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

This web page reviews the energy composition of matter.

An isolated particle is a localized concentration of energy in space. Stable charged particles such as electrons and protons contain a single quantized charge that is uniformly distributed along a stable closed spiral path and moves along that path at the speed of light, thus forming a stable non-propagating solution to the electromagnetic equations that determine the evolution of the universe. This stable solution is known as a spheromak. The potential (rest) energy of each particle consists of the spheromak's electric and magnetic field energy + the confined photon energy.

If this isolated particle interacts with other distant particles part of the isolated particle field energy will be converted into kinetic energy. Generally kinetic energy occurs as a result of field overlaps between particles. In certain circumstances kinetic energy can change into photon energy and be emitted, or photons can be absorbed which increases particle kinetic energy.

A photon is a packet of energy Ep that exists as part of an electromagnetic wave (an electromagnetic field ripple) that propagates at the speed of light. A photon has no net charge and no rest mass. The frequency Fp of a photon is proportional to photon energy Ep via the relationship:
Ep = h Fp
where h is known as the Planck Constant. The origin of the constant h lies in the structure of electromagnetic spheromaks.

A photon of sufficient energy can form a particle and an anti-particle pair. Similarly a particle and an anti-particle can annihilate to form a photon. Particles and anti-particles have equal positive energy but opposite charges.

Random motion of interacting particles with quantized charge causes local changes in the spacial electric and magnetic energy density which result in emission or absorption of electromagnetic radiation photons. When quantized charge forms a particle and follows a stable closed path the charge is uniformly distributed along the path and there is no emission of radiation. However, a charge following a stable closed path can adopt a similar but shorter or longer closed path by absorption or emission of an electromagnetic radiation photon that provides the appropriate difference in energy.

Conservation of total energy requires that the sum of an isolated system's total rest mass, kinetic energy, and radiant energy is a constant. As particles approach each other their field overlaps cause a reduction in field energy and a corresponding increase in kinetic energy. Initially the kinetic energy of free particles is sufficient to allow the particles to escape from the mutual potential energy well that results from overlap of the particle's fields. However, in a low radiation density environment part of the excess kinetic energy tends to convert to photons which radiate away into space. When photons are emitted without off setting photon absorption the average kinetic energy of the remaining particles decreases. These particles are then trapped together in a mutual potential energy well.

The additional average kinetic energy per particle required to allow a particle to escape from this mutual potential energy well is known as the particle binding energy. Evolution is set by photon emission which carries away positive energy into deep space and thus leads to formation of clusters of particles mutually bound by potential energy wells. Atomic nuclei, atoms, molecules and solids all form by radiative emission of binding energy.

The early universe likely consisted of a collection of nearly isolated electrons and protons known as a plasma. Each isolated particle had positive energy related to its electric and magnetic fields and confined photons and negative energy related to its gravitational field.

The electrons had quantum negative charges and the protons had quantum positive charges. Each particle was stable due to its spheromak structure.

The interaction distance of spheromak confined photons is only of the order of one atomic particle diameter. Hence for widely separated particles the confined photon energy component is constant independent of particle separation.

The static magnetic fields of spheromak structured particles decreases relatively rapidly with radial distance. Hence at long distances the magnetic field energy density is negligible.

The electric fields of nearby positive and negative particles interact to reduce the total amount of electric field energy and increase the total amount of particle kinetic energy.

Some of the kinetic energy converted into electromagnetic photons which were radiated away leaving the electrons and protons mutually bound into hydrogen atoms.

In accumulations of hydrogen atoms there are equal numbers of positive charges and negative charges so that at large distances the electric fields cancel.

It is believed that about 300,000 years after the theoretical "big bang" the initial electon-proton plasma which condensed to form neutral hydrogen atoms. We cannot look further back in time before the formation of hydrogen because the electromagnetic radiation which astronomers rely upon is rapidly absorbed by a plasma. Hence prior period cosmological theory is nothing more than informed speculation.

The apparent frequency of the photon emission from initial hydrogen condensation and the angular distribution of that emission has given rise to various cosmological theories, all of which are outside the scope of this web site.

When the gravitational fields of separate particles interact the total gravitational field energy becomes more negative and the particles kinetic energy becomes positive, causing particle motion toward a mutual central point.

Some of that kinetic energy converts to photons which are emitted into deep space carrying with them positive energy.

The material left behind is matter containing positive energy trapped in a mutual negative gravitational potential energy well. This is the mechanism of matter accumulation for star formation and then galaxy formation.

A star is formed by such accumulation of particles. As the particles come together the gravitational field energy density becomes yet more negative and the particle's kinetic energy density becomes yet more positive. When the star's mass is sufficient the internal pressure is enough to form neutrons and/or deuterium nuclei from electrons and protons. When the deuterium nuclei concentration is sufficient the star can commence fusion reactions.

Objects can move around at the bottom of a gravitational potential energy well almost as if that well did not exist. However, deep space is outside this potential energy well. The radial arms of a rotating spiral galaxy lie on the sloped walls of the galaxy's potential energy well.

On the walls of the potential energy well of a spiral galaxy there is a change in gravitational potential energy Ep with respect to radial position (dEp / dR) that does not exist either in deep space or at the bottom of the potential energy well.

Thus a spiral galaxy is held together not by "dark matter" but by an accumulation of negative gravitational energy. This accumulation of negative energy is a result of cumulative emission of photons carrying away positive energy for billions of years.

A physical analogy is a metal. Electrons can easily move around inside a metal. However, to get the electrons into free space where they can again easily move around an amount of energy must be supplied to each electron equal to the metal's work function, which is the depth of the electron potential energy well in the metal. The walls of this energy well occur at the surface of the metal.

Thus the behavior of electrons at the metal surface is quite different from in the bulk of the metal.

Gravity makes the reference energy level in space a function of position. Conversion of kinetic energy into emitted photon and graviton energy makes this reference energy level negative.

My understanding of energy is built on the assumptions that:
a) Space which contains no particles, no fields and no radiation has a zero energy density and
b) Gravitational fields from normal matter contain negative energy.

By photon emission an electron can join a proton and form a hydrogen atom. The presence of the proton's electric field allows the existence of up to 2 electron spheromaks in a poloidal field cancelling configuration.

A He nucleus can support 2 electon spheromaks in a poloidal field cancelling configuration plus up to one additional electron in a new larger spheromak.

Similarly a Li nucleus can support 2 electron spheromaks in a poloidal field cancelling configuration plus 1 or 2 larger electron spheromaks, also in a poloidal field cancelling configuration.

When discrete electron spheromaks aggregate together there is usually photon emission, so that the total aggregated spheromak energy is less than the sum of the energies of the individual isolated electron spheromaks. Most energy aggregation processes emit radiation to their surroundings and are termed exothermic. A few energy processes, such as photosynthesis, absorb radiation from their surroundings and are termed endothermic. An endothermic process cannot run if there is no external radiant energy available to drive the process.

There are several general classes of particle binding:
1) Processes that are not yet fully understood that bind stars in into galaxies.

2) Gravity and emission of kinetic energy bind planets to stars.

3) Electromagnetic fields and emission of low energy thermal photons bind molecules into a solid;

4) Electromagnetic fields and emission of medium energy photons bind atoms into molecules as in chemical reactions;

5) Electromagnetic fields and emission of higher energy photons bind electrons to atomic nuclei (ionization)

6) Electromagnetic fields and emission of soft gamma photons bind He-4 nuclear groups into atomic nuclei(weak nuclear force);

7) Emission of gamma photons binds protons and neutrons together to form He-4 groups. A typical hard gamma photon results from a change in confined photon energy.

A multi-particle nucleus with a relatively small binding energy per particle may be unstable. The particles composing the nucleus may randomly exchange energy until one of them acquires enough kinetic energy to escape from the mutual potential energy well. The remaining particles will then be in a lower energy state which is likely more stable. Alternatively the nucleus may over time discharge a succession of particles or fission. Each particle discharge lowers the nuclear energy (increases the binding energy per particle) and improves the nuclear stability. The more stable a nucleus the longer its half life. The particle types that are normally discharged are photons, electrons, positrons, neutrons and He-4 nuclei. Occasionally discrete protons are discharged.

Matter is a general name applied to an assembly of particles that has rest energy in the frame of reference of an inertial observer. Most atomic nuclei are the result of aggregations of the highly stable atomic particles known as protons and electrons. In a suitable high radiation density environment such as the center of a star electrons and protons can aggregate to form neutrons and atomic nuclei. An atom is an ordered aggregation of atomic particles. A molecule is an ordered aggregation of atoms. Matter is usually an aggregation of molecules. In a neutral gas there is no molecular order. In a liquid there is short range molecular order. In a crystaline solid there is long range molecular order. Matter at temperatures above zero degrees K also contains nuclear kinetic energy, lattice well potential energy, electron excitation energy and radiation photons. There are additional small amounts of gravitational and neutrino energy.

When the total rate of radiant energy absorption by matter equals the total rate of radiant energy emission by that matter the matter is said to be in a Steady State Condition.

When the rate of radiant energy absorption as a function of frequency by matter equals the rate of radiant energy emission as a function of frequency by that same matter the matter is in a Thermal Equilibrium Condition. At Thermal Equilibrium no work can be done because there is no means of achieving net emission of the heat resulting from doing work.

The center of the Earth is in a near Thermal Equilibrium Condition. The center of the Earth is surrounded by other material of similar composition and equal temperature. Hence across the electromagnetic spectrum absorbed radiation equals emitted radiation and no work is done.

The total energy consists of random thermal kinetic energy arising from particle motion with respect to the matter Center of Momentum (CM) plus CM kinetic and potential energy in the observers frame of reference. For most matter at room temperature the CM kinetic energy is small compared to the random thermal kinetic energy, which in turn is very much smaller than the CM potential (rest mass) energy. Hence, in most practical situations the CM kinetic energy is only a microscopic ripple in the total energy.

Some nuclei are unstable energy arregations that eventually randomly decay into more stable particles and nuclei. Neutrons are often stable in an atomic nucleus but as free particles decay into an electron, proton and neutrino. From a practical engineering perspective the decay of unstable atomic particles is dealt with using tables which show the half life and decay products along each decay path.

The stable particles that have rest energy are the electron, proton and various stable atomic nuclei. In the absence of interactions with anti-matter these particles have half lives in excess of tens of billions of years. Antimatter particles are believed to be equally stable as long as they do not interact with normal matter.

Stable particles located in an external magnetic field exhibit quantized energy states. These quantized energy states readily absorb and emit photons having a frequency dependent on the externally applied magnetic field.

Stable electron spheromaks have quantized charge Q and a characteristic natural frequency F. The natural frequency is related to the spheromak's rest energy E by the equation:
E = h F
where h is known as the Planck constant. The Planck constant is actually a composite of other physical constants.

The measured total rest energy of a free electron is 0.511 MeV and the measured total rest energy of a free proton is 938.2 MeV. Recall that 1 MeV = 10^6 eV. Every free electron at rest in a field free environment has the same rest energy and hence the same rest mass and same natural frequency as every other free electron at rest in a field free environment. Similarly, every free proton at rest in a field free environment has the same rest energy and hence the same rest mass and same natural frequency as every other free proton at rest in a field free environment.

For water the total rest energy per molecule is about:
938.2 MeV X 18 = 16.89 GeV / molecule. Recall that 1 GeV = 10^9 eV.

The measured net electron charge is - 1.60217646 X 10^-19 coulomb. The measured net proton charge is + 1.60217646 X 10^-19 coulomb. As far as is known the net electron charge precisely balances the net proton charge and the magnitude of this net charge is the same for all electrons and all protons. This quantization of stable particle net charge lies at the root of quantum mechanics. The mechanism of this precise charge quantization is not known. However, charge quantization sets the Planck constant.

Semi-stable particles are particles that are stable inside some atomic nuclei but which become unstable when ejected from a nucleus. An example of a semi-stable nuclear particle is a neutron, which within some isotope nuclei has a half life of billions of years but which when ejected from an atomic nucleus spontaneously decays with a half life of about 11 minutes. There are other semi-stable nuclear particles, such as mesons, that have much shorter half lives.

An atomic nucleus consists of an aggregation of stable and semi-stable particles. Some atomic nuclei, such as helium-4, are extremely stable. Other atomic nuclei are unstable and may have very short half lives. Some atomic isotopes have simple decay paths that release as much as 25 MeV per decay. A nuclear fission process may release over 200 MeV per fissioning atom. The energy release may be via decay product particle kinetic energy and/or photons. Most nuclear reactions proceed by emission of a particle with kinetic energy and/or radiant energy at every step. A few nuclear reactions are endothermic and only proceed in a high radiation or high particle kinetic energy environment. An example of such a reaction is:
(Li-7) + n + (kinetic energy) = (Li-6) + 2 n
This endothermic reaction is of great importance in production of tritium and its decay product He-3.
The follow on reaction is:
(Li-6) + n = (He-4) + (H-3)

Nuclei tend to build up in multiples of deuterium. (proton-neutron pairs which in essence are assemblies of 2 protons plus 1 electron).

Free electrons and an atomic nucleus become bound into a mutual potential energy well known as an atom by emission of photons. The electron charges are uniformly distributed along the closed electron motion path of the spheromak(s) so that in a stable cold atom there is no emission or absorption of energy. The electrons tend to form pairs with cancelling poloidal magnetic fields. Helium has a 2 electron spheromak. As the atomic number increases the 2 electron spheromak becomes surrounded by a 7 electron spheromak. As one more charge is added to the nucleus the two spheromaks merge. The spheromaks continue to build up in this manner and give an atom its chemical properties and its characteristic spectroscopic emission-absorption lines. As the atomic diameter increases the binding energy associated with single electron ionization decreases.

An ion is an atomic nucleus that does not have the exact number of bound electrons required to balance the positive nuclear charge.

A plasma consists of a mixture of ions and free electrons. Typical laboratory plasmas have free electron kinetic energies in the range 20 eV to 10,000 eV. In a cool plasma typically only one electron per atom is an isolated spheromak. In a hot plasma all the electrons exist as isolated spheromaks.

The electron binding energy for a hydrogen atom is about 13.6 eV. This is the energy per electron necessary to cause ionization of hydrogen. Hydrogen atoms tend to bind together in pairs to form H2 gas molecules. For helium the minimum energy per atom necessary to cause single electron ionization is about 24.6 eV.

In most molecules the minimum electron binding energy in the outer electron spheromak determines the maximum inter-atomic binding energy.

Stable spheromaks have the lowest energy per electron. Hence atoms tend to chemically bind together by exchange of electrons to form stable multi-electron spheromaks. The multi-electron spheromaks are made stable either by electron exchange (ionic bonding) or by electron sharing (covalent bonding).

MOLECULES: When suitable atoms come together and emit a photon(s) they may become bound together into molecules or crystals. The interatomic binding energy (also known as chemical energy) that forms atoms into chemically bound molecules is typically about 1.0 eV per molecule. The intermolecular binding energy that forms the latent heat of vaporization is typically about 0.05 eV per molecule.

Most chemical reactions proceed by emission of nuclear kinetic energy (heat) or by emission of photon radiation at every step. However, some chemical reactions can be reversed by supply of energy via application of pressure, heat, electricity and/or by selective physical removal of a particular reaction products as they form. Some chemical reactions can be accelerated by introduction of a catalyst that provides a higher probability energy exchange pathway.

A gas is a cluster of molecules in which the individual kinetic energy of each molecule exceeds the intermolecular binding energy. Hence the movement of individual molecules of a gas is constrained only by the enclosure walls.

Random thermal kinetic (heat) energy can be spontaneously emitted from a cluster of gas molecules via thermal electromagnetic radiation (photons) or via enclosing wall thermal conduction. If there is not a corrsponding amount of ongoing heat absorption this heat loss process eventually reduces the average random kinetic energy per molecule remaining in the gas to a level below the intermolecular binding energy. The remaining molecules then become bound together by the intermolecular potential energy well to form a liquid or a solid. This process occurs during the condensation of water vapor in the Earth's atmosphere.

A liquid is a bound cluster of molecules in which the individual molecules have sufficient random kinetic energy that they can rotate in place and can easily slide past one another. Hence a liquid in a gravitational field adopts the shape of the lower part of its container.

For water the intermolecular binding energy that defines the transition from the liquid phase to the vapor (gas) phase is given by:
(heat of vaporization) / (Avogadro's number)]
= [(40.65 X 10^3 J / mole) / [(1.602 X 10^-19 J / eV) X (6.023 X 10^23 molecules / mole)]
= .4213 eV / molecule
= 421.3 X 10^-3 eV / molecule

Random thermal kinetic (heat) energy can be spontaneously emitted from a liquid surface via either evaporation or via thermal electromagnetic radiation (photons). These cooling processes reduce the average random kinetic energy per molecule remaining in the liquid to a level below that necessary for individual molecules to rotate in place. The remaining molecules are then bound together by the potential energy well to form a solid. A crystal is a solid consisting of a highly ordered assembly of molecules. The heat that must be removed to make the transition from a liquid to a solid is known as the heat of fusion.

The highly ordered nature of crystals makes them structurally weak in certain directions with respect to the crystal axes. For this reason materials such as steel contain small amounts of key impurities and are forged to reduce the material to an aggregation of small randomly oriented crystals that is more capable of reliably bearing structural and impact loads than is an aggregation of larger crystals.

A solid is similar to a liquid except that the molecules can not rotate in place and can not slide past each other. An unstressed solid will maintain its shape without a container. The intermolecular binding energy that prevents molecular rotation can be obtained from the heat of fusion of the material. For water this binding energy per molecule is:
(heat of fusion) / [(Avogadro's number) X (unit change)]
= [333.55 X J / g X 18 g / mole] / [6.023 X 10^23 molecules / mole X 1.602 X 10^-19 J / eV]
= 622.2 X 10^-4 eV / molecule
= 62.22 X 10^-3 eV / molecule

In a real material due to thermal kinetic energy molecules in a gas are constantly in random linear, rotational and vibrational motion and in a solid or liquid the molecules are constantly vibrating.

The random molecular motion is particle kinetic energy which due to the law of conservation of energy is accompanied by emission and absorption of photons. At the material surface some of the emitted photons escape into the surrounding space. This photon emission is known as thermal radiation. Thermal radiation is a result of conversion of kinetic energy into photons by charged particles (spheromaks). Since the spheromak energy is quantized so also are the emitted photons.

Emission of thermal radiation will cause a material to gradually cool until the radiation power emitted via thermal radiation equals the absorbed thermal radiation power. Similarly, if the radiation absorption from the environment exceeds the materials thermal radiation emission the material will gradually warm until the absorbed radiation power equals the emitted radiation power. Hence thermal radiation has a characteristic temperature. In deep space this radiation temperature is about 2.7 degrees K.

At room temperature the molecular thermal kinetic energy is about 0.025 eV / molecule
= 25 X 10^-3 eV / molecule

In mechanical equipment a typical maximum CM motion velocity is 50 m / s. The corresponding CM molecular kinetic energy for water is:
(18 X 10^-3 kg / mole) X (50 m / s)^2 / [2 X 6.023 X 10^23 molecules / mole x 1.602 X 10^-19 J / eV]
= 2331.9 X 10^-7 eV / molecule
= .2331 X 10^-3 eV / molecule

For humans a typical maximum CM motion velocity is 10 m / s. The corresponding CM molecular kinetic energy for water is:
(18 X 10^-3 kg / mole) X (10 m / s)^2 / [2 X 6.023 X 10^23 molecules / mole x 1.602 X 10^-19 J / eV]
= .9327 X 10^-5 eV / molecule
= .009327 X 10^-3 eV / molecule

The above representative calculations show that the CM molecular kinetic energy available for doing work is many orders of magnitude smaller than the potential (rest) energy and is also usually several orders of magnitude smaller than the thermal kinetic energy components on which it is superimposed. Generally:
(particle rest energy) >> (nuclear particle binding energy) >> (electron binding energy) >> (molecular random kinetic energy) >> (molecular CM kinetic energy)

A well designed single stage combustion turbine operated at its maximum safe material stress produces work output that is still an order of magnitude less than its thermal kinetic energy input. Higher energy conversion efficiencies are realized through the use of heat recovery boilers and additional turbine stages.

Human activity has negligible effect on the Earth's potential energy distribution and produces only a small change in the Earth's thermal kinetic energy distribution. However, life forms can only exist and flourish within a relatively small absolute temperature range. From the perspective of life forms a less than 1% change in the Earth's thermal kinetic energy distribution produces major climate change.

This web page last updated May 12, 2020.

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