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

This web site section addresses basic energy issues.

Modern science rests on belief in the existence of a set of physical laws, which are independent of position and time, that govern the evolution of the universe. These physical laws account for the behavior and interaction of all observable objects. From a religious perspective, these physical laws are an expression of the will of God. The physical laws are consistent with the existence of the universe and the evolution of life as we know it. Were that not the case, we would not exist.

The physical laws are best described by mathematical equations. At the macroscopic level the equations usually have unique real solutions. An important exception is computer memory where electronic positive feedback is used to give each memory bit two real stable states.

At the microscopic level the mathematical equations for atomic particle interactions often have multiple discrete real solutions, generally known as energy states. The existence of these multiple discrete real solutions makes evolution slightly non-deterministic which gives life forms a limited degree of free will. In adverse circumstances the continued survival of a particular life form may depend on how prudently that life form exercises its free will.

The universe is a large assembly of quantized charge, static particle vector fields and propagating vector field energy packets (radiation). Particle relative position fluctuations cause particle vector field fluctuations that propagate at the speed of light C.

The vector fields contain energy. Energy is a scaler, not a vector quantity. Specification of only energy conveys no sense of relative position, orientation or movement. Position, orientation and movement are vector parameters.

A propagating vector field fluctuation is a wave that conveys energy in a particular direction at the speed of light C.

The universe contains a large number of independent particles and propagating vector field fluctuations. At any instant t in time energy packet i is characterized by: its energy Ei, its position Xi relative to the observer at Xo:
(Xi - Xo),
and its relative energy motion vector known as momentum Pi. In general:
Pi = [Ei / C^2] [Vi]
where C is the speed of light and:
Vi = d(Xi - Xo) / dt
is the energy packet velocity at its relative position:
(Xi - Xo).

For a vector field fluctuation (radiation):
Vi = C
C = speed of light.

Radiation energy packets are known as photons for electromagnetic radiation, gravitons for gravity radiation and neutrinos for neutron decay radiation.

For an isolated photon i both photon energy Ei and photon momentum Pi are constant. During isolated photon interactions at a particular point both the total energy E and the total momentum P with respect to that point are conserved. A photon has zero rest energy.

The other type of energy packet is a particle. Particles have velocities Vi in the range:
|Vi| < C
and have non-zero rest energy when:
|Vi| = 0

A particle has a quantized net charge Qi. In any isolated interaction between particles the total charge before the interaction equals the total charge after the interaction.

An important relationship governing energy exchange between energy packets is:
dEi dt= [dPi].[dXi]
which can be expressed as:
dEi = [dPi / dt].[dXi]
[Change in energy of energy packet i]
= [Force acting on energy packet i] . [Change in position of energy packet i]

Note that both force and the change in position are vector quantities.

The force on particle i is the change in particle vector potential energy with respect to position.

A change in linear momentum with respect to time is a change in kinetic energy. Frequently there is an energy exchange between potential energy and kinetic energy or vice versa. There are also energy exchanges between kinetic energy and radiation photons.

There are a few common atomic particles such as electrons, protons and neutrons. Each atomic particle has a high energy density near its nominal position and has surrounding vector fields of declining energy density that extend from the nominal particle position to infinity. Each particle has both core energy and a vector field. The core energy component is very stable and can only be modified via an apparatus such as a high energy particle accelerator or a nuclear reactor which can impart very high energies to individual particles or which can produce anti-matter.

In reality part or all of each particle's rest energy is contained in its associated static vector fields. The rest energy is finite because at large radii R from the nominal particle position the static radial electric and gravitational field energy densities decline in proportion to (1 / R^4). This energy density decline with increasing R has the effect of limiting the total energy of a particle.

Charged particles also contain internal circulating currents. These particles have internally sourced magnetic fields that decline even more quickly with increasing distance R from the nominal particle position. On application of an external magnetic field an internal circulating current together with the particle moment of inertia results in a characteristic particle resonant frequency that varies with the externally applied magnetic field strength.

The particle rest energy has gravitational, electric, magnetic and core components which are caused by the presence of concentrated energy, charge and charge motion. In addition to rest energy each particle can have kinetic energy caused by particle motion with respect to the observer.

In circumstances where there are multiple particles there are additional vector field energy components related to interparticle vector field overlap. Interparticle vector field overlap causes nonlinear changes in the local field energy density, which in turn cause particles to experience potential energy gradiants, also known as a forces. Potential energy gradiants cause particle relative motion.

Energy motion, known as linear momentum, is the result of conversion of part of the vector field potential energy into kinetic energy, or vice versa. In certain circumstances kinetic energy can convert to radiant energy.

The net vector field at any point X in space and time t is the vector sum of all the individual particle field vector contributions. The field energy density at point X and time t is the sum of the squares of the net electric, magnetic, and gravitational field vectors at point X and time t.

Vector field fluctations (radiation photons) propagate at the speed of light C and convey both energy and linear momentum.

Radiation often conveys energy away from interacting particles leaving these particles bound together in a mutual potential energy well.

Linear momentum is the energy packet motion vector. For an isolated energy packet i with energy Ei the particle linear momentum Pi is:
Pi = [(Ei Vi) / C^2].
where C is the speed of light. Linear momentum is the tendency of particle i with energy Ei to continue to move in the direction indicated by the particle velocity vector Vi where:
Vi = d(Xi - Xo) / dt
t = time.

In 1905 Albert Einstein showed that for an energy packet i its energy Ei and its linear momentum Pi are related by the formula:
Ei^2 = |Pi|^2 C^2 + Eio^2
Eio = Mio C^2,

This expression replaces the Newtonian expression:
Ei - Eio = (Mio / 2) |Vi|^2
which is only approximately valid for:
|Vi| < < C


For an isolated particle i the particle energy Ei and the particle linear momentum Pi are both constant. In circumstances where separate particles interact energy and linear momentum can be exchanged between particles but in each interaction the total energy and the total linear momentum at the point of interaction are both conserved. Thus the total particle energy immediately before the interaction equals the total particle energy immediately after the interaction. Similarly the net linear momentum vector immediately before the interaction equals the net linear momentum vector immediately after the interaction. Some particle interactions involve absorption or emission of photons or other particles in order to conserve both total energy and total momentum.

Power is a net rate of energy flow in a particular direction from one spacial region to another spacial region. While the energy Ei of particle i is only a function of location Xi, power also involves the energy velocity vector Vi. Power may change with time.

When no particles pass between regions the inter-region flow of particles with rest mass is zero. However, there may still be radiant energy flow between the regions. Similarly, there can be particle flows between regions with little or no radiant energy flow.

Examples of various different forms of power are electric power, thermal power, mechanical power, radiant power and mass flow.

Work involves delivery of energy from an available power flow in order to do something useful for mankind, such as pumping water uphill, creating artificial light or moving an automobile. In most circumstances work is a result of harnessing momentum that arises from changes in field potential energy due to changes in particle field overlap.

Frequently the particle core energy is many orders of magnitude larger than the particle field energy, but the core energy is difficult for mankind to change.

Photons are quantum field fluctuations that propagate through space at the speed of light C. Photons convey energy and momentum but have no net charge or rest energy. If not absorbed, guided or confined, photons eventually spread through the entire universe.

At time t each photon has an energy, a nominal position, a vector momentum and in combination with other photons acts as a wave propagating at the speed of light in the frame of reference of an inertial observer.

Photons can convey energy into or out of a potential energy well.

When isolated free particles approach each other so that their fields overlap, often part of the original particle field potential energy is converted into particle relative linear momentum which causes the particles to further accelerate toward each other. Then part of that relative linear momentum becomes kinetic energy and then photon energy, which is radiated away into deep space. This radiant energy loss causes the previously free particles to become bound together within a mutual potential energy well. Stars, planets, liquids and solids that hold together assemblies of atoms are examples of mutual potential energy wells. Light nuclei are assemblies of protons and neutrons that are bound together by a mutual potential energy well.

The binding energy of a mutual potential energy well is the energy per particle that must be supplied in order to make the particles that are mutually bound free again. In a metal the binding energy that must be supplied to cause the metal to release electrons is known as the metal work function. In liquid water the binding energy that must be supplied to make steam (free H2O molecules) is known as the latent heat of vaporization.

At steady state an assembly of particles within a mutual potential energy well will both absorb and emit radiation photons. In a large assembly of particles within a mutual potential energy well the interior particles exist in an environment where the average rate of photon energy emission by each particle equals the average rate of photon energy absorption by that particle. However, particles near the outside surface of the assembly of particles can be either net emitters of photons or net absorbers photons, depending on the magnitude of the internal photon energy flux with respect to the photon energy flux in the surrounding space.

In the nucleus of a heavy atom the issue of binding energy is complex. Heavy nucleii such as uranium are formed by stellar super nova. A heavy nucleus consists of mutually bound particles that are further bound by extra neutrons and a substantial amount of positive binding energy. However, if the structure of a heavy nucleus is suitably disturbed, such as by addition of a neutron, the nucleus can fission causing release of its constituant particle assemblies (fission products) as well as large amounts of positive binding energy. Hence fission nuclear power is a result of release of positive nuclear binding energy that is collected during a stellar super nova.

The existence of positive nuclear binding energy is enabled by short range neutron-proton interactions which effectively reduce the short range electrostatic forces between protons and introduce negative neutron-proton binding energy. The net nuclear charge is determined by the number of protons but the neutron presence and nuclear geometry prevents the nucleus flying apart due to the positive proton coulomb binding energy. However, disturbing a nucleus by changing its number of neutrons can cause it to become unstable. A nucleus usually spontaneously reconfigures itself to achieve additional stability by some form of particle and radiation emission.

Low atomic weight nuclei are formed in normal solar interactions. For example, deuterium (H-2) and tritium (H-3) nuclei can combine to form He-4 nuclei. During this combination high kinetic neutrons are emitted. The remaining particles are trapped in a mutual potential energy well that we know as He-4. In this case the binding energy is negative. Hence fusion power is a result of emission of neutrons with positive kinetic energy which leave behind negative binding energy.

In our universe mutual potential gravitational energy wells (stars, planets) and mutual electric energy wells (light atoms) exist in a sea of negative gravitational field energy and propagating low positive energy radiation photons.

Heat is the thermal energy (energy associated with random particle motion and random photon motion) contained within a large assembly of interacting particles. These particles are usually confined by some form of rigid container or by a mutual potential energy well. Within that energy well are random photons that are in equilibrium with the random moving particles. Temperature is an indication of the average thermal energy per particle. Heat tends to flow from a region of high temperature to a region of lower temperature. A consistent heat flow in a particular direction is thermal power. With an appropriate heat engine a portion of this thermal power can be harnessed to do work.

Due to the relatively low temperature of photons in deep space (2.7 degrees K), deep space tends to absorb photons emitted during random particle interactions within higher temperture planets and stars. The radiation emitted by random particle interactions is known as thermal radiation.

Each electromagnetic radiation photon has energy Ep given by:
Ep = h F
F = photon frequency
h = Planck Constant

Each radiation photon has zero rest mass (Mo = 0) and hence from Einstein's formula:
E^2 = |P|^2 C^2 + Mo^2 C^4
carries linear momentum P given by:
|P| = Ep / C = (h F / C)

Total energy E and total linear momemtum P are conserved in all energy packet interactions.

An assembly of stable conserved particles generally transitions between energy states by emitting or absorbing photons of discrete frequencies.

The field potential energy of a particle arises from its charge quantum circulating around a complex closed path at the speed of light. The relative geometric shape of the closed path is stable but the length of that path increases with decreasing particle rest energy. A consequence of this relationship is that charge quantization causes photon energy quantization.

A stable free charged particle has a non-zero energy at rest and has nominal position and velocity vectors, where the velocity magnitude is less than the speed of light.

Our local universe contains highly stable particles known as electrons and protons, although most of these particles have already combined to form hydrogen. Every free electron in its ground state exhibits the same charge, rest energy and magnetic field properties as does every other free electron in its ground state. Every free proton exhibits the same charge, rest energy and magnetic properties as does every other free proton in its ground state. Anti-electrons are particles equal in rest energy to electrons but with opposite charge. Anti-protons are particles equal in rest energy to protons but with opposite charge.

Neutrons behave as quasi-stable particles. When bound to an adjaent proton in a nucleus neutrons can exhibit very long life. However, in a nuclear reactor a free neutron decomposes into an electron, a proton and a neutrino with an apparent half life of about 12 minutes.

Classical physics provides formulae that allow convenient solution of many practical physical probems. However, classical physics is a simplification of reality. In order to properly represent microscopic particle behaviour it is necessary to invoke quantum mechanics and relativity.

In quantum mechanics there are often multiple possible discrete real energy state solutions for a particular particle but what is experimentally observed with a large number of particles is an average of these real solutions. When single particles are tracked, one at a time, each particle adopts only one of the possible discrete solutions. (eg electrons passing through a slit)

A seemingly strange feature of quantum mechanics is that in circumstances where there are multiple possible real solutions the solution adopted by a particular particle often appears to be random.

A free particle moves unimpeded by other particles. Particles interact with other particles via vector field overlap in which case the total system energy, integrated over all space, including emitted or absorbed radiation photons, remains constant.

At every point in space the local field energy density has mathematically orthogonal electric, magnetic and gravitational vector components from various particle species that add vectorially. The gravitational unit vector is imaginary, which causes the gravitational field energy density to be negative. The local field potential energy density is the sum of the squares of these field vector components. Each particle also has both core rest mass and a kinetic energy component arising from its momentum with respect to the center of mass in the observer's frame of reference.

There are a large number of unstable particle assemblies that form during high energy particle interactions. However, unstable particle assemblies eventually spontaneously decay into more stable particle assemblies, so that most of the unstable particle assemblies are of little relevance to this web site, which is primarily concerned with sustainable supply of energy to humans. As a general note, the more stable an atomic nucleus is the less quickly it decays. For light nuclei the most common form of spontaneous decay is electron emission. For heavy nuclei the most common form of spontaneous decay is emission of He-4 nuclei. These emissions are accompanied by gamma photons to simultaneously conserve energy and momentum.

Interaction of a free particle with its corresponding anti-particle often results in conversion of the total rest mass into high energy gamma photons. Similarly, in appropriate circumstances high energy gamma photons can form particle-anti-particle pairs. There are some nuclear decays that result in conversion of a high energy gamma photon into an electron-positron pair with immediate electron absorption and positron emission. However, very little anti-matter seems to exist in our local universe, so from the perspective of this web site, which is concerned with sustainable supply of energy to humans, the issue of anti-matter is almost irrelevant.

The long range interaction between electrically neutral mutual potential energy wells is known as gravity. The gravitational unt vector contains i = (-1)^0.5 which results in a negative field energy density.

Gravitons are experimentally observable wave like gravitational field disturbances which propagate through space at the speed of light C.

In a very high energy density environment, such as the center of a star, electrons and protons can absorb sufficient energy from their environment to form semi-stable particles with zero net charge known as neutrons. Free neutrons are unstable but can acquire long term stability by coupling with protons to form stable nuclei.

For stable low atomic weight atoms the maximum number of neutrons per proton is about 1 whereas for stable high atomic weight atoms the maximum number of neutrons per proton is close to 1.6. When an extra neutron is added to a very high atomic weight nucleus the nucleus may become unstable and break into two smaller nuclei while liberating surplus particles and photons. This process is known as nuclear fission.

High kinetic energy (1.3 GeV) protons, when they impact a high atomic weight nucleus such as lead, by a process known as neutron spallation, can knock off small nucleus pieces such as individual neutrons. When a 1 GeV proton impacts lead nuclei, typically about 25 free neutrons are released per impacting proton.

Neutrinos are experimentally observable energy packets with no charge and almost negligible rest mass that are emitted during the decay of a free neutron into an electron and proton. Neutrinos propagate through space at close to the speed of light.

Deep space contains a sea of experimentally observable photons known as the cosmic background. These photons have an energy distribution corresponding to a thermal radiation temperature of about 2.7 degrees K. Superimposed on the cosmic background are small angular intensity variations. Deep space also contains higher energy photons directly emitted by stars with typical surface temperatures of about 5800 deg K, as well as bursts of much higher energy x-ray and gamma photons emitted by various transient stellar processes.

Planet Earth continuously absorbs solar spectrum thermal radiation from the sun (5800 degrees K) and continuously emits thermal infrared radiation into deep space having an average radiation temperature of about 270 degrees K. The main source of the infrared radiation emitted from planet Earth is top of cloud atmospheric water molecule transitions from liquid phase to solid phase. Thus planet Earth is constantly absorbing solar radiant energy primarily comprised of visible photons and is constantly emitting a larger number of lower energy thermal infrared photons.

Spheromaks are natually occurring electromagnetic structures that concentrate electromagnetic field energy as required for the existence of stable charged particles such as electrons, protons and atoms.

Semi-stable spheromaks can also form in plasmas.

A spheromak circulates current at the speed of light around a geometrically stable closed path. The spheromak current path is a filament that traces out a closed surface known as the spheromak wall. The spheromak size and the filament length are inversely proportional to the spheromak's field energy.

An isolated quantum charged spheromak is a stable quasi-toroidal shaped structure consisting of a circulating quantum charge forming the closed spheromak wall and electric, toroidal magnetic and poloidal magnetic fields that contain finite amounts of energy. The radial electric and poloidal magnetic fields extend from the spheromak wall to infinity. The energy field inside the spheromak wall is toroidal magnetic. The electromagnetic field energy stored by a spheromak contributes to the particle's rest mass.

Stable spheomak geometry arises from the properties of prime numbers. The Spheromak geometry accounts for the Planck Constant and the Fine Structure Constant.

Spheromaks account for the absorption and emission of electromagnetic photons by charged particles in an externally imposed magnetic field. This phenomena is known as nuclear magnetic resonance.

Spheromaks also account for the absorption and thermal emission of electromagnetic photons by matter.

Spheromaks interact with one another at a distance via overlap of their external fields. Interacting spheromaks convert field potential energy into kinetic energy with respect to the particles' center of mass, or vice versa. During such interactions spheromaks can emit or absorb radiation photons.

Net emission of radiation photons by interacting spheromaks causes formation of mutual potential energy wells which tend to bind particles together. By this means particles form light weight atomic nuclei, electrons bind to nuclei to form atoms, atoms bind together to form molecules and molecules bind together to form solids, liquidsand stars.

Under normal circumstances interaction between the particles' extended fields does not endanger spheromak stability. However, at very high particle kinetic energies particle interactions can cause spheromaks to restructure in what are termed nuclear reactions.

Spheromaks are at the foundation of quantum mechanics. In quantum mechanics the mathematical equations governing interacting particles have multiple discrete real energy solutions known as energy Eigenvalues. This multiplicity of real energy solutions causes uncertainty with respect to the actual energy state of any particular particle at any moment in time. However, there is statistical certainty regarding the collective behaviour of a large number of identical particles. The multiple real energy state solutions lead to quantum mechanical phenomena known as wave-particle duality and entanglement.

The quantized net charge Qs of a spheromak circulates at speed of light C around a complex closed spiral path of length Lh. Hence a spheromak has a natural frequency Fh given by:
Fh = C / Lh.

A change in spheromak energy dE is proportional to the spheromak's change in natural frequency dFh, via the formula:
dE = h dFh
where h is known as the Planck constant. However, h is not an independent physical constant. In reality h is a function of the charge quantum Q, the speed of light C, the permiability of free space Muo and the spheromaks geometrical shape.

The formula:
dE = h dFh
applicable to a charged particle leads to the equation:
Ep = h Fp
which relates the size of the quantum of radiant energy Ep to the radiation frequency Fp where:
dE ~ Ep
dFh = Fp.
Thus the energy and frequency of a photon of absorbed or emitted radiant energy are closely related to the changes in the energy and frequency of the spheromak which absorbs or emits the photon. In fact it appears that photon energy quantization is a direct result of spheromak behaviour.


Basic Physical Laws

Energy Sources

Energy Balance

Vector Identities


Energy Basics

Basic Physical Concepts Part A - Relativity, Energy & Momentum

Basic Physical Concepts Part B - Energy Aggregation

Basic Physical Concepts Part C - Work

Basic Physical Concepts Part D - Rigid Bodies

Energy Composition of Matter

Solar Energy

Solar System History

Field Theory

Quantum Mechanics

Spheromaks - Introduction

Charge Filament Properties

Spheromak Structure

Spheromak Approximation

Theoretical Spheromak

Spheromak Energy

Electromagnetic Spheromak

Spheromak Winding Constraints

Planck Constant

Magnetic Flux Quantum

Nuclear Magnetic Resonance

Confined Photons

Plasma Spheromaks

Atomic Particles

Atomic Electrons



This web page last updated April 30, 2023.

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