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

This web site section addresses basic energy issues.

During the 19th century energy was defined as "capacity to do work". However, that definition of energy is too narrow. Energy is a fundamental building block of the universe. Everything that exists contains some amount of energy.

Energy exists in two major forms, energy concentrations at or near mobile discrete points known as particles and spacially distributed radiation.

The universe contains a large but finite number of particles. Every discrete particle can be uniquely identified by an integer i value. With respect to an inertial observer at time t each particle i is characterized by an associated energy Ei, an associated charge Qi, a relative position vector Xi and a velocity vector at that position:
Vi = dXi / dt

A stable particle has a quantized constant charge Qi and a stable rest energy:
Ei = Eio
Vi = 0

Part of the energy associated with a particle is contained in the particle's surrounding field. The field energy density drops off rapidly with increasing distance from the nominal particle position Xi so that the total energy associated with the particle is finite.

Stable particles with surrounding fields have a combination of rest energy and kinetic (motion) energy. The rest energy includes gravitational field energy, poloidal magnetic, toroidal magnetic and radial electric field energies. In circumstances where there is a cluster of particles there are additional energy components caused by field overlap between nearby particles. Often there is a tradeoff between the energy increment caused by field overlap and kinetic energy,

Stable particles exist within a sea of radiation photons. At time t each radiation photon has an energy, a nominal position, a vector momentum and acts as wave propagating at the speed of light in the frame of reference of an inertial observer

An assembly of charged particles can emit or absorb radiation photons. In a large assembly of particles the interior particles exist in an environment where the rate of radiation emission equals the rate of radiation absorption. Particle temperature is an indication of average random particle kinetic energy with respect to the assembly center of mass. Particles near the outside surface of the assembly can be either net emitters of radiant energy or net absorbers of radiant energy, depending on their temperature with respect to the photon radiation temperature in the surrounding space. Photon radiation tends to move energy from places of higher temperature to places of lower temperature.

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

Each radiation photon carries momentum P given by:
|P| = (h F / C)

Vector momemtum is conserved in all particle-photon interactions.

Thus an assembly of stable conserved particles takes discrete energy values and can only transition between these discrete energy values by emitting or absorbing photons of discrete frequencies.

The energy of a particle is thought to arise from charge quanta circulating around a stable 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. This issue causes charge quantization to result in energy quantization.

A particle is mobile discrete point with quantized charge which in the frame of reference of an inertial observer: 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. All free electrons exhibit the same charge, rest energy and poloidal magnetic properties as every other free electron. All free protons exhibit the same charge, rest energy and poloidal magnetic properties as every other free proton. Anti-electrons are particles equal in rest energy to electrons but have opposite charge. Anti-protons are particles equal in rest energy to protons but have opposite charge.

In classical physics a particle has a high energy density at its nominal position. The particle's energy density decreases rapidly with increasing distance from that nominal position. The region of decreasing energy density with increasing distance from a particle's nominal position is known as the particle's field. The local field energy density is proportional to the field intensity squared. A particle's total energy integrated over all space is finite.

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 particle behaviour it may be necessary to invoke quantum mechanics.

In quantum mechanics the particle energy density as a function of displacement from the nominal particle position is replaced by the probability of finding a point particle at the same displacement from the nominal particle position. Hence integrating over all space gives a probability of unity of finding the particle. In quantum mechanics there are often multiple possible discrete real solutions 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 follows one of the possible discrete solutions.

The field energy density as a function of position for an isolated particle is proportional to the probability of finding the particle at that position. That probability is proportional to the sum of the squares of the particle's component wave functions. Thus in quantum mechanics electromagnetic waves have particle like characteristics, and particles have wave like characteristics.

One of the strange features of quantum mechanics is that particle paths can interact even if only one particle seems to be present.

A free particle moves unimpeded relative to other particles. Particles interact with other particles via field overlap in which case the total system energy, integrated over all space, including emitted or absorbed radiation photons, remains constant. At each position the interacting wave function vectors add.

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

Particle interactions convert part of the particles' field energy into kinetic energy. In suitable circumstances kinetic energy can convert into photon radiant energy, which after photon emission result in the previously free particles being mutually bound within a local potential energy well. The binding energy is the energy per particle that must be added to that local energy well to make the particles bound by that well free again.

There are a large number of unstable particles that form during high energy particle collisions and nuclear reactions. However, in small fractions of a second these unstable particles decay into stable particles and hence most of the unstable particles are of little relevance to this web site, which is primarily concerned with sustainable supply of energy to humans.

Interaction of a free particle with its corresponding anti-particle often results in conversion of the entire rest mass into gamma photons. Similarly, in appropriate circumstances high energy gamma photons with sufficient energy can form particle-anti-particle pairs. There are some nuclear decays that result in conversion of a high energy gamma photon into and electron-positron pair with electron absorption and positron emission. However, very little anti-matter exists 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.

Discrete particles in external magnetic fields and assemblies of mutually bound charged particles absorb and emit electromagnetic radiation in energy quanta known as photons. Photons are wave like quantized electromagnetic field disturbances which propagate through space at the speed of light C. Photons convey energy and momentum but have no net charge or rest energy. If not guided or confined, photons eventually spread through the entire universe.

The long range interaction between electrically neutral potential energy wells is known as gravity.

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

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 an atomic nucleus the nucleus often becomes unstable and decays into a different configuration while liberating energy. If the decay path is via either alpha or beta particle emission this process is known as neutron activation. If the two largest decay products are of comparable atomic weight the decay process is known as nuclear fision.

Neutrinos are experimentally observable neutral energy packets which are emitted during the decay of a free neutron into an electron and proton. Neutrinos propagate through space at the speed of light.

Deep space contains a sea of experimentally observable low energy 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 thermal photons directly emitted by stars with typical surface temperatures of about 5800 deg K as well as bursts of higher energy x-ray and gamma photons emitted by various transient stellar processes.

Planet Earth continuously absorbs solar spectrum radiation from the sun and continuously emits thermal infrared radiation into deep space having an average radiation temperature of about 270 degrees K. The main source of the thermal infrared radiation emitted from planet Earth is atmospheric water molecule transitions from liquid phase to ice 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.

Power is a rate of flow of energy from one region to another. Power flows can occur in multiple ways. Examples are electric power, thermal power, mechanical power, radiant power and mass flow. When no particles pass between regions the inter-region flow of particles with rest energy is zero. However, there may still be radiant energy transfer between the regions. Similarly, in principle there can be particle flows between regions with minimal radiant energy flow.

A spheromak is a naturally occurring structure which stores electromagnetic energy. This structure is adopted by stable quantum charged particles. Spheromaks have a characteristic current path geometry, electric and magnetic field shapes and size dependent electromagnetic energies and frequencies. Spheromaks enable the existence of quantum charged particles and are part of the structure of electrons and protons and atoms.

A spheromak enables quantized net charge circulation around a stable closed path at the speed of light, as required for the existence of a stable charged particle.

An isolated quantum charged spheromak is a stable quasi-toroidal shaped structure consisting of a circulating quantum charge(s) and static radial electric, toroidal magnetic and poloidal magnetic fields. A spheromak's external radial electric and poloidal magnetic fields extend to infinity but contain only a finite amounts of energy. The electromagnetic energy stored by a spheromak contributes to or forms the particle's rest mass.

Spheromaks account for the absorption and emission of electromagnetic photons by charged particles in an externally imposed magnetic field.

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 the particles together. By this means particles bind together to form atomic nuclei, electrons bind to nuclei to form atoms, atoms bind together to form molecules and molecules bind together to form solids and liquids.

At normal low particle kinetic energies interaction between the particles' extended fields does not endanger spheromak stability. However, at high particle kinetic energy such interactions can cause spheromaks to restructure in what we term nuclear reactions.

The quantized net charge Qs of a spheromak circulates within the spheromak's quasi-toroidal shaped wall 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
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.

Spheromak interactions 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 such particles. The multiple real energy state solutions lead to quantum mechanical phenomena known as wave-particle duality and entanglement.

This website section reviews the natural physical laws that govern the behavior of charge and energy and hence the evolution of the universe.

The natural physical laws embody the natural physical constants that permitted the evolution of life forms. Were that not the case we would not exist to observe these physical laws.

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

Spheromaks - Introduction

Quantum Mechanics

Charge Hose Properties

Spheromak Structure

Spheromak Approximation

Theoretical Spheromak

Spheromak Energy

Electromagnetic Spheromak

Spheromak Shape Parameter

Planck Constant

Neutral Spheromak

Magnetic Flux Quantum

Nuclear Magnetic Resonance

Confined Photons

Plasma Spheromak

Atomic Particles

Atomic Electrons



This web page last updated December 3, 2021.

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