flux, and nuclear flux are passed from the parent to daughter states. This interaction requires the springs (strengths of the fields ) to be strong and equivalent.

This authorÂ’s theorem, Â“The constants of the motion tend toward the electromagnetic in a Bose condensate that is stimulated at a dimensional frequency of 1.094 megahertz-metersÂ” describes the velocity of the transitional quantum state. It reveals that the energy levels of the atom are established as a condition of electromagnetic and gravitational accessibility. The velocity of the macroscopic transitional state is expressed below.

The elastic limit of space sets a minimum in the displacement between the Compton undulations of the electron. It has been shown (in Chapter10 ) that this minimum of displacement r_{p} is equal to the classical radius of the electron.

r_{p} = ( 1.409 x 10^{-15} ) meters

The product of this displacement r_{p} and the transitional Compton frequency F_{t} determines the velocity of the transitional quantum state. Lengths of energetic accessibility exist at integer multiples n of length r_{p}. The velocity of the centric transitional state is expressed below.

( 2 pi n r_{p} ) F_{t} = 1.094 x 10^{6} hertz-meters

A solution yields the frequency of the transitional quantum state F_{t}.

F_{t} = 1.094 x 10^{6} / ( 2pi n r_{p} )

The frequency of the stationary electronic state is a function of its simple harmonic motion. The frequency of hydrogen’s ground state is the Compton frequency F_{c} of the electron. This relationship was developed in Chapter_10_Pg 11 and is expressed below.

F_{c} = [ K / M_{-e} ] ^{1/2} / 2pi

F_{c} = [ ( 29.05 / r_{h} ) (1 / M_{-e}) ] ^{1/2} / 2pi = 1.24 x ^{20} Hertz

Harmonics lengths rs exist at fractions m of the fundamental vibrational length r_{h}.

r_{s} = r_{h} / m

Substituting m r_{s} for r_{h} yields:

F_{s} = [ ( 29.05 / m r_{s} ) (1 / M_{-e}) ] ^{1/2} / 2pi

Setting the frequency of the transitional state F_{t} equal to the frequency of the stationary state F_{s} provides a simultaneous solution for r_{s}.

1.094 x 10^{6} / ( 2pi n r_{p} ) = [ ( 29.05 / m r_{s} ) (1 / M_{-e}) ] ^{1/2} / 2pi

Solving for r_{s} yields.

r_{s} = ( n^{2} / m ) [ 29.05 (r_{p})^{2} / { ( 1.094 x 10 ^{6} ) ^{2} M_{-e} } ]

The quantity within the brackets [ ] equals the radius of the hydrogen atom. Substituting the radius of the hydrogen atom for the quantity within the brackets yields the solution below.

r_{s} = ( n^{2} / m ) .529 x 10 ^{-10} meters

The outward centrifugal force on the electron must balance the inward electrical force. This condition holds when the constant m equals the atomic number Z. Substituting Z for m yields the radii of the atoms..

r_{s} = ( n^{2} / Z ) .529 x 10 ^{-10} meters

Setting n = 1 the above relationship yields the radii of the ground atomic states. The ground state radii are established through the action of an elastic discontinuity. The radii r_{s} of atomic states n are determined as conditions of energetic accessibility.

**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 is not weak. It is very strong at a dimension 1/560 the radius of the proton . It equals the strong nuclear force at a dimension 1/580 the size of the proton ( r_{p} ). 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 1.094×10^{6} hertz-meters places the natural forces within a reactive state. The megahertz-meter relationship for non-centric forces is expressed below.

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

(2 r_{p} / 580 ) F_{p} = 1.094 x 10^{6} hertz-meters

Solving the above equation for frequency yields.

F_{p} = 580 ( 1.094 x 10^{6} ) / 2 r_{p}

F_{p} = 2.27 x 10^{23} hertz

The result F_{p} is the Compton frequency of the nucleons. The nucleons vibrate naturally at their 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 structures within the nucleon.

The electromagnetic force also 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.

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

(2 pi r_{p} ) F_{e} = 1.094 x 10^{6} hertz-meters

Solving the above equation for frequency yields.

F_{e} = ( 1.094 x 10^{6} ) / 2 pi r_{p} ; F_{e} = 1.236 x 10^{20} hertz

The result F_{e} 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 r_{p} The 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.

F_{c} = [ K / M_{p} ] ^{1/2} / 2pi

2.27 x 10^{23} hertz = (1/2pi ) [ f_{max} / ( r_{p} M_{p} ) ]^{1/2}

Solving for f_{max} yields:

f_{max} = ( 2pi )^{2} ( 2.27 x 10^{23} ) ^{2} 2 r_{p} M_{+p}

f_{max} = 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.

M_{w} = ( 9.58 x 10 ^{6} Newtons ) ( 1.409 x 10^{-15} meters ) / c^{2} = 1.5 x 10 ^{-25} Kg

The energy of the W particle stretches the weak 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.

**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 quantum ensemble has a greater capacitance than a single state. The increased capacitance lowers the height of the potential wall allowing an alpha particle to pass over it. Both this author’s and the standard methods produce the same results. This author’s method is logically consistent. 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.

**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.

**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 downshifts. Electrons can condense around the downshifted Compton vibration. The stimulation of a Bose condensate at the dimensional frequency of one megahertz-meter invites electrons to condense at the downshifted Compton frequency. This type of electron condensation places each electron into a state of transition. The forces interact strongly within this state.

A normal conductor conducts electrons. The hydrides of certain metals conduct protons. For example, an applied voltage will drive dissolved hydrogen through a palladium wire. The mobile protons act on fixed electrons to form a condensate ( inverse Bose condensate ). The low velocity associated with thermal protons 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

** ” PHYSICS NEWS UPDATE : The American Institute of Physics Bulletin of Physics News, Number 500 August 31, 2000 by Phillip F. Schewe and Ben Stein **

NUCLEAR ENERGY USED TO EXCITE ATOMS

A multinational team of physicists has observed for the first time a process in which the energy freed up by a nucleus relaxing to a lower state is used to excite an electron in the surrounding atom to a higher energy state. Normally atomic and nuclear phenomena are separate, mainly because the energies typifying atomic transitions (an electron moving from one quantum state to another) is measured in electrons volts (eV) or less, whereas analogous nuclear transitions are typically on the order of thousands or millions of eV. But for some heavy ions, which have been relieved of many their electrons (making the attraction between the nucleus and the remaining unshielded electrons all that much more powerful), the spacing between atomic states can actually exceed the spacing between nuclear states. In the case of a Bordeaux-Gif sur Yvette-Darmstadt- Orsay-Manchester-Caen-Stanford experiment (Jean-Francois Chemin, Center for Nuclear Studies at Bordeaux-Gradignan, ) conducted at the GANIL accelerator in France, tellurium atoms, with 47 or even 48 electrons removed, are smashed into a target. In these collisions, energy from the nucleus serves to promote a deeply bound electron (in the 1s electronic, or “K shell” state) into a barely bound “Rydberg” orbit. This observation has extraordinary implications. It means that energy can pass resonantly between the nuclear and electronic parts of the atom…. ” 9, 10

Energy flows between the nucleus and the atom after an energy match is achieved. The energy match may be obtained by a single electron jumping through many energy levels or by many electrons jumping through a single energy state. Energy flows between the electronic and nuclear states of matter. The gravitational field is also involved. The sum of the nuclear, electromagnetic, and gravitational affects tend to push the motion constants toward the electromagnetic. 11.

**A SEMI-CLASSICAL ANALYSIS**

Electrons orbit the nucleus and planets orbit the sun. Planetary objects can drop into the sun, however, electrons cannot drop into the nucleus. Electrons must maintain a minimum zero point orbit. The velocity associated with the minimum orbit is given by:

**Velocity = Z * c/137 megahertz-meters ** ; Z = The atomic number ; c = Light speed ; 137 = The fine structure constant

The velocity of the ground state electrons is determined by the stiffness of the medium. The maximum stiffness is limited by the or elastic limit of the medium. This limit determines the velocity of hydrogen’s ground state electron. This velocity is two million meters per second.

Velocity is expressed in units of meters/second. Hertz is given in units of 1/seconds. Velocity can also be expressed in units of megahertz-meters. Using this nomenclature the velocity of the hydrogen’ ground state electron is two megahertz meters.

Substituting 1/2 in for Z yields the ground state stiffness of a Bose condensate. In general the value of Z is one for Bosons and 1/2 for Hardrons. The result is now interpreted in terms of a frequency associated with a certain sized Bose condensate. The frequency represents the ground state energy of a Bose condensate. The external stimulation of a Bose condensate at this frequency tends to reinforce the condensate. This frequency is one megahertz-meter. The energy levels within the condensate are given by:

**Total_energy = N* n* h* Z*c / (137*L) Joules ** ; h = Planck’s constant ; N = The number of electrons participating in the condensation. ; n = The energy levels within the condensate. n is an integer multiple of one. ; L = The diameter of the condensate ; Z = 1/2

The megahertz-meter stimulation of a Bose condensate removes the potential energy barriers within the condensate. An energy barrier, however, is established at the physical limit of the condensate. This energy barrier determines the ground state frequency of the macro spin one system. This frequency is one megahertz-meter. The number of electrons N that participate in the condensate is increased by stimulating the condensate a dimensional frequency of one megahertz-meter. This increases the kinetic energy difference between energy levels within the condensate. When the total energy exceeds a few thousand electron volts energy can be directly exchanged between the nucleus and the condensate. This process allows low level nuclear reactions to proceed. A similar process has been discovered in large ionized atoms. In these atoms the energy match is achieved by a single electron which jumps through many energy levels.

**THE REST OF PHYSICS **

This author has now presented to most remarkable aspects of his work. Extending his work to the rest of physics would take several lifetimes. This is beyond the scope of this text. The method and motivation for doing so will, however, be presented. Sprinkled throughout current texts is the constant of Planck’s accompanied with the variable of frequency. The formulation describes the energy of the emitted. This author describes the constant of Znidarsic (1.094 megahertz) accompanied with the variable of wavelength. The formulation describes the geometry of the emitter. The extension of this author’s work involves the swapping Planck’s and Znidarsic’s constants. If done correctly the finished results would be identical. As this would confound the physics community there would have to be a powerful motivation to do so. There are several important benefits to this author’s approach. In the area of pure physics this author’s approach reveals the elastic limit of space. The elastic limit of space is a classical property. Quantum effects emerge as the elastic limit of space is exceeded. The quantum regime now becomes a subset of the classical world. This is quite the opposite of current thinking. Znidarsic’s constants of the motion theorem emerges from this model. This theorem reveals the path of the quantum transition. Znidarsic theorem also has several important technological implications. Gravity which is described by General Relativity will, with an adjust to its motion constants, be described by equations similar to those of classical electro-mechanics. The nuclear forces which are described by quantum exchange interactions will, with an adjustment to their motion constants, likewise be described by equations similar to those of classical electro-mechanics. The technologies that will emerge from this fundamental insight will change man’s position within the universe. This is reason enough to confound the physics community. Hopefully we will soon realize this potential.

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 one megahertz-meter is equivalent to a spin state in Planck’s system of units. Spin one states obey Bose Einstein statistics. Many Bosons can occupy the same state. No potential barriers within exist within a system of Bosons. In terms of Znidarsic’s units the megahertz-meter stimulation converges the motion constants. The convergence of the motion constants eliminates potential energy barriers within the spin one state. Bosons experience an elastic discontinuity at the edge of the condensate. Hadrons experience elastic discontinuities at the elastic limit of space.

**CONCLUSION **

The geometry of a quantum system effects the magnitude of the electromagnetic, gravitational, and nuclear motion constants. Superconductivity affects the electrical motion constants. The nuclear and gravitational motion constants are affected by a Bose condensate that is stimulated at a dimensional frequency of one megahertz-meter. The process lowers the elastic limit of space. The reduced stiffness is expressed in several ways. The range of the forces tend towards the length of the superconductor. The constants of the motion tend toward the electromagnetic. The frequencies of matter downshift. The affects are those of the quantum transition. The understanding of the nature of the quantum transition will allow many new technologies to be developed.

**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** Â” Physical Review E, March 2003

– 3.E. Podkletnov and A.D. Levi,” **A Possibility of Gravitational Force Shielding by Bulk YBa2Cu307-xsuperconductor,** ” 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 4thMeeting 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 Engineerin 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 EnergyVol 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

**Appendix sample calculation **

**given**: h = Planck’s constant = 6.6 x 10 ^{-16} ev/sec; Y = 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 = ( Y * 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.

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

# **CHAPTER 12, STATES OF THE ELECTRON **, http://www.angelfire.com/scifi2/zpt/chapterc.html

**Bohr’s quantum condition**

Bohr’s quantum condition forms the foundation of modern physics. Bohr’s quantum condition states that the momentum around any closed loop is an integer multiple of Planck’s constant.

nh = P Â•ds

“Bohr emphasized the point of view that the quantization of angular momentum was a postulate, underivable from any deeper law, and that its validity depended simply on the agreement of his model with experimental spectra.” 1

Bohr’s quantum condition expresses the value of a stationary quantum state. It says nothing about the path of the quantum transition.

** “When the electron undergoes transition, we don’t know what path it takes.” ** Quote from “What is quantum Mechanics” The LEX foundation

Znidarsic developed his model from the observation of cold fusion experiments and the analysis of the elastic limit of space. His model is based on the idea that quantum states are pinned in at discontinuities. Discontinuities are produced when the intensity of the matter wave exceeds the elastic limit of space. Znidarsic’s theorem emerges from this model. The theorem describes the process of quantum transition. It states that quantum transitions progress at a dimensional frequency of 1.094 megahertz-meters [c / (2*137)]. This is a vital new understanding. It is fundamental to Bohr’s quantum condition. During transition the nuclear, gravitational, and electromagnetic motion constants converge. The process can be induced in a macroscopic Bose condensate. The constants of the motion converge in a Bose condensate of electrons or protons that is vibrationally stimulated at a dimensional frequency of one megahertz-meter.

BohrÂ’s quantity of angular momentum [ h / ( 2 pi ) ] describes the angular momentum of the stationary quantum state. ZnidarsicÂ’s dimensional frequency 1.094 megahertz-meters describes the velocity of the transitional quantum state. These two constants define the quantum condition. The capacitance of an isolated sphere was employed to describe the basic geometry of the stationary quantum state. This capacitance is given below.

C_{s} = 4 pi e_{o} r Farads

The derivative of the above equation expresses the velocity of the transitional quantum state.

d(C_{s} ) / dt = 4 pi e_{o} ( dr / dt ) Farads/second

Znidarsic constant of 1.094 megahertz-meters describes the velocity of the transitional quantum state. Substituting ZnidarsicÂ’s constant for ( dr / dt ) yields.

d(C_{s} ) / dt = 4 pi e_{o} ( 1.094 x 10 ^{6} ) Farads / second

The energy E contained by a capacitor with a charge of one is given below.

E = Â½ q^{2} / C Joules

Please note that the value of capacitance associated with the transitional quantum state is expressed in Farads / second. The inclusion of seconds produces a result in units of joules-seconds. Angular momentum P is expressed in units of joules-seconds. Substituting the dynamic capacitance of the transitional quantum state for C yields.

P = Â½ q^{2} / [ 4 pi e_{o} 1.094 x 10 ^{6} ] joules-second

Reducing the equation above produces PlanckÂ’s quantity of angular momentum P.

P = 6.625 x 10 ^{-34} / 2 pi joules-seconds

PlanckÂ’s constant describes the angular momentun of the stationary quantum state. ZnidarsicÂ’s constant describes the velocity of the transitional quantum state. The stationary quantum state is an affect of the transitional quantum state. Planck’s constant is elegant. ZnidarsicÂ’s constant demonstrates that the natural forces can be controlled with technology.

**THE BIRTH OF THE UNIVERSE **

The greatest minds have studied the birth of the universe. This author cannot even begin to appreciate the formulations of the great works of these geniuses. This author is an **Electrical Engineer** whose designs have always worked. Given a burst of confidence from this, **I have tried to find new sources of energy and space propulsion**. This quest has taken me into the field of physics and directly into the realm of the great geniuses. I want to stay where I belong as an engineer working with low energy machinery. I do, however, want this low energy machinery to produce limitless free energy and to propel us to the stars. That goal forces me to look squarely at the birth of the universe. I donÂ’t want or need to know everything about the birth of the universe. **I only need to understand the process of energy creation**. Energy flows through a series of **cascading quantum transitions**. The birth of the universe was a flow of energy. This flow of energy proceeded through the process of quantum transition(s). This transition(s), as **all transitions, progressed at a dimensional frequency of one megahertz-meter**. Energy was conserved during the moment of creation. **The positive energy of the universe was balanced by its negative gravitational potential**. All quantum transitions conserve energy, however, the first transition was different from the later ones. The first transition established the amount of positive energy contained within the universe. All subsequent quantum transitions have conserved this quantity of positive energy. Why did the principle of the conservation of energy change the way in which it is expressed? Mainstream physicists tend to look for answers to this question at high energy. **Perhaps a symmetry broke or the Higgs particle expressed itself in another way**. I look to the conservation laws for an answer to this fundamental question. The loosening of the energy conservation laws must have been precipitated by a loosening of the momentum conservation laws.

In this I have been inspired by the work of **V. Arunasalan ( Â“ Superfluid Quasi Photons in the Early Universe** Â“, Physics Essays Vol 5, #1, 2002) Arunasalan writes:

** Â“..The Universe had a brief period of extraordinary rapid inflation, or expansion, during which its diameter increased by a factor of 10 to the 50th powerÂ…In the course of this stupendous growth all of the matter and energy in the universe could have been created from virtually nothing. Â“ **

Arunasalan describes a superfluid early universe. The superfluid state was mediated by photons not phonons. The superfluid state is that of single body. The principle of the conservation of angular momentum does not make sense for the single bodied early universe. This could be the key understating that will enable mankind to make substance form nothing. This author has already shown that the forces interact strongly during the quantum transition. This strong interaction can be induced in a macroscopic Bose condensate through **stimulation at the dimensional frequency of one megahertz-meter**. The strong interaction can be employed for propulsion and to induce low level nuclear reactions. **A special ingredient needs to be added to produce substance from nothing**. As I presented at the First Conference on Future Energy; **that ingredient is angular momentum**. 2

** ” A process in which a spin one photon and a spin two gravition are simultaneously emitted does not conseve angular momentum. ” ** Frank Znidarsic The Journal of New Energy. , Vol. 1, No. 2, 1996

Genesis progresses through a process in which the quantum transition absorbes angular momentum. The process proceeds at low energy. I keep the practicable embodiments of this and many other processes to myself.

**The Double Slit Experiment **

The electron appears as a particle in many experiments. The path of the particle like electron can be clearly seen in a cloud chamber. The **formulations of Heisenberg and Bohr** produce results with a construct that considers the electron to be a particle. **The electron appears as a wave in many other experiments**. The double slit experiment projects the electron through two closely spaced slits and onto a screen. The wave pattern associated with the electron can clearly be seen on the screen. The **formulations of SchrÃ¶dinger and deBroglie** produce results from a construct that considers the electron to be a wave. **How can the electron be both a particle and a wave?** Electrons that are passed one at a time through the double slit experiment produce a dot as they impact the screen. This dot is characteristic of a particle. After many electrons have passed through the double slit arrangement a pattern emerges from the collection of dots. The pattern is characteristic of a wave. **It appears that the properties of the electron depend upon how it is observed**. Born attempted to clarify this quantum mystery by stating that electrons are not material waves. According to Born electrons are waves of probability. Einstein had a problem with Born’s interpretation and stated, “God does not play dice!”. SchrÃ¶dinger never accepted Born’s interpretation. In spite of these objections Born’s interpretation is now central to man’s understanding of the quantum nature of the universe.

**This author contends that Born’s interpretation is wrong**. Born’s error has impacted our society for 100 years. **The electron is a material wave**. It interferes with itself as it passes simultaneously through both slits in the double slit experiment. **The electron wave consists of the gravitational, electrical, and magnetic fields**. These fields have vastly differing strengths, ranges, and motion constants. The differing motion constants prevent the various fields from strongly interacting. A strong interaction requires a convergence of the motion constants. This author’s theorem states,** “The gravitational, nuclear, and electromagnetic motion constants converge within a Bose condensate that is stimulated at a dimensional frequency of one megahertz-meter.” **A dot is produced on the screen of the double slit experiment at the point where the motion constants converged. Born would state that the probability wave collapsed. This author contends that the quantum transition is not associated with Born’s probability wave. The transition is associated with the stimulation of a quantum system at a dimensional frequency of one megahertz-meter.

http://www.angelfire.com/scifi2/zpt/stim.html Java Script Animation, “The Path of the Quantum Transition”.

Random motions within the quantum system produce the required stimulation. The amplitude of this stimulation determines the probability of transition. This author’s interpretation is material. It exposes a path of the quantum transition.

THE EXCITED STATES OF THE ELECTRON

The harminic oscillator describes the motion of the electron in a linear restraining force. The energy levels for the harmonic electronic oscillator are commonly found using SchrÃ¶dinger’s wave equation. This is done by inserting a value for potential energy “PE” into SchrÃ¶dinger’s equation.

PE = kx

The potential energy is restricted to states that have an angular momentum “M” equal to:

M = n h / 2 pi

The result is mathematically elegant, however, it cannot explain why atomic states are restricted. SchrÃ¶dinger’s method describes the properties of the emitted particle. This author’s method describes the geometry of the emitter. This author’s method provides a classical explanation for the quantum condition. The author qualifies the effective geometry of the emitter in terms of its capacitance.

A quantum state can be descirbed by its potential and kinetic energy. The total energy (KE + PE) of the stationary quantum state is static. The dynamic energy of the transitional state crystallizes into the static energy of the stationary state. The kinetic and potential energy of the transitional state are set at crystillization. As in the static atomic state, the minimum kinetic energy of the transitional state equals half of its potential energy. The relationship between the kinetic “KE” and potential “PE” energy of the ground transitional quantum state is expressed below.

KE = PE / 2

The kinetic energy of the transitional state is fixed by the megahertz-meter relationship. The potential energy of the transitional resides at harmonics of the ground state. The equation below expresses the total energy “U” of the transitional state.

U = n PE + KE

Substituting

U = n PE + PE / 2

The potential energy of the electron is determined by the capacitance “C” of the emitting structure.

PE = q^{2} / 2C

Substituting

U = n q^{2} / 2C + q^{2} / 4C

U = [ q^{2} / C ] (n / 2 + 1/4 )

The isotropic capacitance of a conductive sphere was used to represent the effective geometry of the emitting structure.

C = 4 pi e_{o} r

therefore

U = [ q^{2} / (4 pi e_{o} r)] (n /2 + 1/4)

The process of quantum transition will now be exposed. The constants of the motion converge at a dimensional frequency of one megahertz-meter. Atomic states can only be entered and exited at points where the motion constants converge. This phenomena, not angular momentum, limits the available states within atoms. The dimensional frequency of one megahertz-meter expresses the relationship between the frequency and frequency and the linear displacement of a quantum system during transition. This relationship is:

2 r = ( 1.093 x 10^{6} ) / f

substituting

U = [ q^{2} / (4 pi e_{o} 1.093 x 10^{6}) ] f (n + 1/2)

The term within the bracket [ ] equals Planck’s constant.

** U = h f (n + 1/2) joules **

The energy levels of electrinic harmonic motion have been found with a technique employing the elastic limit of space. The flow of the mathematics revealed the structure of the transitional state. This author’s construct demonstrates that the energy levels of the electron are determined by the process of quantum transition. The method does not require the ad-hoc injection of Planck’s constant.

**THE SPECTRAL INTENSITY OF HARMONIC OSCILLATION **

The intensity of a classical wave is determined by the square of its amplitude. The amplitude of the matter wave was determined early in the 20th century. The matter wave was represented as a Fourier wave packet. This packet was placed into the equations of simple harmonic motion. BohrÂ’s quantum condition and PlanckÂ’s constant were incorporated to restrict the allowed states. The intensity of a spectral line is determined by the square of the amplitude of a probability wave.

This author has reservations about this method. Energy cannot be restrained by the Fourier addition of waves. The incorporation of PlanckÂ’s constant and BohrÂ’s quantum condition is ad-hoc. The inclusion of a complex probability wave confused the issue. The construct is not material.

**THE CORRECTION **

The intensity of a spectrial line is determined by the probability of a quantum transtion. The quantum transtion is described by the megahertz-meter relationship. **The amplitude of vibration at the dimensional frequency of one megahertz-meter determines the probability of transition. **

The quantum of capacitance Cq is a classical phenomenon Ref. Ch 10 Pg 7 .

C_{q} = q^{2} / ( 2 m_{-e} c^{2} )

The quantum of reciprocal capacitance qualifies the elastic limit of space. The elastic limit of space sets a maximum in the displacement of the leptonic field. The geometry and isotropic capacitance of the ground state electron are also determined by this displacement.

The ratio of the radius of the hydrogen atom to the radius of the proton equals twice the fine structure constant squared.

r_{h} / r_{p} = .529 ^{-10} / 1.409 x 10^{-15} = 2*137 ^{2}

Capacitance is a basic quantum unit. The capacitance of the ground state electron was expressed as a number of quantums. The number of quantums was determined by employing a factor of twice the fine structure constant squared.

C_{-e} = 2 137 ^{2} C_{q}

The transitional states of the electron can contain n times this capacitance.

C_{-e} = 2n 137 ^{2} C_{q}

The effective capacitance of the transitional state can be represented by the isotropic capacitance of a sphere.

4 pi e_{o} r = 2n137 ^{2} C_{q}

4 pi e_{o} r = 2n137 ^{2} q^{2} / ( 2 m c^{2} )

Solving for r

r = 2n137 ^{2} q^{2} / [8 pi m_{-e} e_{o} c_{1} c_{2} ]

The intesity of vibration at the dimensional frequency of 1.094 megahertz-meters determines the probability of transition. This intensity may be expressed in terms of cirumferential velocity “V”.

This intensity may be experssed as the product of frequency and linear displacement 1.094 x 10^{6} hertz-meters.

c_{2} = 2 * 137 * 1.094 x 10^{6} hertz-meters

Substituting

r = 2n137 ^{2} q^{2} / { 8 pi m e_{o} (2 f 137 2 pi r ) ( 2 * 137 * 1.094 x 10^{6}) }

Regrouping.

r^{2} = n [ q^{2} / { 4 e_{o} 1.094 x 10^{6} ] 8 pi^{2} m_{-e} f }

The quantity between the brackets [ ] equals PlanckÂ’s constant. Substituting.

**r ^{2} = n h / { 8 pi^{2} m_{-e} f } meters^{2}**

The known intensity of electronic harmonic oscillation has been determined. The intensity varies directly with the amplitude of vibration at the dimensional frequency of one megahertz-meter. The stimulation drives the quantum transtion. It determines the probability of transtition. The geometry of the emitting structure and the path of the quantum transition were employed in the solution. The solution did not require the ad-hoc addition of mysterious quantum variables.

**THE RYDBERG CONSTANT **

Rydberg was the first to qualify the energy levels of the atom “n_{a}“. For the hydrogen atom the Rydberg relationship is:

Energy = Rhc / n_{a}^{2}

The ground state geometry contains a quantity of capacitance equal to 137 ^{2} C_{q}. The atomic ground state holds two electrons. Its capacitance equals the capacitance of its two electrons:

C = 2*137 ^{2} C_{q} / Z

For the hydrogen atom ( Z = 1 ) the capacitance of the ground state is:

C = 2*137 ^{2} C_{q}

Each electron contributes a minimum of capacitance to the atom. The atom is unstable when isotropic capacitance of the atom is greater than the capacitance of its electrons.

Capacitance of a sphere of radius ( r_{o} n_{r}^{2} ) > ( The number of electrons n_{e} ) x ( The capacitance of each electron )

4 pi e_{o} ( r_{o} n_{r}^{2} ) > ( n_{e} ) 137 ^{2} C_{q}

Energy can can flow at points were the motion constants converge. These points are described by the megahertz-meter relationship. The atomic states are such points. The number of electrons n_{e} residing in full atomic energy states is ( 2 n_{a}^{2} ) .

4 pi e_{o} ( r_{o} n_{r}^{2} ) > ( 2 n_{a}^{2} ) 137 ^{2} C_{q}

The atom is stable when the capacitance of the atom C_{s} equals the capacitance carried in its full energy states.

C_{s} = 2 n_{a}^{2} 137 ^{2} C_{q}

The capacitance of a classical system C_{s} is less than the sum of its quantums.

C_{s}e * C_{q}

These concepts transcend the Pauli Exclusion Principle and define the quantum regime.

The energy contained within a capacitor is given by:E = (1/2) q^{2} / C

Substituting the capacitance of the stable atomic state into the formula for the energy of a capacitor yields.

E = (1/2) q^{2} / ( 2 n_{a}^{2} 137 ^{2} C_{q} )

Setting Rydberg’s energy relationship equal to the energy of the electronic state yields:

Rhc / n_{a}^{2} = (1/2) q^{2} / ( 2 n_{a}^{2} 137 ^{2} C_{q} )

Solving for the Rydberg constant.

R = (1/2) q^{2} / ( 2*137 ^{2} C_{q} hc )

The solution is the Rydberg constant.

**R = 1.0968 x 10 ^{7}**

The Rydberg constant has been produced from a technique employing the elastic limit of space. The elastic limit of space pins electrons into stable atomic states. The elastic limit releases its grip on these electrons the dimensional frequency of one megahertz-meter.

**THE ELECRON IN A BOX **

SchrÃ¶dinger’s wave equation is used to find the energy levels of an electron in a box. The is done by setting the potential energy level equal to zero and solving the differential equation. Using this method the energy levels are given by equation 2B.

E = h^{2} / 8L^{2}m

In 1989, in his book “Elementary Antigravity” Znidarsic introduced **the elastic limit of space**. The concept may be applied to generate a very clear visual image of an electron in a box. Znidarsic has shown that the deBrogle wave is a beat note. In order to maintain the structure of the beat note the electron must keep moving. SchrÃ¶dinger called to the zero point vibrational motion of the electron zitterbewegung.

http://www.angelfire.com/scifi2/zpt/Waves.html Pick the link to view the relationship between the velocity and wavelength of the DeBroglie beat note.

The fundamental mode of vibration is Â½ wavelength. Substituting 2 L for wavelength yields equation 7B.

E = (Â½) M [ h / (M 2L ) ]^{2}

Simplifying equation 7 B yields equation 8B. Equation 8B expresses the energy levels of the electron in a box.

**E = h ^{2} / 8L^{2}m joules **

This analysis produces a very clear visual image. The deBrogle wave is a beat note. In order to maintain its structure the electron must juggle when confined. The motion has kinetic energy. The kinetic energy of the motion equals the energy of an electron in a box.

**The Mining of the Dark Matter **

Ninety percent of the universe is composed of dark matter. This matter does not interact with ordinary matter. It, in fact, may be currently passing directly though your body. The authorÂ’s understanding of the process of quantum transition may enable him to mine this dark matter. Why doesnÂ’t dark matter participate in the quantum transitions of ordinary matter? This author’s megahertz-meter relationship describes the quantum transitions of ordinary matter. Does dark enter into transition at another dimensional frequency? Can we couple dark matter to ordinary matter through the stimulation of Bose condensate at another dimensional frequency? I donÂ’t know these answers. I do, however, know how to construct the experiments that may find them. I hope to live long enough to see an intersteller space ship that gains momentum by expelling dark matter.

**CONCLUSION **

Discontinuities are produced when the intensity of a force field exceeds the elastic limit of space. The natural forces are pinned into the structure of matter by these discontinuities. This is the condition of the stationay quantum state. The stimulation of a quantum system at the dimensional frequency of 1.094 megahertz-meters releases the elastic limit’s grip on the natural forces. The forces slip into another configuration. This is the process of quantum transition. These concepts have been applied from the energy levelsof the atomic states (a few electron volts) to the energy levels associated with the nuclear transmutations (millions of electron volts).

This understanding reveals several revolutionary technologies. This author keeps the practicable embodiments of these technologies to himself.

**NOTES **

– 1. Serway, Moses, Moyer”Modern Physics” 1997

– 2. http://users.erols.com/iri/speakerlist.html

end of chapter 12 ………………………….

**The Author’s World Wide Web Links **

**ZNIDARSIC’S PUBLICATIONS **

– “The Genesis of the Universe and Zero Point Energy.” Frank Znidarsic, Infinite Energy,http://www.infinite-energy.com/iemagazine/issue5/index.html Concord NH, Vol 1, No. 5 & 6, 1996

– “Force and Gravity”, Frank Znidarsic, Infinite Energy, http://www.infinite-energy.com/iemagazine/issue22/index.html Vol 4, Issue #22, 1998

– For copies call Infinite-Energy at 603-228-4516 or write to E-mail_Infinite_Energyeditor@infinite-energy.com

– “Elementary Antigravity”, Frank Znidarsic ; Vantange Press, 1989, New York, NY ; Currently out of print.

– “The Zero Point Interaction.” Frank Znidarsic, The Journal of New Energy Fall 1996 ; P.O. Box 58639 ; Salt Lake City, Utah

For copies call Hal Fox at 801-583-6232 Journal of New Energy, Volume 1, Number 2 http://www.padrak.com/ine/JNEV1N2.html

– “The Constants of the Motion” ; Frank Znidarsic, Transactions of the American Nuclear Societyhttp://www.osti.gov/energycitations/product.biblio.jsp?osti_id=787504; Vol 83, TANSAO 83 1-536 (2000), ISSN: 0003-018X

– “The Constants of the Motion” ; Frank Znidarsic, The Journal of New Energyhttp://www.padrak.com/ine/JNEV5N2.htmlVol. 5, No. 2 Pg 130 September 2000

– Nickola Tesla Journey to Marshttp://btobsearch.barnesandnoble.com/booksearch/isbnInquiry.asp?userid=2XW7BTTO5T&btob=Y&isbn=1892062313 , Global Communications ; Chapter 5, Frank Znidarsic, October 2002

– Published comment “Popular Mechanics”http://www.popularmechanics.com/ October 2004, Page 16

**ZNIDARSIC ‘S TELEVISION APPEARANCES **

– French national television French TV http://www.canalplus.fr/archives/cyclone2/mai/sauver2.html

**ZNIDARSIC’S MEDIA APPEARANCES **

– Plutonium films http://www.weirdvideos.com/alternat.html

– Bill Boshures Show, Clear Channel Communications 2003

**ZNIDARSIC’S PUBLIC APPEARANCES **

– COFE_Washington_DC http://www.erols.com/iri/speakerlist.html

– The American Nuclear Society,http://www.ans.org/ November 16, Washington DC

**FREE ENERGY LINKS**

– Cold Fusion Timeshttp://world.std.com/~mica/cft.html

– Low Level Nuclear Reactions (Jed Rothwell)http://lenr-canr.org/

– Weird Science (Bill Beaty) http://www.eskimo.com/~billb/weird.html

– Wired_Magazinehttp://www.wired.com/wired/archive/6.11/coldfusion.html

– Institute for Advanced Study (Puthoff and Little) http://www.earthtech.org/

– LanL & ENECO ( Edmund Storms ) http://home.netcom.com/~storms2/index.html

– Los Alamos cold fusion page ( Thomas Claytor ) http://www.nde.lanl.gov/cf/tritweb.htm

– Infinite Energy Magazinehttp://www.mit.edu:8001/people/rei/CFdir/CFhome.html

– Neutrons_detected ( Steve Jones ) http://www.aps.org/meet/4CF02/baps/abs/S80.html

– Cold Fusion Times http://world.std.com/~mica/cft.html

– Jean-Louis Naudin Francehttp://jlnlabs.imars.com/cfr/

– Russ Georgehttp://www.d2fusion.com/

– Institute for new energy ( Padrak Baily ) http://www.padrak.com/ine

– BlackLight Power Home (R. Mills) http://www.blacklightpower.com/

– The Naval Weppons Labhttp://www.evworld.com/databases/storybuilder.cfm?storyid=393

– Pure Energy Systems (Sterling D. Allan) http://freeenergy.greaterthings.com/

– Cold Fusion from South Korea (Dr. Hyunik Yang)http://iesiusa.com/

**ANTIGRAVITY LINKS **

– Breakthrough Physics Workshop (NASA Lewis) http://www.lerc.nasa.gov/WWW/bpp/

– Podkletnov at LanLhttp://xxx.lanl.gov/abs/physics/0209051

– Podkeltnov at LanLhttp://xxx.lanl.gov/abs/cond-mat/9701074

– NASA’s antigravity program http://infinity.msfc.nasa.gov/Public/ps01/deltag.html

– The Gravity Societyhttp://www.gravity.org/

– American Antigravityhttp://www.americanantigravity.com/gravitywaves.shtml

– Antigravity in Indiahttp://www.indiadaily.com/editorial/12-04e-04.asp

– Popular Mechanicshttp://www.popularmechanics.com/science/research/1281736.html

– Failure to replicatehttp://www.ingentaconnect.com/content/els/09214534/2003/00000385/00000004/art02284;jsessionid=5pdf9csnaeka3.victoria

**BALL LIGHTNING LINKS **

– Chukanov Energyhttp://www.chukanovenergy.com/

– Electron Power Systems (Clint Seward)http://www.electronpowersystems.com/

**CAVITATIONAL FUSION LINKS **

– Cavitational fusion in acetonehttp://www.rpi.edu/~laheyr/SciencePaper.pdf

– Impulse Deviceshttp://www.impulsedevices.com/index.html

– New Scientisthttp://www.newscientist.com/article.ns?id=dn7315

– Naturehttp://www.nature.com/news/2005/050228/full/050228-7.html