Before we proceed any further in classifying the various levels and kinds of energies responsible for our universe, let us take a minute to look at several other definitions for physical or material energies (figure 5).

**Figure 5**

**Several Forms of Energy Equations**

**Relativistic Energy = mass x speed light squared = m*c**2**

**Kinetic Energy of motion = 0.5 x mass x velocity squared**

**Gravitational Potential Energy = g*c x mass x distance**

**Nuclear Binding Potential = (g**2/S*c)**[exp(-S/m*c)]/r**

Einstein (1879 – 1955) and the relativistic physicists of the early 1900s established through theory and experiment that an absolute equivalence exists between physical matter and energy; that is, matter and energy are intraconvertible such that energy is conserved. This relationship is given by the famous equation,

**E = M0*c**2/{1 – (v/c)2}**1/2 (7)**

where E equals energy, mo equals the inertial mass of a body at rest relative to the observer, c equals the speed of light (a universal constant of nature) and the denominator represents the relativistic correlation to the rest mass because of motion relative to the observer. Regardless of the particular formulation used to express a quantity of energy or work, energy units are always the same, mass-length**2/time**2.

This equation is structurally similar to the classical, Newtonian, energy equation relating the mass of a body to its motion, e.g.,

** E = m*v**2/2 (8)**

where m equals the inertial mass of a body and v equals the velocity of the body. This form of energy is commonly known as kinetic energy, a term introduced by the English physicist Lord Kelvin in 1856.

Energies other than the energy of motion are also possible; such as the energy potentially available for a body held in a gravitation field, the potential energy of configuration available from a stretched rubber band, the potential electrical energy stored in a battery and so on. For example, the classical equation for the gravitational potential energy is given by,

** E = m*g*d (9)**

where m equals the mass of a body, g equals the gravitational acceleration of the earth and d equals the distance the object is held above a reference plane.

A more recent formulation of energy equations useful for dealing with particles or wave packets of very small scale, such as subatomic particles and radiation, are those derived by early quantum physicists like Planck (1858 – 1947), Heisenberg (1901 – 1976) and Bohr (1885 – 1962).

Quantum mechanics has demonstrated that for all physical systems whose variables (position, momentum, energy and so on) are periodic functions over time, the integral of any variable over a complete cycle of its motion must be equal to an integer times Planck’s constant, h,

** pi*d*qi = ni*h; ni = 1, 2, 3, …. I (10)**

where h represents the fundamental scaling parameter of nature, pi is the generalized momentum associated with the generalized coordinate qi, and ni is a general quantum number.

The equation is the most general formulation for the quantization of energy on the microcosmic scale and was introduced in 1916 by Wilson and Sommerfield.

Applying the Wilson and Sommerfield equation to the energy-time domain provides an expression for quantization of energy based upon the intrinsic vibrational state of the wave packet associated with any quantum or subatomic particle,

** E = n*h*v (11)**

where n is a general quantum number, h is Planck’s constant which has units of energy-time and v equals the frequency of an oscillator in reciprocal time. This equation is particularly interesting since it states the possible energy states of a system are not continuous and can only occupy certain defined quantum energy states.