isotrop

Isotrop, commonly expressed in English as isotropy or isotropic, refers to the property of being identical in all directions. In physics, geometry and related fields, a system or material is isotropic if its characteristics are invariant under rotations; no direction is preferred.

In optics and materials science, an isotropic medium has the same optical or mechanical properties in every direction. For example, an isotropic liquid has uniform pressure in all directions, and an isotropic optical medium has the same refractive index regardless of light’s travel direction. By contrast, anisotropic materials, such as many crystals, show directional dependence of properties.

In engineering and statistics, isotropy is often an assumption that simplifies models. In materials engineering, many bulk properties of polycrystalline metals are treated as isotropic at macroscopic scales, although real materials can exhibit anisotropy due to texture or oriented phases. In spatial statistics, isotropy means that correlation between measurements depends only on the distance between them, not the direction.

In cosmology, the cosmological principle postulates that the universe is isotropic on large scales, i.e., looks the same in all directions to a sufficiently distant observer. Observations of the cosmic microwave background reveal small deviations from perfect isotropy, which carry information about early-universe physics.

Mathematically, isotropy is formalized as invariance under the rotation group. An isotropic tensor or field remains unchanged under any rotation. In summary, isotropy characterizes symmetry under direction changes across disciplines, with slight variations in meaning by context.