System of units

A system of units , previously a system of measurement , is a collection of units of measurement in which exactly one unit is assigned to each type of size . In Germany, the International System of Units (SI, for systême international) is generally used. Other systems of units are the CGS system or the Anglo-American measurement system .

meaning

Physical quantities can only ever be specified as a multiple of a unit of measurement (short: unit). This is the equation for the relationship between place , time and speed with non-accelerated movement

${\displaystyle {\frac {x}{x_{0}}}=K\cdot {\frac {v}{v_{0}}}\cdot {\frac {t}{t_{0}}}}$

where is the unit of length, the unit of speed and the unit of time. is a real constant of proportionality that depends on the choice of units. ${\displaystyle x_{0}}$ ${\displaystyle v_{0}}$ ${\displaystyle t_{0}}$ ${\displaystyle K}$

The constants can be summarized and obtained by transforming this equation

${\displaystyle x=C\cdot v\cdot t}$

With

${\displaystyle C=K\cdot {\frac {x_{0}}{v_{0}\cdot t_{0}}}}$.

For example, if the location is given in meters (m), the time in seconds (s) and the speed in multiples of the vacuum speed of light ( ), then is and the constant is ${\displaystyle c}$ ${\displaystyle K=299\,792\,458}$ ${\displaystyle C}$

${\displaystyle C=299\,792\,458\ \mathrm {\frac {m}{s\cdot c}} }$

So if you have, for example, a speed of 0.5 c and a time of 2 s, the equation results

${\displaystyle x=299\,792\,458\ \mathrm {\frac {m}{s\cdot c}} \cdot 0{,}5\ \mathrm {c} \cdot 2\ \mathrm {s} =299\,792\,458\ \mathrm {m} }$

- a conclusive result.

Since it is impractical to include such a constant in every equation, it makes sense to choose units so that many constants become 1. As defined one (thus m / s according to the above example, the unit of velocity in meter / second ), and thus the constant is found to be in the above equation , then what the familiar equation ${\displaystyle v_{0}={\frac {x_{0}}{t_{0}}}}$ ${\displaystyle C=1}$

${\displaystyle x=v\cdot t}$

results.

The constant in this equation says something about the system of units used. Many natural constants are in truth "unit system constants". The Boltzmann constant is nothing more than a conversion factor between energy and temperature (which is why the temperature is often given in units of energy). So it actually says nothing about nature , only something about the temperature scale used. ${\displaystyle k_{\mathrm {B} }}$

variants

While it makes little sense to define a system of units in which it does not apply, for reasons of visualization, different ways of writing size equations have become established especially for the physical quantities of electrodynamics . This is the first Maxwell equation in a vacuum in SI units ${\displaystyle x=vt}$

${\displaystyle \operatorname {div\,} {\vec {E}}={\frac {\rho }{\varepsilon _{0}}},}$

in Gaussian cgs units

${\displaystyle \operatorname {div\,} {\vec {E}}=4\pi \rho ,}$

and in Heaviside-Lorentz units (also called rationalized cgs)

${\displaystyle \operatorname {div\,} {\vec {E}}=\rho .}$

From the point of view of the SI, these spellings differ only in that the constant is arbitrarily set equal to a number in the two CGS systems . This has the consequence that the electric current strength loses the character of a basic quantity in these unit systems; in addition, units of measurement and dimensions are ambiguous: a size value such as B. 2.0 cm can then be the measure of a length, but also z. B. also that of the capacitance of a capacitor. ${\displaystyle \varepsilon _{0}}$

Some important systems of units are:

• SI unit system (and its predecessor MKS system and MKSA system )
• Technical measurement system
• CGS system of units
• Gaussian system of units
• Heaviside-Lorentz unit system
• Geometric units (in relativity theory )
• Natural units (in high energy physics )
• Atomic units (in atomic physics )
• various systems of astronomical units
• Planck units

See also

• Measurement
• Electromagnetic units

Individual evidence

1. ↑ Practical course in physics , Wilhelm Walcher, Teubner Verlag.

Web links

• Spectrum Akademischer Verlag (Hrsg.): Units systems - Lexicon of physics . Heidelberg 1998 ( Spektrum.de [accessed November 4, 2016]).
• Articles on the math planet about systems of units