# Isotropy

Isotropy (from ancient Greek ἴσος isos "equal" and τρόπος tropos "rotation, direction") is the independence of a property from the direction.

The property under consideration can be any property (e.g. physical property, biological parameter, societal or social parameter).

The directional independence of such properties is synonymous with their homogeneous spatial structure . The opposite of isotropy is anisotropy .

## Isotropy in Physics

Isotropic radiation usually means radiation that is radiated uniformly in all directions of 3-dimensional space , for example the heat radiation of a hot sphere or the light of a star.

In physics, matter is basically not isotropic at the atomic level. If one considers such a building block z. If, for example, an atom can still be regarded as isotropic, it already plays a role with neighboring atoms whether one looks in a direction in which, for example, an atomic nucleus is located. If, however, these building blocks are not arranged regularly and the environment is viewed at a macroscopic distance, these differences can be canceled out on average, and the matter appears isotropic on the outside. This case is also known as quasi-isotropy . In the case of matter that has a regular structure (see grid ), the properties can also be anisotropic on a macroscopic length scale .

In theoretical physics, the isotropy of space (3-dimensional) leads to three of the ten classical symmetries. According to Noether's theorem , every symmetry implies the conservation of a physical quantity, for example, temporal symmetry implies the conservation of energy. The conservation of angular momentum can be derived from the isotropy of space .

If the property under consideration is an optical one such as B. reflection or transmission , the textbooks generally do not differentiate between isotropy and quasi- isotropy . As a result, the term optical isotropy is usually equated with the property can be characterized by a scalar dielectric function . However, this is e.g. B. for polycrystalline materials only correct if the crystallites are small compared to the wavelength. Otherwise, polycrystalline materials generally depolarize linearly polarized light even if they are randomly oriented, unless the light is also coherent .

## Transverse isotropy in materials science

In a fiber-plastic composite or laminate , transverse isotropy denotes a UD layer , i.e. a layer that only has direction-dependent properties in the fiber direction. In the plane perpendicular to this, however, the properties are independent of direction.

## Isotropy and homogeneity

With homogeneity there are the same number of parts in the same volumes, with isotropy the number of parts is the same in all directions.

## Isotropy in Mathematics

The term isotropy is used in mathematics with different meanings:

• In synthetic geometry a straight line is called isotropic if it is perpendicular to itself, see Pre-Euclidean Plane .
• An element of a bilinear space is called isotropic if it satisfies the equation .${\ displaystyle x}$ ${\ displaystyle (V, b)}$${\ displaystyle b (x, x) = 0}$