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**INTRODUCTION:**

This web page addresses basic energy and momentum issues and provides a Table of Website Contents relating to Energy Physics.

**PHYSICAL LAWS:**

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, 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.

**ENERGY CONCEPT SUMMARY:**

Everything in the universe contains energy. Energy exists as energy density (energy per unit volume).

Energy density is a relative quantity. Thus when we refer to energy density we are normally referring to the difference in energy density between the situation under study and the energy density of a local field free vacuum.

Modern astronomical observations seem to indicate that the energy density of a field free vacuum is greater than zero. However, as long as the energy density of a field free vacuum is relatively small and is locally constant, most energy calculations can be validly done relative to the local energy density of a field free vacuum. Thus on this web site when we refer to energy density we are really talking about the amount by which the local energy density exceeds the energy density of a field free vacuum. Thus a local energy density that is less than the local energy density of a field free vacuum is negative.

The amount of energy in a container is the integral over the container's volume of the energy density in that container. Again these energy densities are all relative to a field free vacuum.

Energy is conserved. Energy conservation means that for any three dimensional container, the amount of energy Eb in the container at time t = tb always equals the amount of energy Ea in the container at time t = ta plus the amount of energy that flows into the container between time t = ta and time t = tb. Expressed mathematically:

(Eb - Ea) = Integral from t = ta to t = tb of (dE / dt).

Since at all times the reference energy density is constant it disappears from the calculation of (Eb -Ea).

The total energy content of the universe is believed to be constant. Energy can neither be created nor destroyed but can be changed in form.

**ENERGY FORMS:**

Energy density has five known components: Field Free Vacuum Reference, Electric, Magnetic, Gravitation, and Momentum.
An expression of energy density is actually an expression of the difference in energy density with respect to a field free vacuum caused by the presence of electric, magnetic and gravitational fields or by the presence of linear momentum. Particles have associated local concentrations of electric, magnetic and gravitational field energy. Gravity usually only becomes significant in situations involving a very large number of particles.

At every point in space there are corresponding vectors indicating the local direction and magnitude of the electric, magnetic and gravitaional fields and linear momentum. The energy density at that point is the sum of the squares of these vectors. Care must be taken in calculating energy density because the gravity vector is imaginary and adds a small negative component to the total energy density.

Charge exists in particles as circulating closed filaments. Charge presence causes an electric vector field. Charge motion causes a magnetic vector field. Electric and magnetic field energy causes a gravitational vector field.

Charged particle relative position fluctuation causes electric, magnetic and gravitational vector field fluctuations that propagate as photons (or gravitons) at the speed of light C. The speed of light is the same for all inertial (non-accelerating) observers.

The vector fields contain energy. Energy is a scaler, not a vector quantity. Specification of only energy density at a particular position conveys no sense of relative motion. Position and motion are vector parameters.

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

Energy motion in a particular direction is known as linear momentum **P**. Linear momentum **P** is a vector quantity that conveys energy and is always conserved.

A particle is a packet of charge and energy that moves at less than the speed of light with respect to an observer. The universe contains a large number of particles and propagating vector field fluctuations. At any instant in time t energy packet Ei is characterized by: its nominal position **Xi** relative to the observer at **Xo**:

(**Xi - Xo**),

and its relative energy motion vector known as momentum **Pi** at location **Xi - Xo**. In general:

**Pi** = [Ei / C^2] [**Vi**]

where:

C = the speed of light

and:

**Vi** = d(**Xi - Xo**) / dt

is the energy packet velocity vector at its nominal relative position:

(**Xi - Xo**).

**PARTICLES:**

Particles are energy packets with velocities **Vi** in the range:

|**Vi**| < C

and have non-zero rest energy when:

|**Vi**| = 0

A particle may have a quantized net charge Qi. Charge is conserved. In any isolated interaction between particles the total charge before the interaction equals the total charge after the interaction.

Particle potential energy is the sum of the particle's electric, magnetic and gravitational field energy components. Kinetic energy is the particle's momentum energy component.

**RADIATION:**

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

For a vector field fluctuation (radiation photon):

**Vi** = **C**

where:

C = speed of light.

A photon has zero rest energy.

A photon with energy Ep conveys liner momentum **Pp** = (Ep / C^2)**C**

For an isolated photon both photon energy Ep and photon momentum **Pp** are constant.

Ep = h Fp

where:

h = Planck constant

and

Fp = photon frequency

Radiation conveys no net charge.

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

If not absorbed, emitted photons will eventually spread through the entire universe.

**INTERACTIONS:**

Particle-particle and particle-photon interactions effectively occur at specific points in space.

During isolated particle-particle and particle-photon interactions total energy E, total linear momentum **P** and total charge Q are conserved.

Particles interact with each other via field overlap. Field overlap causes a change in total assembly potential energy and an equal and opposite change in assembly kinetic (momentum) energy. Frequently part of this kinetic energy converts into radiation which propagates away into deep space carrying momentum. The conversion of potential energy into momentum can potentially do useful work. After such interactions previously free particles are often left bound together in mutual potential energy wells.

The ongoing conversion of particle potential energy into particle kinetic energy and then radiation is the main source of energy that can do useful work. This overall process is often referred to as an increase in entropy.

**RADIATION EMISSION AND ABSORPTION:**

An assembly of randomly moving particles trapped in a common potential energy well will emit thermal radiation to its environment and will absorb thermal radiation from its environment. If the assembly's temperature is larger than the environmental temperature there is net radiant power emission causing the assembly to gradually lose energy. If the temperature of the assembly is less than the temperature of the environment there is net radiant energy asorption causing the assembly to gradually rise in temperature.

**COMMON PARTICLE TYPES:**

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 a ground state. The ground state 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.

**FIELDS:**

In reality 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 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 the particle exhibits a characteristic particle resonant frequency that varies with the externally applied magnetic field strength.

The particle rest energy has gravitational, electric, magnetic 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 acceleration and 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.

**STABLE PARTICLE ASSEMBLIES:**

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.

**POWER:**

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:**

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.

**MUTUAL POTENTIAL ENERGY WELLS:**

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:**

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.

**ENERGY TRANSITION:**

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 net charge 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.

**STABLE PARTICLES:**

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 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.

**UNSTABLE PARTICLE ASSEMBLIES:**

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 also known as alpha particle emission. These emissions are accompanied by gamma photons that simultaneously conserve energy and momentum.

**MATTER AND ANTI-MATTER:**

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.

**GRAVITY:**

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.

**NEUTRONS:**

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.

**COSMIC RADIATION:**

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:**

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 filament path. The spheromak filament traces out a closed surface known as the spheromak wall. The spheromak linear size and the filament length are inversely proportional to the spheromak's total 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 finite in size and is toroidal magnetic. The electromagnetic field energy stored by a spheromak forms the particle's rest mass.

The stable spheomak geometry arises in part from the properties of prime numbers. This 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, liquids and 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.

**SPHEROMAKS CAUSE PHOTON ENERGY QUANTIZATION:**

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

and

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, photon energy quantization is a direct result of spheromak behaviour.

**SCOPE:**

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

This web page last updated April 30, 2023.

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