Physics:Units

Typical for high-energy physics is the natural unit system, which fixes by convention two universal constants to 1:

where h is Planck's constant and c is the speed of light in vacuum.

Thus, the number of fundamental mechanical units (L = length, M = mass, T = time) is reduced to one: Mass is usually measured in GeV in the natural unit system. The presently adopted SI (the international system of units, also known as MKSA) is related to the natural unit system through the values of three fundamental constants:

where e is the elementary charge.

These relations allow one to calculate the conversion factors between different units.

In spite of the attempted standardization to SI, several other unit systems are in use in electromagnetism: the Gaussian, CGS electrostatic and electromagnetic, and Heaviside-Lorentz system (for details on conversion of the units Jackson75and the physical quantities , appendix). Electrostatic and electromagnetic units differ only by factors of c.

The parallel use of different unit systems can produce confusion, as physical quantities are defined up to multiplicative constants, which depend on the unit system. For instance, in all unit systems the force File:Hepb img672.gif on a charge q in an electric field is File:Hepb img673.gif , hence (unit of force) = (unit of charge) File:Hepb img674.gif (unit of field).

However, this does not fix the units of charge and field separately, only their product. One way to fix the unit of charge is to fix by convention the proportionality constant k in Coulomb's law

F is the force between two point charges q₁ and q₂ separated by a distance r. In Gaussian units k=1, in Heaviside-Lorentz units File:Hepb img676.gif , and in SI units

with File:Hepb img678.gif  Fm^-1 the permittivity of free space. Strictly speaking, the SI unit C = coulomb is defined not from Coulomb's law, but from Ampère's law for the force between parallel currents, plus the relation File:Hepb img679.gif between the units for charge, current and time.

The fine structure constant is

If one combines natural mechanical units, with File:Hepb img681.gif , and Gaussian electromagnetic units, then electric charge becomes dimensionless. Thus, in these units the elementary charge is

Charge is also dimensionless in ``natural Heaviside-Lorentz units:

but not in natural mechanical units combined with SI electromagnetic units.

Gaussian and Heaviside-Lorentz units are different by factors of File:Hepb img684.gif . Some conversion factors from SI units into Gaussian units (see Jackson75 for more detail) are:

Hybrid unit systems are often used in which, for example, momentum is measured in GeV/c, length in m and magnetic induction ( ) in T = tesla. In these particular units, the elementary charge is