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


Energy is the name that we give to one of the most basic constituants of the universe. Everything that we can conceive of is composed of energy. Energy arises from the existence and motion of quantized charge. Energy takes several forms: electric field energy, magnetic field energy, gravitational field energy, gravitational potential energy, kinetic energy and radiation.

Most mass is primarily composed of concentrated electric field energy and magnetic field energy but has associated with it some kinetic energy, internal radiation and gravitational field energy. There is uncertainty as to whether or not all forms of nuclear energy are electromagnetic in nature.

The absolute energy of a universe which contains no energy is zero.

Gravitational field energy and gravitational potential energy are a result of the presence and density of other energy forms. When other forms of energy are zero there is zero gravity. Unlike the other energy forms which are normally positive, gravitational field energy and gravitational potential energy are normally negative.

The effect of an energy concentration is to form a local gravitational potential energy well. Gravitational forces are a result of interaction between these potential energy wells.

Most energy measurements and calculations are expressions of energy differences. However, cosmology is concerned with absolute energy.

An isolated packet of energy bits Ei has a center of momentum location at which the vector sum of all:
Ei (dRi / dT) = 0
Ri is a vector from the center of momentum to the ith energy bit Ei:
T = time as measured at the center of momentum.

If an energy packet is isolated from external fields its center of momentum moves at a constant velocity in the frame of reference of an inertial observer (an observer not subject to acceleration).

It is convenient to distinguish between energy in the frame of reference of the center of momentum and energy related to motion of the center of momentum with respect to an external observer.

Potential energy in the frame of reference of the center of momentum is usually chemical potential energy. Kinetic energy in the frame of reference of the center of momentum is usually heat or kinetic energy of rotation.

Energy related to the position of the center of momentum is commonly referred to as gravitational potential energy of position. Energy related to motion of the center of momentum is commonly referred to as kinetic energy.

An isolated stable concentration of potential energy with a nominal position and motion is known as a particle. Each particle has radial fields that extend to infinity but that contain finite amounts of energy.

Interactions between fields of different particles cause part of the field potential energy of the particles to convert to kinetic energy (energy of motion) in the frame of reference of the center of momentum or vice versa. This energy form change causes particles to accelerate or decelerate. However the net energy motion (linear momentum) of the center of momentum of the cluster of isolated particles remains unchanged. This principle is known as conservation of linear momentum.

Radiation removes quanta of energy at the speed of light. A radiation quantum may be an electromagnetic photon or a graviton.

Under circumstances of charge separation and low electromagnetic radiation density kinetic energy can become electromagnetic radiant energy which then propagates away from the center of momentum at the speed of light. Under circumstances of charge separation and high electromagnetic radiation density electromagnetic radiation can be absorbed and converted into kinetic energy and then potential energy. In our local universe the radiation density in outer space is very low compared to the thermal radiation density on Earth which means that Earth emits thermal infrared radiation.

Elementary charged particles such as electrons and protons are believed to be composed of spheromaks. A spheromak contains a quantum of charge that circulates around a stable closed path at the speed of light. A spheromak has associated vector electric and vector magnetic fields that each contain potential energy. Generally the field energy density is high near the nominal particle position (center of momentum) and diminishes rapidly with increasing radial distance from the nominal particle position. The total energy contained in a vector field is finite even though the field radially extends to infinity. The field energy forms part of the particle's total energy. Motion of a particle in the frame of reference of an inertial observer gives the particle kinetic energy and linear momentum.

The extended electric and magnetic fields of different particles interact. Such interaction converts field rest potential energy into kinetic (motion) energy. In circumstances of low external radiation density kinetic energy can convert into photons that are radiated away, leaving the interacting particles bound together in a mutual potential energy well. The emitted photon energy and frequency are a result of the electromagnetic spheromak structures of elementary particles.

Thus, each free particle has an energy consisting of rest (potential) energy and kinetic (motion) energy in the observer's frame of reference. Each bound particle has an additional binding energy (negative potential energy) component relating to the gravitational interaction of that particle with other particles.

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

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

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

A bit of energy Ei that is in linear motion at point Xi has a vector property known as linear momentum. The linear momentum Pi of energy bit Ei at point Xi moving with velocity Vi = dXi / dT in the frame of reference of an inertial observer is:
P = (Ei / C^2)Vi
C = speed of light
T = time in the observers frame of reference

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

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

The origin of the Planck constant arises from the structure of electromagnetic spheromaks.

An alternative definition of the Planck Constant is:
h = dE / dFh
E = spheromak energy contained in a charged particle
Fh = spheromak natural frequency.

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

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

Positive potential energy is contained in static electric and magnetic fields. These fields occur as a result of the existence and closed path motion of electric charge. At the microscopic level the mathematical equations that determine the spacial distribution of energy may have multiple real solutions. This issue leads to a branch of physics known as quantum mechanics. Atomic particles have characteristic natural frequencies and exhibit electromagnetic wave like properties. Due to the multiple real solutions there is uncertainty in simultaneous measurements of particle energy and time and in simultaneous measurements of particle position and particle momentum.

Overlap of gravitational fields reduces the total potential energy of a collection of particles. Gravitational fields are believed to be a result of concentrations of energy affecting the structure of space-time. The relationship between energy and the structure of space-time is the subject of general relativity. The exact manner in which the energy of galaxies affects the structure of space-time is a subject of current astronomical research. For the purpose of this web site gravity is treated as a simple imaginary field. This treatment may be imperfect, but it is adequate for most practical engineering purposes.

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

Up until the late 19th century energy was thought of as "capacity to do work". Work was measured by capacity to lift water uphill. That definition of work is still useful today for quantifying major changes in energy.

During the 17th century Issac Newton realized that gravity caused acceleration and defined the change in kinetic energy dEk of an object by the vector dot product:
dEk = (dP / dT).dX
M = object mass
V = object's velocity vector
P = M V = objects momentum vector
dT = change in time
dP = the change in the object's momentum vector during time increment dT
dX = the change in the objects position vector during time increment dT.

Newton's definition of change in kinetic energy dEk was mathematically excellent but it provided no insight into absolute energy. However, it was recognized that in any isolated system the total energy Et is constant or:
dEt = 0
implying that total energy is conserved.

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

Early in the 20th century Einstein showed that an objects rest mass Mo indicates its absolute potential energy Eo via the formula:
Eo = Mo C^2
C = speed of light
and that absent external fields an object's total energy Et is given by:
Et = M C^2

Einstein further showed that electromagnetic energy propagates through space in quanta known as photons. Einstein further showed that the absolute energy density at every point in space and time causes an apparent gravitational field that affects the absolute energy density at other points in space at later times.

During the first half of the 20th century it was shown that every large mass consists of an aggregation of stable atomic particles with quantized charges and corresponding discrete energies. Subject to structural constraints the atomic particles vibrate or move randomly with thermal kinetic energy. Planck showed that the vibrating atomic particles constantly emit and absorb quanta of thermal electromagnetic radiation.

Later during the 20th century it was shown that a sufficient concentration of mass would cause formation of a black hole that absorbs both mass and radiant energy from its surroundings.

In the early 21st century it became apparent that electrons, positrons, protons and anti-protons consist of concentric spheromaks formed by massless quantized charge that circulates around a closed path at the speed of light. A spheromak has associated with it electric and magnetic fields that contain potential energy. These fields give the particle its rest mass and give the spheromak's charge motion path geometrical stability. The electrons circulating around an atomic nucleus also form spheromaks. Changes in spheromak energy dE caused by emission or absorption of a photon follow the equation:
dE = h dF
dE = photon energy
h = Planck constant
dF = change in spheromak natural frequency

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

The universe can be viewed as consisting of an energy and charge motion distribution in space. Electric charge is a conserved parameter. The integral of the net electric charge density over all space is believed to be close to zero. A significant net electric charge would cause rapid expansion of the universe. Cosmologists usually assume that the net charge in the universe is zero.

Each element of electric charge causes a radial vector electric field. Circulating charge motion causes a vector magnetic field. At every point in space and time the prevailing static three dimensional electric and magnetic field vectors separately add causing an electromagnetic field energy density.

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

Electric charge, electric charge motion and electric and magnetic field vectors and energy densities are mathematically intertwined. Electric charge causes an electric field. Electric charge motion (current) causes a magnetic field. A change in magnetic field with time causes an induced electric field. A change in electric field with time corresponds to charge motion which causes a magnetic field. Thus the spacial electric charge distribution over time defines the electric and magnetic vector field distributions and vice-versa. The sum of the squares of these orthogonal net field vectors is the static local electromagnetic field energy density.

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

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

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

Thus field energy density arises from the squares of the net electric, magnetic and gravitational vector field terms. Alternatively the field energy distribution can be viewed as arising from the energy, charge and charge motion distribution. Note that this formulation is only valid for fields that are static with respect to an inertial observer. The general case of an accelerating observer and/or propagating field changes is more complex.

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

The history of the universe prior to the formation of charged particles is highly speculative. It is believed that particle rest mass energy came from high energy gamma ray photons originating in a "big bang".

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

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

A closed spiral path forming a spheromak is like a a uniform single layer wire winding on a toroid with the two ends of the winding connected together. The spiral path makes 222 turns around both the toroid's major axis and 305 turns around the toroid's minor axis before retracing its path. Thus an electric current following a closed spiral path causes both toroidal and poloidal magnetic fields. In order for a charged particle to be stable the path must repeat itself.

In stable charged particles the electric charge is quantized. The mechanism of charge quantization is unknown. The known universe is primarily an assembly of electrons, protons and photons. All electrons seem to exhibit exactly the same net charge and characteristic isolated rest energy. All protons seem to exhibit an exactly equal but opposite net charge and a characteristic isolated rest energy. Neutrons can be viewed as being composed of an electron-proton assembly with zero net charge plus some additional energy. Electromagnetic radiation photons have an oscillating electric field vector and an oscillating magnetic field vector but have no net charge and no rest energy.

If uniformly distributed electric charge continuously circulates around a closed spiral path with no change in spacial charge distribution and no change in current, then the electric and magnetic fields are static and there is no absorption or emission of radiation. Hence there is no change in energy. The result is a spheromak forming a stable charged particle. The electric and magnetic fields of stable charged particles at rest contain the particle's spheromak potential energy. Examples of highly stable particles are electrons and protons.

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

To realize a stable spheromak the geometry of the closed spiral path must correspond to a total energy minimum. For quantum atomic particles that energy minimum occurs at number of poloidal charge path turns Np = 222 and at number of toroidal charge path turns Nt = 305. This integer pair leads to the Planck Constant.

The stable spheromak structure enables the existence of highly stable elementary atomic particles such as electrons and protons as well as semi-stable particles and plasmas. The electric and magnetic fields associated with stable particles contain energy which contributes to the atomic particles rest mass. The external fields caused by these particles radially extend out to infinity. However, the total energy of an isolated particle is finite.

Real charged particles such as electrons and protons appear to consist of multiple concentric spheromaks. The central spheromaks are physically small and provide most of the particle's rest mass. The outer spheromak is physically larger and provides most of the particle's net magnetic moment. The net charge of the central spheromaks adds to zero. The frequencies of the concentric spheromaks are likely harmonically related. These assumptions are necessary to explain the combined mass, charge and magnetic resonant behaviour of real charged particles.

Stable particles have external fields. Progressive overlap between between the external fields converts a portion of the isolated particle potential energy into kinetic energy. In a low radiation environment part of this kinetic energy may be lost to outer space via net emission of radiation photons, leaving the stable particles bound in a mutual potential energy well. By this process in a low radiation environment particles tend to aggregate to form stable atomic nuclei, atoms, molecules, liquids, crystals, rocks, planets and stars.

At steady state the rate of energy absorption by particles bound in a mutual potential energy well equals the rate of radiation emission. At steady state in a high radiation density environment the rate of photon emission must be high to equal the relatively high rate of photon capture. Thus in a high radiation density (high temperature) environment particle aggregations are less stable than in a low radiation density (low temperature) environment.

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

The field interaction equations involving stable atomic particles with quantized charge often have multiple real solutions corresponding to discrete energy states that are separated by energy gaps. A transition from such one energy state to another such energy state is usually accompanied by absorption or emission of a photon and/or by a particle carrying kinetic energy equal to the energy difference between the two separated energy states.

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

Atomic nucleons behave as if composed of mathematical sub-units known as quarks, but quarks do not exist in isolation. In the "standard model" a hydrogen nucleus is composed of 3 quarks. A deuterium nucleus may involve six quarks. A helium-4 nucleus may be assembled from two deuterium nuclei containing 12 quarks. The exact relationship between quarks and spheromaks is uncertain. Larger nuclei involve a collection of spheromaks bound together in a common mutual potential energy well.

For many practical engineering calculations involving assemblies of large numbers of aggregated particles (such as planets) the energy content of the net external electric and magnetic fields is small compared to the energy content of the net gravitational field. For these cases the field complexity of the universe can be ignored and the universe can instead be represented as a time dependent spacial energy (or mass) distribution, for which both energy and linear momentum are conserved parameters.

Our local universe ages by gradual aggregation of isolated energy packets into mutual potential energy wells. During the aggregation process radiation is emitted. Most of the radiation energy escapes from the mutual gravitational potential energy well. Thus there is an apparent ongoing decrease in the average energy density of the local universe, which intuitively is equivalent to local universe expansion. This process is known as an increase in entropy and establishes the apparent direction of time.

Gravitational aggregation of particles eventually leads to formation of a deep gravitational potential energy well known as a black hole from which radiation cannot easily escape. A gravitational black hole acts as a net radiation sink rather than a net radiation source. The issues of what happens to average particle energy, average energy density and the direction of time within a gravitational black hole are beyond the scope of this web site.

Black holes perform an important life enabling function of absorbing radiation, which cools the space around them. Life processes on Earth rely on emission of thermal infrared radiation emission from the Earth into a cold universe for temperature maintenance. The issue of whether thermal radiation is absorbed by black holes or is absorbed by a physically expanding universe or by both is beyond the scope of this web site.

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

2) Everything that exists has energy.

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

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

5) Stable particles exhibit charge only in quantum amounts. An element of charge has associated with it a radial vector electric field. An element of charge motion (current) has associated with it a vector magnetic field.

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

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

8) At any instant in time, every stable particle can be characterized by its nominal position Xo with respect to the observer (known as its center of momentum), its rest energy Ett, its momentum vector P, its charge Q, its poloidal magnetic field vector M (angular momentum), its toroidal magnetic field vector (spin) S.

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

10) In the presence of a changing external magnetic field atomic particles gain or lose energy via absorption or emission of quanta of radiant energy known as photons. Photons have no rest energy and propagate at the speed of light. Thus when a stable particle in state a with energy Ea emits a photon and hence shifts to state b with energy Eb the change in energy (dE) is given by:
(dE) = (Ea - Eb)
~ h (Fa - Fb)
= h (Fp)
(dE) = change in particle energy [(dE) is positive for photon emission, (dE) is negative for photon absorption];
|Fp| = photon frequency
Thus to the extent that stable particles exhibit discrete energy states photon energies are also discrete.
Photon categories in order of increasing frequency |Fp| are:
AC power, audio, radio, microwave, infrared, optical, ultra-violet, x-ray and gamma ray.

11) The total energy of an atomic particle has a potential energy component and a kinetic energy component. If the particle is in an external field there may also be potential energy of position. This position dependent potential energy results from overlap of the particle's electric, magnetic and gravitational fields with the corresponding external fields.

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

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

14) Total energy is always conserved. For an isolated system a decrease in potential energy causes a corresponding increase in kinetic energy and vice-versa. The energy of a non-isolated system can change via energy absorption from another system or via energy emission to another system. Often these energy exchanges occur via photons.

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

16) Particles interact with each other via their extended vector fields. At each point in space field vectors of a particular type vectorially add. Each orthogonal net field vector (electric field, magnetic field, gravitational field) squares to yield a field energy density component. Progressive vector field overlap causes a change in total potential energy and a corresponding change in kinetic energy. Since the vector fields extend from an object's nominal position to infinity, objects that are widely separated still weakly interact. The apparent force between distant objects is really the change in the total system potential energy with respect to a change in an object's position relative to the other objects in the system. Conservation of total energy requires that the change in potential energy either become an equal change in kinetic energy or be converted into emitted/absorbed radiation.

17) Most chemical reactions occur in low radiation environments in which the reactants shift from a high energy state to a lower energy state by net emission of infrared photons. An exception is the photosynthesis reaction which occurs in a high radiation environment (sunlight) in which the reactants shift from a low energy state to a higher energy state by net absorption of solar photons. Another exception is electrolysis driven chemical reactions in which the reactants gain energy from an externally applied electric field.

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

19) In most spontaneous nuclear decay reactions the reactants shift from an unstable high energy state to a more stable lower energy state by emission of kinetic energy and x-ray or gamma photons. However, there are some important nuclear reactions such as gamma initiated fission that are triggered by net absorption of gamma photons.

20) An important physical state change is absorption of solar photons by fine wind blown sea water droplets at ambient temperature to form water vapor. The inter-molecular binding energy per molecule is the latent heat of vaporization. However, this energy per molecule is less than the energy of a solar photon.

21) Another important physical state change is freezing of liquid water droplets in lower temperature clouds which converts the molecular vibration energy into far infrared radiation.

22) The sun is constantly emitting solar photons into deep space. Since the sun's energy is finite the potential energy contained in the sun is decreasing and hence the period during which the sun can support life on Earth is finite.

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

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

25) The temperature at the Earth's surface is nearly constant over prolonged time indicating that the Earth's average rate of energy loss via infrared radiation emission is close to the Earth's average rate of energy gain via solar radiation absorption plus heat gain via radio isotope decay.

26) The flow of energy which is absorbed by the Earth from the sun and then emitted by Earth into deep space can be tapped do useful work. eg To grow plants and to produce hydroelectric, solar and wind power.

27) A difference between the flow of energy absorbed by Earth from the sun and the flow of energy emitted by Earth into deep space causes changes in stored thermal energy which in turn causes formation or melting of polar ice and/or a gradual change in ocean surface temperature. Changing the flow of solar energy absorbed by Earth or the flow of infrared energy emitted from Earth leads to long term climate change.

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

This web page last updated April 24, 2018.

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