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**INTRODUCTION:**

THIS WEB PAGE SUMMARIZES BASIC ENERGY CONCEPTS.

**CHARGE, FIELDS, ENERGY:**

The universe is composed of quantum charges, vector fields and energy which are mathematically intertwined. The existence of an element of charge at a position in space relative to an observer causes a specific local vector electric field distribution. Motion of that element of charge causes a specific local vector magnetic field distribution. At any point in space and time the sum of the squares of the net electric, net magnetic and net gravitational field vector magnitudes is the local potential energy density. There is also a motion component known as kinetic energy. Total energy content is computed by integrating energy density over volume. The total amount of energy is invariant over time.

Everything that exists contains some energy. The energy density of field free space is zero.

Radiation consists of vector field fluctuations which propagate at the speed of light. Radiation conveys both energy and momentum (energy motion) without conveying net quantum charge.

**PARTICLES:**

The universe consists of assemblies of particles within a sea of propagating radiation. At reference time T = To each particle has a quantized net charge Q, a nominal relative position **(X = Xo)**, a nominal relative momentum **(P = Po)** and a relative energy (E = Eo). The particle initial energy has nuclear, magnetic, electric, gravitational and motion components. The rest potential energy is contained in mathematically orthogonal fields that extend to infinity but for each orthogonal field type the field energy density decreases sufficiently quickly with increasing radial distance from **Xo** that the total spacial energy content of that field type is finite.

**PARTICLE INTERACTION:**

Particles interact with each other at a distance via overlap of their extended fields. Field overlap causes the net field vector at each point in space to change which in turn causes part of an assembly of particles potential energy to convert into kinetic energy (momentum related energy) or vice versa. During interparticle interactions there is also an energy exchange between particle random motion kinetic energy and radiation. Photons (quanta of energy) may be emitted to the radiation environment and/or absorbed from the radiation environment.

**FORMATION OF MUTUAL POTENTIL ENERGY WELLS:**

Progressive overlap of gravitational fields may cause an assembly of particles to gain more positive kinetic energy by acquiring more negative potential energy via field overlap. Then net emission of radiation may cause the assembly of particles to lose random kinetic energy. Hence there is an overall tendency for the total potential energy of an assembly of particles to become more negative which causes the particles to become mutually bound to each other in a common potential energy well.

Absorption of radiation from an external radiation source such as sunlight at a sufficient rate can in principle reverse this particle binding process.

In all particle interactions the total isolated system energy, including emitted radiant energy, is unchanged during a particle interaction. This principle is known as **the law of conservation of energy**.

In all particle interactions the total isolated system energy motion vector (linear momentum), including emitted photons, is unchanged during a particle interaction. This principle is known as **the law of conservation of linear momentum**.

In the case of four hydrogen atoms going through a succession of interactions to form one helium atom the particle aggregation process is known as fusion. The photons emitted during fusion reactions are the main nearly continuous source of energy emitted by the sun and the stars.

High atomic weight nuclei result from end-of-life stellar explosions. There are a few high atomic weight atomic nuclei such as U-233, U-235 and Pu-239 that, when suitably stimulated by neutron or gamma photon absorption, break into smaller particles and liberate large amounts of both kinetic energy and photons. This process is known as nuclear fission. Fission is the main source of nuclear energy available on Earth.

There are a large number of semi-stable atomic nuclei that over time gradually break down into more stable nuclei by random spontaneous emission of electrons, positrons or alpha particles (He-4 nuclei), as well as gamma photons. These semi-stable nuclei are known as radio isotopes.

Dark matter is a term used by astronomers to account for the apparent non-luminous gravitational mass component of galaxies. There are competing theories.

Dark energy is a term used by astronomers to account for the apparent accelerating expansion of the visible universe. There are competing theories.

**ENERGY AND MOMENTUM OF A PARTICLE:**

The differential equation relating the change in energy E of a particle to its change in linear momentum **P** is:

E dE = C^2 **P dP**

where:

C = speed of light.

Integrating both sides of this equqtion from state "a" to state "b" gives:

(Eb^2 - Ea^2) / 2 = C^2 (Pb^2 - Pa^2) / 2

For particles with rest mass it is often convenient to choose the initial condition reference point (To = Ta, Xo = Xa, Po = Pa, Eo = Ea) as the state when the particle is at rest in the observers frame of reference. Then:

**Pa** = 0 at E = Ea to get:

Eb^2 = Ea^2 + C^2 Pb^2

Einstein recognized that:

Ea = Mo C^2

where Mo = rest mass

and that:

**Pb** = (Eb **V**) / C^2

= M **V**

where M = moving mass.

Alternatively:

M = Eb / C^2

or

Eb = M C^2

which is one of the most famous equations in physics.

**NEWTONIAN KINETIC ENERGY:**

For (V / C) << 1

the equation:

Eb = (Mo C^2) / [1 - (V^2 / C^2]^0.5

simplifies to:

Eb = (Mo C^2)[1 + [V^2 / 2 C^2]

= Mo C^2 + Mo V^2 / 2

where the term Mo C^2 is the rest mass potential energy and the term [(Mo V^2) / 2] is Newtonian kinetic energy.

**POTENTIAL ENERGY WELLS:**

As a particle following a constant energy path with respect to field free space enters a gravitational potential well its rest potential energy Ea with respect to field free space will decrease or become more negative. However, Eb remains unchanged as required to maintain a constant particle energy with respect to field free space. Hence on entering the gravitational potential energy well there is an increase in the particle's (Eb - Ea) value and hence an increase in particle momentum P. This momentum increase causes a decrease in the wavelength of a photon and hence a deflection of a photon following a path tangential to a mass concentration.

Within a potential energy well a particle's Ea value is lower than outside the potential energy well. If while within the potential energy well a particle loses sufficient energy that the particle's kinetic energy becomes less than than the potential energy well depth:

(Ea|outside - Ea|inside)

then the particle will be trapped within the potential energy well. A simple physical example of such trapping is the presence of planets orbiting around our sun. The planets cannot escape from our sun because they are trapped in our sun's gravitational potential energy well. However, if two orbiting planets interact in a manner that transfers energy from one planet to the other the planet with the higher energy might be able to escape the energy well.

Solid matter is simply a collection of atoms that are mutually bound together in a common potential energy well.

**FORCES:**

Recall the differential equation:

E dE = C^2 **P dP**

can be rewitten as:

dE = C^2 (**P** / E) d**P**

= C^2 (E **V**) / (C^2 E) d**P**

= **V dP**

However:

**V** = d**X** / dT

Hence:

dE = [d**X** / dT] d**P**

or

dE dT = d**X** d**P**

which equation links a particles changes in energy, time, position and momentum.

Alternatively:

(dE / dX) = dP / dT

= d(M V) / dT

= [M (dV / dT) + V (dM / dT)]

(dE / dX) = M (dV / dT)

or

(force) = (mass) X (acceleration)

A force is simply a change in particle potential energy with respect to a change in particle position with respect to the other particles with which it is interacting.

Thus the differential equation:

E dE = C^2 **P dP**

incorporates many aspects of particle motion.

**MODERN PHYSICS:**

Electromagnetic energy propagates through space via radiation. The energy density with respect to a field free vacuum at every point in space and time causes a gravitational field that extends to infinity. Gravitational fields form negative potential energy wells that cause interactions between widely separated particles.

During the first half of the 20th century it was shown that every large mass consists of an aggregation of stable atomic particles with quantized charges and corresponding discrete energies. Subject to structural constraints the atomic particles vibrate or move randomly with thermal kinetic energy. Planck showed that the vibrating atomic particles constantly emit and absorb photons which are quanta of thermal electromagnetic radiation.

Later during the 20th century it was shown that a sufficient concentration of mass would cause formation of a black hole that absorbs both mass and radiant energy from its surroundings. Smaller mass concentrations cause local changes in photon frequency and photon propagation direction.

In the early 21st century it became apparent that the electromagnetic energy of a charged particle is stored in a spheromak formed by massless quantized charge that circulates around a closed spiral path at the speed of light. A spheromak has associated with it electric and magnetic fields that contain potential energy. These fields contribute to the particle rest mass and give the spheromak's charge motion path geometrical stability. Changes in spheromak electromagnetic energy dE caused by emission or absorption of a photon follow the equation:

dE = h dF

where:

dE = photon energy

h = Planck constant

dF = change in spheromak natural frequency

**RELATIVITY:**

The natural physical laws are such that it is impossible to determine absolute position, absolute velocity or absolute time. Position, momentum and time are relative quantites with respect to an observer or a system center of momentum. All inertial (non-accelerating) observers measure the same speed of light. As a consequence the experience of time, distance, momentum and energy are different for observers in relative motion. The change in particle energy with respect to a change in particle momentum gives rise to the concept of kinetic energy.

**CONSERVATION OF ENERGY:**

The law of conservation of energy requires that the amount of energy of a particle at time Tb equals the amount of energy of that particle at time Ta plus the net amount of energy that flows into that particle during the time interval (Tb - Ta). Hence energy cannot be either created or destroyed but can change form and position and can be transferred between particles.

In an isolated system total energy is always conserved. For an isolated system a decrease in potential energy causes a corresponding increase in kinetic energy and vice-versa. The energy of a non-isolated system can change via energy absorption from another system or via energy emission to another system. Often these energy exchanges occur via emission or absorption of quanta of radiant energy (photons).

Energy arises from the existence of atomic particles and the existence of radiation. Energy takes several forms: nuclear energy, magnetic field energy, electric field energy, gravitational field energy, kinetic energy and radiation. Energy may possibly exist in other forms. The energy density of field free empty space is assumed to be zero.

**GRAVITY:**

Gravitational field energy is a result of the presence and density of other energy forms. When other forms of energy are zero there is also zero gravitional field energy. Unlike most other energy forms which are normally positive, the gravitational field energy density is normally negative.

Gravitational fields have an imaginary unit vector which causes a gravitational field to contain negative potential energy. Gravity becomes important when large numbers of quantized negative and positive charges are in nearly exact balance. The exact nature of propagating gravitational field energy quanta is a subject of current research.

Assume that isolated particles have initial zero potential energy as a result of their initial wide separation. Thus gravity causes conversion of isolated particle potential energy into equal amounts of positive kinetic energy and negative potential energy. The kinetic energy then often partially converts into photon or particle energy that is emitted into deep space. Hence the negative energy content of a gravitational field is a result of long term emission of positive energy photons and energetic particles into deep space.

The effect of an energy concentration is to form a local gravitational potential energy well. Far from the potential well the gravitational field energy density approaches zero. Closer to the center of the potential well the gravitational field energy density becomes increasingly more negative. The gravitational field geometry and hence the gravitational field energy and hence the gravitational force changes with relative particle position. Gravitational forces are a result of the change in total gravitational field energy with respect to a change in particle position. The apparent depth of a gravitational field potential energy well is proportional to the amount of energy carried by the sensing particle. Increased overlap of gravitational fields makes the total gravitational potential energy of a collection of particles more negative.

Local concentrations of energy are often mathematically approximated by point masses.

Under circumstances of low incident electromagnetic radiation density kinetic energy can be emitted as electromagnetic radiant energy which then propagates away at the speed of light. Under circumstances of high incident electromagnetic radiation density electromagnetic radiation can be absorbed and converted into kinetic energy and then potential energy. In our local universe the radiation density in deep outer space is very low compared to the thermal radiation density near the sun. Hence emission of solar radiation gradually increases the depth of the solar system's gravitational potential energy well.

**STAR EVOLUTION:**

At present the local universe primarily evolves by gradual aggregation of nearly isolated neutral hydrogen molecules. This aggregation causes formation of negative gravitational field potential energy and positive kinetic energy at star locations. Part of the kinetic energy converts into positive energy radiation which is emitted into deep space. The remaining kinetic energy raises stars to their fusion ignition temperature.

**GRAVITY AND LIGHT:**

If a light beam wave front passes tangentially through a gravitational field gradient the portion of the wave front closest to the gravitation source passes through a region of lower potential energy than the portion of the wave front further from the gravitation source. Within the wave the law of conservation of energy applies. When the photon's potential energy Ea becomes more negative its energy difference:

(Eb - Ea) = h Fp

increases to maintain a constant photon energy with respect to field free space. Since h (the Planck constant) is constant within the gravitational energy well this equation forces the photon frequency Fp to increase and hence its wavelength:

Lamdap = C / Fp

to decrease. Hence from a wave front propagation perspective the photon path slightly bends toward the gravitation source. This bending has been experimentally observed via bending of the path of star light as it passes tangentially past the sun or a black hole.

A photon wave front entering a gravitational energy well gains momentum and hence from the perspective of an external observer increases in frequency. A photon wave front exiting a gravitational energy well loses momentum and hence from the perspective of an external observer decreases in frequency. Hence, if a photon originates from inside a gravitational energy well, on exiting the well the photon decreases in momentum and frequency. This effect contributes to observed astronomical red shifts.

**DIRECTION OF TIME:**

Our local universe ages by gradual aggregation of isolated particles into mutual potential energy wells. During the aggregation process radiation is emitted. Most of the radiation energy escapes from the mutual gravitational potential energy well. Thus there is an apparent ongoing decrease in the average energy density of the local universe, which might be interpreted as local universe expansion. This process is known as an increase in entropy and establishes the direction of energy exchanges over time.

**BLACK HOLES:**

Gravitational aggregation of particles eventually leads to formation of a deep gravitational potential energy well known as a black hole from which radiation photons cannot easily escape. A gravitational black hole acts as an energy sink rather than an energy source. The issues of what happens inside a gravitational black hole are beyond the scope of this web site.

Black holes perform an important life enabling function of absorbing radiation, which cools the space around them. Life processes on Earth rely on emission of thermal infrared radiation into a cold universe for temperature maintenance. The issue of whether emitted thermal radiation is absorbed just by black holes or is absorbed by a physically expanding universe or by both is beyond the scope of this web site.

**COSMOLOGY:**

Gravitational fields are believed to be a result of concentrations of energy affecting the structure of space-time. The spacial energy density at each point in space and time causes a gravitational field vector distribution that slightly modifies the potential energy density at other points in space at later times. The relationship between energy and the structure of space-time is the subject of general relativity.

The exact manner in which the energy of galaxies affects the structure of space-time is a subject of current astronomical research. For the purpose of this web site gravity is treated as an imaginary field causing negative potential energy. This treatment might be imperfect, but it is adequate for most practical engineering purposes.

The history of the universe prior to the formation of neutral hydrogen atoms is highly speculative. It is usually assumed that particle rest mass energy came from particle pair production by high energy gamma ray photons originating in a "big bang".

**MOMENTUM:**

A particle with energy Ei that is in linear motion at point **Xi** relative to an observer has a vector property known as linear momentum. The linear momentum **Pi** of particle with energy Ei at point **Xi** moving with velocity **Vi** = d**Xi** / dT

in the frame of reference of an inertial observer is:

**P** = (Ei / C^2)**Vi**

where:

C = speed of light

and

T = time in the observers frame of reference

**RADIATION MOMENTUM:**

Radiation propagates linearly according to the Poynting vector which is the vector cross product of the electric and magnetic fields. Radiation photons with energy Ep convey both energy given by:

Ep = h Fp

and linear momentum **Pp** given by:

**Pp** = [h Fp **C** / C^2]

where

h = Planck Constant

**CONSERVATION OF LINEAR MOMENTUM:**

A basic physical law is conservation of linear momentum. During any interaction between isolated particles the total linear momentum vector before and after the interaction is unchanged.

**ISOLATED SYSTEM EVOLUTION:**

A system can only evolve along a path that is consistent with both conservation of energy and conservation of linear momentum.

**CENTER OF MOMENTUM**

An isolated assembly of particles each with energy Ei has a center of momentum location **Xc** at which point the vector sum of all:

Ei (d(**(Xi - Xc)** / dT) = 0

where:

**(Xi - Xc)** is a vector from the center of momentum to the ith energy bit Ei:

and

T = time as measured at the center of momentum.

From the perspective of an observer at the center of momentum:

d**Xc** / dT = 0

From the perspective of an external inertial observer the center of momentum has a momentum:

d**Pc**

If an energy packet is isolated from external fields its center of momentum moves at a constant velocity in the frame of reference of an external inertial observer (an observer not subject to acceleration).

**MEASURES OF ENERGY:**

Cosmology is concerned with absolute energy. However, most energy measurements and engineering calculations are expressions of energy differences with respect to some reference energy level. The reference energy level depends on the application and the position and motion of the observer.

It is convenient to distinguish between energy seen by an observer at the center of momentum and energy seen by an observer in constant linear motion with respect to the center of momentum.

Potential energy in the frame of reference of the center of momentum is usually chemical potential energy and/or nuclear potential energy. Kinetic energy in the frame of reference of the center of momentum is usually heat or kinetic energy of rotation.

Potential energy related to the position of the center of momentum is commonly referred to as potential energy of position. Energy related to motion of the center of momentum with respect to the observer is commonly referred to as kinetic energy.

An isolated stable concentration of potential energy with a nominal relative position, relative linear motion and heat content is often treated as a particle. Each particle has radial fields that extend to infinity but that contain finite amounts of energy.

**PARTICLE INTERACTIONS:**

Interactions between fields of different particles cause part of the field potential energy of the particles to convert to kinetic energy (energy of motion) in the frame of reference of the center of momentum or vice versa. This energy form change causes particles to accelerate or decelerate. However the net energy motion (linear momentum) of the center of momentum of the entire cluster of isolated particles remains unchanged. This principle is known as conservation of linear momentum.

Radiation transports quanta of energy away at the speed of light. A radiation quantum may be an electromagnetic photon, a neutrino or a graviton.

**FIELD INTERACTIONS:**

Each isolated free particle has an energy consisting of rest (potential) energy and kinetic (motion) energy in the external observer's frame of reference. Each bound particle has an additional binding energy (negative potential energy) component relating to the interaction of that particle with other particles.

**CHARGE AND CHARGE MOTION DISTRIBUTION IN THE UNIVERSE:**

The universe can be viewed as consisting of a particle distribution in a sea of radiation. Each particle has an energy, motion and charge. Electric charge is a conserved parameter. The integral of the net electric charge density over all space is believed to be close to zero. A significant net electric charge would cause rapid expansion of the universe. Cosmologists usually assume that the net charge in the universe is zero. Some cosmologists also assume that the net angular momentum of the universe is zero.

Each element of electric charge causes a radial vector electric field. A sheet charge causes a step change in electric field. Charge motion causes a vector magnetic field. At every point in space and time the prevailing static three dimensional electric and magnetic field vectors separately add causing an electromagnetic field energy density distribution.

**FIELD DISTRIBUTION IN THE UNIVERSE:**

It is helpful to represent the energy contained in confined radiation by a nuclear field vector. Then at every point in space and time there is a characteristic net static nuclear field vector, electric field vector, magnetic field vector and gravitational field vector. These net vectors are mathematically orthogonal to each other and are the result of the sums of vector fields arising from nuclear density, charge density, charge motion and energy density at other points in space at previous times.

**ELECTRIC CHARGE, FIELDS AND TIME:**

Electric charge, electric charge motion and electric and magnetic field vectors and electromagnetic energy densities are mathematically intertwined. Electric charge causes an electric field. Electric charge motion (current) causes a magnetic field. A change in magnetic field with time causes an induced electric field. A change in electric field with time corresponds to charge motion which causes a magnetic field. Thus the spacial electric charge distribution over time defines the electric and magnetic vector field distributions and vice-versa. The sum of the squares of these orthogonal net field vectors is the local electromagnetic field energy density.

Positive potential energy is contained in static electric and magnetic fields. These fields occur as a result of the existence and closed path motion of electric charge. At the microscopic level the mathematical equations that determine the spacial distribution of energy may have multiple real solutions. This issue leads to a branch of physics known as quantum mechanics. Atomic particles have characteristic natural frequencies and exhibit electromagnetic wave like properties. Due to the multiple real solutions there is always uncertainty in simultaneous measurements of particle energy and time and in simultaneous measurements of particle position and particle momentum.

**POTENTIAL ENERGY DENSITY DISTRIBUTION IN THE UNIVERSE:**

The potential energy density at any point in space and time is a function of:

a) The nuclear field vector at that point and time;

b) The net electric field vector at that point and time;

c) The net magnetic field vector at that point and time;

d) The net gravitational field vector at that point and time;

These four energy components are mathematically orthogonal.

The total field energy density at any position in space at any instant in time is the sum of the squares of the instantaneous values of the four mathematically orthogonal vector field components (nuclear, electric, magnetic, gravity). Each vector field component has three orthogonal dimension components.

**FIELD ENERGY DEFINITION:**

A modern definition of field energy density Rhof at any point **Xo** and time To is:

Rhof = (C0 **N^2** + C1 **E^2** + C2 **B^2** + C3 **(i G)^2**)^2
where mutually orthogonal vectors **N, E, B, (i G)** are defined by:

**N** = net nuclear field vector at **Xo**, To
**E** = net electric field vector at **Xo**, To

**B** = net magnetic field vector at **Xo**, To

**(i G)** = net gravitational field vector at **Xo**, To

C0, C1, C2, C3 are real constants. Note that i^2 = -1

Ideally for simplicity C0, C1, C2 and C3 should be chosen to be unity, so that:
Rhof = N^2 + E^2 + B^2 - G^2.

However, for historical reasons in the MKS unit system that is not the case.

Thus field energy density arises from the squares of the net nuclear, electric, magnetic and gravitational vector field terms. Alternatively the field energy distribution can be viewed as arising from the nuclear, charge, charge motion and energy distribution. Note that this formulation is only valid for fields that are static with respect to an inertial observer. The general case of an accelerating observer and/or propagating field changes is more complex. The local nuclear, electric, magnetic and gravitational fields are functions of the spacial distributions of particles, charge, charge motion and energy elsewhere at earlier times.

**SPHEROMAKS:**

The electromagnetic energy of elementary charged particles such as electrons and protons is held in spheromaks. A charged particle spheromak contains a quantum of charge that circulates around a stable closed path at the speed of light. A spheromak has associated vector electric and vector magnetic fields that each contain potential energy. Generally the static field energy density is high near the nominal particle position (on the spheromak symmetry axis) and diminishes rapidly with increasing radial distance from the nominal particle position. The total energy contained in a vector field is finite even though the field radially extends to infinity. The field energy forms part of the particle's total energy. Much of a particle's energy lies in a confined photon. Motion of a particle in the frame of reference of an inertial observer gives the particle kinetic energy and linear momentum.

The extended electric and magnetic fields of different spheromaks interact. This interaction converts field rest potential energy into kinetic (motion) energy. In circumstances of low external radiation density kinetic energy can convert into photons that are radiated away, leaving the interacting particles bound together in a mutual potential energy well. The emitted photon energy and frequency are a result of the electromagnetic spheromak structures of elementary particles.

**SPHEROMAK STRUCTURE:**

If counterflowing uniform strings of positive and negative electric charge (and hence an electric current) having a net charge follows the path of a closed spiral the result is a physically stable electromagnetic structure known as a spheromak. Inside the closed spiral known as the spheromak wall there is a toroidal magnetic field. Outside the spheromak wall there is a poloidal magnetic field. Due to the net charge on the spiral within the spheromak wall there is a cylindrically radial electric field and in the far field outside the spheromak wall there is a spherically radial electric field. A requirement for geometrical stability is that at the toroidal surface, known as the spheromak wall, formed by the closed spiral path the total static field energy density is equal on both sides of the spheromak wall. There is additional dynamic energy within a confined photon that exists inside the spheromak wall.

To realize a stable spheromak the geometry of the closed spiral path must correspond to a static spheromak total energy minimum. For quantum charged atomic particles that energy minimum occurs at number of poloidal charge path turns Np = 222 and at number of toroidal charge path turns Nt = 305. This integer pair leads to the Planck Constant.

The stable spheromak structure enables the existence of highly stable elementary atomic particles such as electrons and protons as well as semi-stable particles and plasmas. The electric and magnetic fields associated with stable particles contain energy that contributes to the atomic particles rest mass. The external fields caused by these particles radially extend out to infinity. However, the total energy of an isolated particle is finite.

The static spheromak that dominates the particles electromagnetic behavior only accounts for a portion of the particle's rest mass. Most of the rest mass of quantum charged particles is carried by the confined photon.

**CLOSED SPIRAL PATH:**

A closed spiral path forming a spheromak is like a a uniform single layer wire winding on a toroid with the two ends of the winding connected together. The spiral path makes Np = 222 turns around the toroid's major axis and Nt = 305 turns around the toroid's minor axis before retracing its path. Thus an electric current following a closed spiral path causes both toroidal and poloidal magnetic fields. In order for a charged particle to be stable the path must precisely repeat itself.

**QUANTIZED CHARGE:**

In stable charged particles the electric charge is quantized. The mechanism of charge quantization is unknown. An element of charge has associated with it a radial vector electric field. An element of charge motion (current) has associated with it a vector magnetic field.

**SPHEROMAK FORMATION:**

If uniformly distributed electric charge continuously circulates around a closed spiral path with no change in spacial charge distribution and no change in current, then the electric and magnetic fields are static and there is no absorption or emission of radiation. Hence there is no change in energy. The result is a spheromak forming a stable charged particle. The electric and magnetic fields of stable charged particles at rest contain the particle's spheromak potential energy. A stable charged atomic particle at rest has a distribution of energy which is spacially constant over time.

At any instant in time, every stable spheromak can be characterized by its nominal position Xo with respect to the observer (known as its center of momentum), its rest energy Ett, its momentum vector **P**, its charge Q, its poloidal magnetic field vector **M** (angular momentum), its toroidal magnetic field vector (spin) **S**. Note that for a particular M there are two possible S vector values.

**STABLE PARTICLES:**

The known universe is primarily an assembly of stable particles known as electrons, protons and photons. All electrons seem to exhibit exactly the same net charge and characteristic isolated rest energy. All protons seem to exhibit an exactly equal but opposite net charge and a different characteristic isolated rest energy.

Neutrons can be viewed as being composed of an electron-proton assembly with zero net charge plus a small amount of additional energy.

Electromagnetic radiation photons have an oscillating electric field vector and an oscillating magnetic field vector but have no net charge and no rest energy.

The total energy of an atomic particle has a potential energy component and a kinetic energy component. If the particle is in an external field there may also be potential energy of position. This position dependent potential energy results from overlap of the particle's electric, magnetic and gravitational fields with the corresponding external fields.

The kinetic energy component is the energy component due to motion of the particle's nominal position.

Kinetic energy of free rotation is kinetic energy due to rotation of a rigid body about an axis through the body's nominal center of momentum. For reasons of mathematical simplicity it is often convenient to treat kinetic energy of rotation as a component of potential (rest) energy rather than as kinetic energy. Kinetic energy of free rotation can be important in both large rotating rigid bodies and in gases with multi-atomic molecules.

**INTERACTIONS BETWEEN STABLE PARTICLES AND PHOTON EMISSION / ABSORPTION:**

Stable particles have external fields. Particles interact with each other via their extended vector fields. At each point in space field vectors of a particular type vectorially add. Each orthogonal net field vector (nuclear field, electric field, magnetic field, gravitational field) squares to yield a field energy density component. Progressive vector field overlap causes a change in total potential energy and a corresponding change in kinetic energy. Since the vector fields extend from an object's nominal position to infinity, objects that are widely separated still weakly interact. The apparent force between distant objects is really the change in the total system potential energy with respect to a change in an object's position relative to the other objects in the system. Conservation of total energy requires that the change in potential energy either become an equal change in kinetic energy or be converted into emitted/absorbed radiation.

In a low external radiation environment part of the molecular kinetic energy may be lost to outer space via net emission of radiation photons, leaving the stable particles more closely bound in a mutual potential energy well. By this process in a low radiation environment particles tend to aggregate to form stable atomic nuclei, atoms, molecules, liquids, crystals, rocks, planets and stars.

At steady state the rate of energy absorption by particles bound in a mutual potential energy well equals the rate of radiation emission. At steady state in a high external radiation density environment the rate of photon emission must be high to equal the relatively high rate of photon capture. Thus in a high radiation density (high temperature) environment particle aggregations are less stable than in a low radiation density (low temperature) environment.

At steady state the thermal photon density indicates the temperature. Thus the infrared radiation spectrum emitted by matter into a vacuum with low radiation density indicates the temperature of the matter.

When an object is in thermal equilibrium with its environment the rates of photon emission and photon absorption are identical.

Most chemical reactions occur in low radiation environments in which the reactants shift from a high energy state to a lower energy state by net emission of infrared photons. An exception is the photosynthesis reaction which occurs in a high radiation environment (sunlight) in which the reactants shift from a low energy state to a higher energy state by net absorption of solar photons. Another exception is electrolysis driven chemical reactions in which the reactants gain energy from an externally applied electric field.

Absorption of high energy ultra-violet photons causes breakup of plastic hydrocarbon polymers by shifting the polymer components from a low energy bound state to a higher energy unbound state. Absorption of still higher energy X-ray photons and gamma photons can cause destruction of biological tissue compounds such as DNA.

In most spontaneous nuclear decay reactions the reactants shift from an unstable high energy state to a more stable lower energy state by emission of kinetic energy and x-ray or gamma photons. However, there are some important nuclear reactions such as gamma initiated fission that are triggered by absorption of gamma photons.

An important physical state change is absorption of solar photons by fine wind blown sea water droplets at ambient temperature to form water vapor. The inter-molecular binding energy per molecule is the latent heat of vaporization. However, this binding energy per molecule is less than the energy carried by a solar photon.

The free water molecules in the atmosphere exchange energy with free N2 and O2 molecules. The water molecules condense int liquid droplets over a wide range of temperatures and pressures.

Another important physical state change is freezing of liquid water droplets in lower temperature clouds which converts the molecular vibration energy into far infrared radiation. This freezing occurs at exactly 0 degrees C over a wide range of pressures.

The sun is constantly emitting solar photons into deep space. Since the sun's energy is finite the potential energy contained in the sun is decreasing and hence the period during which the sun can support life on Earth is finite.

The Earth is constantly emitting thermal infrared photons into deep space. Absent daily warming by solar radiation Earth's surface would soon cool.

Temperature is an indication of average kinetic energy per particle degree of freedom. Temperature is also related to the steady state infrared radiant energy density spectrum within a material.

The temperature at the Earth's surface is nearly constant over prolonged time indicating that the Earth's average rate of energy loss via infrared radiation emission is close to the Earth's average rate of energy gain via solar radiation absorption plus heat gain via radio isotope decay.

The flow of energy which is absorbed by the Earth from the sun and then emitted by Earth into deep space can be tapped do useful work. eg To grow plants and to produce hydroelectric, solar and wind power.

A difference between the flow of energy absorbed by Earth from the sun and the flow of energy emitted by Earth into deep space causes changes in stored thermal energy on Earth which in turn causes formation or melting of polar ice and/or a gradual change in ocean surface temperature. Changing the flow of solar energy absorbed by Earth or the flow of infrared energy emitted from Earth leads to long term climate change.

**ENERGY QUANTIZATION:**

The field interaction equations involving stable atomic particles with quantized charge often have multiple real solutions corresponding to discrete energy states that are separated by energy gaps. A transition from one such energy state to another such energy state is usually accompanied by absorption or emission of a photon and/or by emission /absorption of a particle carrying kinetic energy equal to the energy difference between the two separated energy states.

**PHOTON-SPHEROMAK INTERACTIONS:**

Under suitable circumstances charged particles can absorb or emit electromagnetic radiation quanta known as a photons. The energy and momentum carried by a photon changes the absorbing or emitting particle's total energy and total momentum. The relationship between the amount of energy Ep contained in a photon and the photon's frequency Fp is:

Ep = h Fp

where:

h = Planck constant = 6.62607004 × 10-34 m2 kg / s

The origin of the Planck constant arises from the structure of electromagnetic spheromaks. Every stable atomic particle spheromak at rest has a characteristic natural frequency Fh. The relationship between spheromak energy E and frequency Fh is:

E = h Fh

The factor h arises from the manner in which energy is stored in a stable charged particle spheromak. The Planck constant and related units have recently been slightly changed due to redefinition of a standard kilogram.

An alternative definition of the Planck Constant is:

h = dE / dFh

In the presence of an external magnetic field atomic particles gain or lose energy via absorption or emission of quanta of radiant energy known as photons. Photons have no rest energy and propagate at the speed of light. Thus when a stable particle in state **a** with energy Ea emits a photon and hence shifts to state **b** with energy Eb the change in energy (dE) is given by:

(dE) = (Ea - Eb)

~ h (Fa - Fb)

= h (Fp)

where:

(dE) = change in particle energy [(dE) is positive for photon emission, (dE) is negative for photon absorption];

|Fp| = photon frequency

Thus to the extent that stable particles exhibit discrete energy states photon energies are also discrete.

Photon categories in order of increasing frequency |Fp| are:

AC power, audio, radio, microwave, infrared, optical, ultra-violet, x-ray and gamma ray.

Note that Ep is not precisely equal to the change in spheromak rest potential energy (Ettb - Etta) due to the photon's momentum that causes recoil kinetic energy in the emitting or absorbing particles.

**PHOTON ENERGY AND MOMENTUM QUANTIZATION:**

Since photons result from quantum energy changes in atomic particles, photon energy and photon linear momentum are also quantized.

Photon energy = Ep = h F

Photon momentum = Pp = h F / C

**EFFECT OF RADIATION DENSITY:**

Under circumstances of charge separation and low electromagnetic radiation density kinetic energy can become electromagnetic radiant energy which then propagates away from the center of momentum at the speed of light. Under circumstances of charge separation and high electromagnetic radiation density electromagnetic radiation can be absorbed and converted into kinetic energy and then potential energy. In our local universe the radiation density in outer space is very low compared to the thermal radiation density on Earth which means that Earth constantly emits thermal infrared radiation. Radiation emission by our sun gradually increases the depth of our solar system's potential energy well.

**CHARGED PARTICLE BEAMS:**

Charged particle beams also exhibit wave like behaviour. A beam of electrons incident upon two parallel slits forms an interference pattern. The effective wavelength Lamda of the electron beam is set by the electron's linear momentum P by the equation:

Wavelength:
Lamda = h / P

Rearranging this equation gives:

P = (h / Lamda)

= (h F / C)

which is the same momentum versus frequency expression as for a photon.

The dominant source of rest mass energy for a charged particle is the particle's confined photon. The confined photon gives a charged particle its wave like behavior and gives the particle most of its rest mass.

**ATOMIC NUCLEI:**

Atomic nucleons behave as if composed of mathematical sub-units known as quarks, but quarks have never been observed in isolation. In the "standard model" a hydrogen nucleus (proton) is composed of 3 quarks. A deuterium nucleus may involve six quarks. A helium-4 nucleus may be assembled from two deuterium nuclei containing 12 quarks. Larger nuclei involve a collection of particles bound together in a common mutual potential energy well. Weak nuclear binding occurs via the spheromak electromagnetic fields. Strong nuclear binding generally involves a loss of confined photon energy.

**LARGE PARTICLE AGGREGATIONS:**

For many practical engineering calculations involving assemblies of large numbers of aggregated particles (such as planets) the energy content of the net external electric and magnetic fields is negligible compared to the energy content of the net gravitational field. For these cases the field complexity of the universe can be ignored and the universe can instead be represented as a time dependent spacial energy (or mass) distribution, for which both energy and linear momentum are conserved parameters.

Chemical reactions generally involve changes in the spheromak field overlaps.

Strong nuclear reactions generally involve changes in confined photons.

This web page last updated July 17, 2018.

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