Natural units

A natural unit of a physical quantity is a measure, which is given by a natural constant or derived directly from natural constants. This distinguishes them from other units, which are determined by, eg prototypes as the standard kilogram, or the properties of a particular type of atom. There are, depending on the choice of the underlying fundamental constants, different unit systems with natural units. The physical constants in question if they are specified in the corresponding natural units, all have the numerical value 1

Examples of natural units

  • The elementary charge of the electric charge.
  • The speed of light for the speed.
  • The (reduced ) Planck constant for the angular momentum.

As a typical feature of natural units is considered that they are the natural processes particularly well appropriate and in some cases play a prominent role in it. For example, the upper limit for the speed with which physical effects can spread. and on the other hand are close to the smallest possible values ​​for charge or angular momentum (if they are not equal to zero ).

Natural Systems of Units

Taken together, enable multiple physical constants different dimension to define natural units for a variety of physical quantities. These form a natural unit system. A complete system contains natural units for the basic quantities of the International System of Units, especially for length, time and mass. There are, depending on the choice of the underlying constants of nature, various natural unit systems. The selected physical constants when they are given in their corresponding natural units, all of the numerical value 1 These constants therefore occur not apparent when numerical value equations are used in concrete calculations. In many cases, the constants are therefore additionally recognized as dimensionless, which are all the formulas for numerical value equations and look much easier. This formal advantage is offset by the disadvantage that one first obtains the results of all calculations as pure numbers and have to add the correct dimension and unit later. A dimensional analysis for a quick check of the calculation is thus excluded.

Planck units

The consistent implementation of the natural units can be found in the 1899 Planck units proposed by Max Planck. In this system of units, the reduced quantum of action (originally ), the speed of light c, the Boltzmann constant kB and the Newtonian gravitational constant G be set to 1:

Therefore, this unit system is considered as fundamental, because the underlying physical constants relate to the general contexts of time and space and are applicable to all kinds of particles and interactions. (. Constant is needed here only for the adjustment of the temperature scale on the energy scale ) Use the natural laws by which these constants are defined, the Planck units can be introduced also by the following relations:

  • During the time unit light travels in a vacuum back a unit of length. ( Natural Law: )
  • The power unit is the quantum energy of an oscillation whose period is equal to a time unit. ( Natural Law: )
  • The unit mass is the mass, which is a unit of energy equivalent. ( Natural Law: )
  • The unit of length is the one distance of two bodies from a mass per unit in which their gravitational energy the size of a unit of energy. ( Natural Law: )

Stoney units

The first natural unit system was proposed in 1874 by George Johnstone Stoney, after he had with the concept of uniform charge carriers in the atoms found the last one to necessary natural constant. In Stoneys unit system, the elementary charge, the speed of light c and the Newtonian gravity constant G can be equal to 1 ( Stoney used to define the charge the electrostatic cgs - system so that the Coulomb 's constant ):

Stoney the natural units of length, weight and time are, therefore, smaller by a factor as according to Planck ( is the fine structure constant ). The Stoney units are today rarely used, but are of historical interest.

Particle Physics

In particle physics ( high energy physics) the gravity plays only a minor role. Therefore, here the units of the gravitational constant are left in the SI system. Only the speed of light and the quantum of action are set equal to 1:

The unit of energy but that will not set. Usually, this unit electron volt is used. All other units can then be expressed in terms of powers of these unit of energy.

Thus, the electron volt is also the unit of mass. Thus, the equivalence of mass and energy is particularly clear. Also get time and space of the same dimension 1/eV. The follows from the concept of space-time. Since different physical variable species in the natural system have the same dimension, the dimensional analysis loses control of physical equations of cogency.

Atomic units

In atomic physics, the system of Atomic units is common. Here electron mass elementary charge e, the quantum of action and the Coulomb constant is me, set to 1:

Relativity theory

In general relativity the speed of light c and the gravitational constant G be set to 1:

Quantum chromodynamics

In quantum chromodynamics is the proton of central interest. Here the speed of light c, the proton mass mp, 's constant and Boltzmann constant kB are set to 1:

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System of measurement Velocity
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