Natural units

In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of speed. A purely natural system of units has all of its units defined in this way, and usually such that the numerical values of the selected physical constants in terms of these units are exactly 1. These constants are then typically omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of fundamental physical constants, such as e and c, unless it is known which units (in dimensionful units) the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined. In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of speed. A purely natural system of units has all of its units defined in this way, and usually such that the numerical values of the selected physical constants in terms of these units are exactly 1. These constants are then typically omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of fundamental physical constants, such as e and c, unless it is known which units (in dimensionful units) the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined. Natural units are intended to simplify particular equations appearing in the laws of physics or to normalize some chosen physical quantities that are properties of universal elementary particles and are reasonably believed to be constant. However, there is a choice of which quantities to set to unity in a natural system of units, and quantities which are set to unity in one system may take a different value or even be assumed to vary in another natural unit system. Natural units are 'natural' because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are often, without qualification, called 'natural units', although they constitute only one of several systems of natural units, albeit the best known such system. Planck units (up to a simple multiplier for each unit) might be considered one of the most 'natural' systems in that the set of units is not based on properties of any prototype, object, or particle but are solely derived from the properties of free space. As with other systems of units, the base units of a set of natural units will include definitions and values for length, mass, time, temperature, and electric charge (in lieu of electric current). It is possible to disregard temperature as a fundamental physical quantity, since it states the energy per degree of freedom of a particle, which can be expressed in terms of energy (or mass, length, and time). Virtually every system of natural units normalizes Boltzmann's constant kB to 1, which can be thought of as simply a way of defining the unit of temperature. In SI, electric charge is a separate fundamental dimension of physical quantity, but in natural unit systems charge is expressed in terms of the mechanical units of mass, length, and time, similarly to cgs. There are two common ways to relate charge to mass, length, and time: In Lorentz–Heaviside units (also called 'rationalized'), Coulomb's law is F = q1q2/4πr2, and in Gaussian units (also called 'non-rationalized'), Coulomb's law is F = q1q2/r2. Both possibilities are incorporated into different natural unit systems.