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By Charles Rhodes, P. Eng., Ph.D.


Energy is the name that we give to the most basic constituant of the universe. Everything that we can conceive of is composed of energy. A localized energy packet with a nominal position that is stationary or is moving at less than the speed of light with respect to an observer is known as a particle. Changes in localized particle energy that propagate through space at the speed of light are known as radiation quanta. A radiation quantum may be an electromagnetic photon, a neutrino or a graviton.

A charged particle contains a quantum of charge that circulates around a stable closed path at the speed of light. A charged particle has associated vector electric and vector magnetic fields that each contain potential energy. Generally the field strength and energy density are high near the nominal particle position and diminish 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. This field energy gives the particle rest mass. Motion of the particle in the frame of reference of the observer gives the particle kinetic energy and momentum.

The extended electric and magnetic fields of different particles interact. This interaction converts field rest potential energy into kinetic (motion) energy. In suitable circumstances kinetic energy can convert into photons that are radiated away, leaving the interacting particles bound together in a mutual potential energy well.

Thus, each free particle has a localized energy consisting of rest (potential) energy and kinetic (motion) energy. Each bound particle has an additional binding energy (negative potential energy) component relating to the interaction of that particle with other particles.

There is an additional comparatively weak field energy component known as gravity. Gravitational fields have an imaginary unit vector which causes a gravitational field to contain negative potential energy. Gravity becomes important when the numbers of quantized negative and positive charges are in balance. The exact nature of propagating gravitational field energy quanta is a subject of current research.

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

A basic physical law is the law of conservation of energy. That law states that the amount of energy contained within any closed surface at time Tb equals the amount of energy contained within that closed surface at time Ta plus the net amount of energy that flows in through that closed surface during the time interval (Tb - Ta). Hence energy cannot be either created or destroyed but can be changed in form.

A packet of energy in linear motion has a vector property known as linear momentum. The linear momentum P of energy E at point X moving with velocity V is:
P = (E / C^2)V
C = speed of light

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

Under suitable circumstances a charged particle can absorb or emit an electromagnetic radiation quantum known as a photon. The energy and momentum carried by the photon changes the particle's total energy and total momentum. The relationship between the amount of energy contained in a photon and the photon's frequency is:
Ep = h Fp
Ep = amount of energy in the electromagnetic quantum
h = Planck constant
Fp = radiation frequency

The origin of the Planck constant lies in the electromagnetic spheromak structure of atomic particles.

An alternative definition of the Planck Constant is:
h = E / Fh
E = total energy of a charged particle
Fh = charged particle natural frequency.

Ep ~ (Eb - Ea) = h (Fhb - Fha) = h Fp

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

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. Due to the multiple real solutions there is uncertainty in simultaneous measurements of particle energy and time and in simultaneous measurements of particle position and momentum. Atomic particles have characteristic natural frequencies. These frequencies give atomic particles wave like properties.

Overlap of gravitational fields reduces the total potential energy of a collection of particles. Gravitational fields are a result of concentrations of energy affecting the structure of space-time. 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 a simple imaginary field. This treatment may be imperfect, but it is adequate for most practical engineering purposes.

The ability of mankind to harness natural flows of energy distinguishes man from other animals.

Up until the late 19th century energy was defined as "capacity to do work". That definition is still useful today for commercial exchanges of energy.

During the 19th century it was shown that electric and magnetic fields contain energy and that electromagnetic field energy fluctuations propagate at the speed of light in the direction defined by the cross product between the electric field vector and the magnetic field vector.

In the early 20th century Einstein showed that rest mass is energy and that electromagnetic energy propagates through space as photons. Einstein further showed that the energy density at every point in space and time causes a gravitational field that affects the energy density at other points in space at later times.

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. The atomic particles constantly emit and absorb thermal electromagnetic radiation.

During the second half of 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.

In the early 21st century it became apparent that electrons and protons are spheromaks formed by massless quantized charge that circulates around a closed path at the speed of light. A spheromak has associated with it electric and magnetic fields that contain energy. These fields give the particle rest mass and give the spheromak's charge motion path geometrical stability. It is believed that stable charged atomic particles such as electrons and protons are spheromaks.

Astronomers have concluded that to account for the observed behavior of galaxies these galaxies must contain non-observable energy referred to as dark matter. The issue of whether or not black holes fully account for dark matter is beyond the scope of this web site. Astronomers further claim that the observable universe is expanding at an accelerating rate. The cause of this expansion is also beyond the scope of this web site.

The universe can be viewed as consisting of an electric charge and charge motion distribution in space. 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.

Each element of electric charge causes a radial vector electric field. Circulating 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.

At every point in space and time there is a characteristic net static electric field vector, a net static magnetic field vector and a net static gravitational field vector. These net vectors are mathematically orthogonal to each other and are the results of the sums of vector elements arising from charge density, charge motion and energy density at other points in space at previous times.

Electric charge, electric charge motion and electric and magnetic field vectors and 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 the orthogonal net field vectors is the static local field energy density.

The spacial energy density at each point in space and time causes a gravitational field vector distribution that slightly modifies the energy density at other points in space at later times.

The potential energy density at any point in space and time is a function of:
a) The net electric field vector at that point and time;
b) The net magnetic field vector at that point and time;
c) The net gravitational field vector at that point and time.
These three vectors are mathematically orthogonal.

A modern definition of potential energy density Rhoo at any point Xo and time To is:
Rhoo = (C1 E^2 + C2 B^2 + C3 (i G)^2)^2 where mutually orthogonal vectors E, B, (i G) are defined by:
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
C1, C2, C3 are real constants. Note that i^2 = -1

Thus potential energy density arises from the squares of the net electric, magnetic and gravitational vector field terms. Alternatively the potential energy distribution can be viewed as arising from the charge and charge motion 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 fields is more complex.

At present the local universe primarily evolves by gradual aggregation of nearly isolated charged particles which aggregation converts field potential energy into kinetic energy. The kinetic energy causes emission of radiation photons. Various processes convert high energy photons into a larger number of low energy photons. At steaady state photon emission into into deep space maintains a nearly constant average kinetic energy per charged particle (temperature).

The history of the universe prior to the formation of charged particles is highly speculative. It is thought that charged particle rest mass energy came from high energy gamma ray photons originating in a "big bang". However, the exact origin of charged particles is almost irrelevant to the material on this web site.

Radiation photons propagate linearly according to the Poynting vector which is the vector cross product of the electric and magnetic fields. Radiation photons convey energy and linear momentum.

Changes in charge distribution or charge flow rate at any point in space and time cause changes in the vector energy field distributions that propagate to other points in space and time at the speed of light. Physical laws are such that it is impossible to determine absolute position, absolute velocity or time. Position, velocity and time are relative quantites with respect to an observer's frame of reference. All inertial (non-accelerating) observers measure the same speed of light. As a consequence the experience of time and energy are different for observers in relative motion. This issue gives rise to kinetic energy.

A closed spiral path is like a a uniform single layer wire winding on a toroid with the two ends of the winding connected together. The spiral path may make multiple turns around both the toroid's major and minor axes before repeating its course. 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 repeat itself.

In stable charged particles the electric charge is quantized. The mechanism of charge quantization is unknown. The known universe is primarily an assembly of 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 characteristic isolated rest energy. Neutrons can be viewed as being composed of an electron-proton assembly with zero net charge plus some 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 mass energy.

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 rest mass potential energy. Examples of highly stable particles are electrons and protons.

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

To realize a stable spheromak the geometry of the closed spiral path must correspond to a total energy minimum. For 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 which give 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.

Stable particles have external fields. Progressive overlap between between the external fields converts a portion of the isolated particle potential energy into kinetic energy. In a low radiation environment part of this kinetic energy may be lost to outer space via net emission of radiation photons, leaving the stable particles 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 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.

Thus at steady state the radiation density indicates the particle temperature. The infrared radiation spectrum emitted by matter into a vacuum with low radiation density indicates the temperature of the matter.

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 such one energy state to another such energy state is usually accompanied by absorption or emission of a photon and/or by a particle carrying kinetic energy equal to the energy difference between the two separated energy states.

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

Atomic nucleons behave as if composed of mathematical sub-units known as quarks, but quarks do not exist in isolation. A hydrogen nucleus is composed of a single spheromak containing a single quantized charge. A deuterium nucleus may involve a single spheromak containing three quantized charges. A helium-4 nucleus may be composed of two deuterium nucleus spheromaks. Larger nuclei involve a collection of spheromaks bound together in a common mutual potential energy well.

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 small 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.

Our local universe ages by gradual aggregation of isolated energy packets 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 intuitively is equivalent to local universe expansion. This process is known as an increase in entropy and establishes the apparent direction of time.

Gravitational aggregation of particles eventually leads to formation of a deep gravitational potential energy well known as a black hole from which radiation cannot easily escape. A gravitational black hole acts as a net radiation sink rather than a net radiation source. The issues of what happens to average particle energy, average energy density and the direction of time within 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 emission from the Earth into a cold universe for temperature maintenance. The issue of whether thermal radiation is absorbed by black holes or is absorbed by a physically expanding universe or by both is beyond the scope of this web site.

1) All distance, time, and velocity measurements referred to on this web page are made in an inertial observer's frame of reference.

2) Everything that exists has energy.

3) The potential energy density at a point in space and time is the weighted sum of the squares of the net orthogonal vector field components at that point.

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

5) Stable particles exhibit charge only in quantum amounts. 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.

6) The local electric, magnetic and gravitational fields are functions of the spacial distributions of charge, charge motion and energy elsewhere at earlier times

7) A stable charged atomic particle at rest has a distribution of energy which is spacially constant over time. The energy density diminishes sufficiently rapidly with increasing distance from the particle's nominal position that the result of an energy density integral over all spacial volume is finite.

8) At any instant in time, every stable particle 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.

9) Every stable atomic particle at rest has a characteristic frequency Fh. The relationship between particle energy E and frequency Fh is:
E = h F
where h is known as the Planck constant. The factor h arises from the manner in which energy is stored a stable charged particle.

10) In the presence of a changing 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 or absorbs a photon and hence shifts to state b with energy Eb the change in energy (dE) is given by:
(dE) = (Eb - Ea)
~ h (Fb - Fa)
= h (Fp)
(dE) = change in particle energy [(dE) is positive for photon absorption, (dE) is negative for photon emission];
|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.

11) The energy of an atomic particle has a rest energy component and a linear motion kinetic energy component. If the particle is in an external field the rest energy may include 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.

12) The kinetic energy of linear motion component is the energy component due to linear motion of the particle's nominal position in the observers frame of reference.

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

14) 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 photons.

15) In an isolated system linear momentum is conserved. An isolated system can only evolve along a path that is consistent with both conservation of energy and conservation of linear momentum.

16) 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 (electric field, magnetic field, gravitational field) squares to yield a potential 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.

17) 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.

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

19) 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 net absorption of gamma photons.

20) 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 equal to the latent heat of vaporization. However, this energy is less than the energy of a solar photon.

21) 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.

22) 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.

23) The Earth is constantly emitting infrared photons into deep space. Absent daily energy replenishment by the sun the Earth's surface would soon cool.

24) Temperature is an indication of average kinetic energy per free particle. For materials with molecular charge separation that can readily interact with radiation temperature is also related to the steady state infrared radiant energy density within a material.

25) 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.

26) 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.

27) 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 which in turn cause formation or melting of polar ice and/or a gradual change in ocean 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.

28) The issue of long term climate change triggered first by an increasing atmospheric CO2 concentration and then by melting of ice is the biggest single threat facing mankind today.

This web page last updated October 31, 2016.

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