The classic solution of the Einstein field equations that describes a homogeneous and isotropic universe is called the Friedmann–Lemaître–Robertson–Walker metric, or FLRW, after Friedmann, Georges Lemaître, Howard Percy Robertson and Arthur Geoffrey Walker, who worked on the problem in 1920's and 30's independently of Friedmann.
This was addressed by a generalization published in 1995 by W. R. Stoeger, Roy Maartens and George Ellis, which shows that an analogous result holds for observers who measure a nearly isotropic background radiation, and can justly infer to live in a nearly FLRW universe.
Russian mathematician Victor Veselago predicted that a material with simultaneously negative electric and magnetic polarization responses would yield a negative refractive index (an isotropic refractive index of −1), a ‘left-handed’ medium in which light propagates with opposite phase and energy velocities.
The solution of the Schrödinger equation (wave equations) for the hydrogen atom uses the fact that the Coulomb potential produced by the nucleus is isotropic (it is radially symmetric in space and only depends on the distance to the nucleus).
; Cell biology: If the properties of the cell wall are more or less the same everywhere, it is said to be isotropic.
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Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.
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; 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.
They generally decrease rapidly as the temperature approaches the Curie temperature, so the crystal becomes effectively isotropic.