Isotropy - Physics

Physics

Quantum mechanics or Particle physics

When a spinless particle (or even an unpolarized particle with spin) decays, the resulting decay distribution must be isotropic in the rest frame of the decaying particle regardless of the detailed physics of the decay. This follows from rotational invariance of the Hamiltonian, which in turn is guaranteed for a spherically symmetric potential.

Kinetic theory is also an example of isotropy. It is assumed that the molecules move in random directions and as a consequence, there is an equal probability of a molecule moving in any direction. Thus when there are many molecules in the gas, there will be an equal number moving in one direction as any other hence demonstrating isotropy.

Thermal expansion

A solid is said to be isotropic if the expansion of solid is equal in all directions when thermal energy is provided to the solid.

Electromagnetics

An isotropic medium is one such that the permittivity, ε, and permeability, μ, of the medium are uniform in all directions of the medium, the most simple instance being free space.

Optics

Optical isotropy means having the same optical properties in all directions. The individual reflectance or transmittance of the domains is averaged if the macroscopic reflectance or transmittance is to be calculated. This can be verified simply by investigating, e.g., a polycrystalline material under a polarizing microscope having the polarizers crossed: If the crystallites are larger than the resolution limit, they will be visible.

Cosmology

The Big Bang theory of the evolution of the observable universe assumes that space is isotropic. It also assumes that space is homogeneous. These two assumptions together are known as the Cosmological Principle. As of 2006, the observations suggest that, on distance scales much larger than galaxies, galaxy clusters are "Great" features, but small compared to so-called multi-verse scenarios.