Energy

Energy (Greek εργον ergon work) is the capacity to do work. It is a fundamental system variable and state-change quantity.

Conservation of energy
According to the Law of Conservation of Energy, also known as the first law of thermodynamics, energy can neither be created nor destroyed. Thus the total energy in any isolated system, including the universe, remains constant.

The discoveries of nuclear fission and nuclear fusion appeared to violate that law. However, Albert Einstein gave his simple relationship between mass and energy:

$$\,\!E = mc^{2}$$

This relationship is remarkably robust. For example, the kinetic energy of a moving body at speeds approaching that of light is actually an infinite series. This series has second-, third-, and higher-order corrective terms which each have an increasing power of the square of the radius of the speed of the body to the speed of light. But the original mass-energy equation still holds, if m in that equation is the relativistic mass, not the rest mass. As a result, one can write:

$$\,\!E = m_{0}c^{2} + E_{k}$$

More generally, the total energy in the universe is the sum of the total rest-mass energy and all the other forms of energy (kinetic, potential, thermal, etc.).

Today scientists define a Law of Conservation of Mass-Energy. According to this, while mass and energy might be transformed, the total amount of mass-energy in the universe will not change.

Definition of work
Work is the most common form of energy transfer. Classically, work is the exertion of force to displace an object. In mathematical terms,

$$W = \int F \cdot ds$$

Here W is work and s is displacement.

Potential energy
In general, potential energy is the work that one would have to do on an object to overcome any restriction on its motion. Therefore,

$$E_{p} = - \int F \cdot ds$$

The specific potential energy due to gravity of an object at or near the surface of a celestial body is

$$\,\!E_{p,g} = mgh$$

m = mass of the body, g = acceleration due to gravity, and h = any distance through which a body, if released, might fall.

The general potential energy due to gravity between any two objects is

$$E_{p,g} = - G\frac{m_{1}m_{2}}{r}$$

G = gravitational constant, each m is the mass of an object, and r is the distance between the object's centers of mass.

Kinetic energy
The kinetic energy of any object is the integral of velocity multiplied by change of momentum. Thus

$$E_{k} = \int v \cdot dp = \frac{1}{2}mv^2$$

At relativistic speeds,

$$E_{k} = mc^{2}\Bigg(\frac{1}{\sqrt{1 - (v/c)^2}} - 1\Bigg)$$

Electrical energy
The potential electric energy between two bodies of like charge (both positive or both negative) is the amount of work required to bring them from infinite separation to a fixed distance r. The potential electric energy of two bodies of opposite charge would be the work required to separate the two bodies from contact (actually, hypothetical coincidence of centers) to a fixed distance. This is given by:

$$E_{p,e} = \frac{1}{4\pi\epsilon_{0}}\frac{Q_{1}Q_{2}}{r}$$

where

$$\epsilon_{0} = \frac{10^{7}}{4\pi c_{0}^{2}}$$

is the electrical permittivity of a vacuum.

Magnetic energy
The work, or rather, torque on an object of magnetic dipole moment m in a magnetic field of magnetic flux density B is

$$E_{p,m} = -m \cdot B$$

Dimensions and Units
The dimensions of energy are those of mass multiplied by the square of distance, divided by the square of time.

The standard SI unit of energy is the joule, named after James Joule. One joule is the amount of work done by exerting a force of one newton to displace an object by one meter.

Problems for uniformitarian theories
The most important problem that energy poses for uniformitarian astronomy and cosmology is that astronomers cannot account completely for all the gravitational and kinetic energy in the universe. galaxies often rotate faster than their total observed mass will allow. Furthermore, the observed redshift of virtually every object other than our own galaxy shows that objects appear to be retreating from our galaxy faster than the hypothetical explosion called the big bang should have accounted for.

To account for the difference between observed and expected mass and energy, cosmologists have invented the concepts of dark matter and dark energy to explain the excess gravitational and kinetic energy, respectively. Conventional cosmologists estimates that 70 percent of the mass-energy in the universe, according to standard chronologies (including the big bang), consists of dark energy, and another 25% consists of dark matter. On the other hand, creation cosmologist John Hartnett contends, from cosmological relativity, that those concepts are not necessary.