Isotropic in the context of Anisotropy

The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dark. However, a sufficiently sensitive radio telescope detects a faint background glow that is almost uniform and is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the electromagnetic spectrum. Its energy density exceeds that of all the photons emitted by all the stars in the history of the universe. The accidental discovery of the CMB in 1964 by American radio astronomers Arno Allan Penzias and Robert Woodrow Wilson was the culmination of work initiated in the 1940s.

The CMB is landmark evidence of the Big Bang theory for the origin of the universe. In the Big Bang cosmological models, during the earliest periods, the universe was filled with an opaque fog of dense, hot plasma of sub-atomic particles. As the universe expanded, this plasma cooled to the point where protons and electrons combined to form neutral atoms of mostly hydrogen. Unlike the plasma, these atoms could not scatter thermal radiation by Thomson scattering, and so the universe became transparent. Known as the recombination epoch, this decoupling event released photons to travel freely through space. However, the photons have grown less energetic due to the cosmological redshift associated with the expansion of the universe. The surface of last scattering refers to a shell at the right distance in space so photons are now received that were originally emitted at the time of decoupling.

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the very early universe. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).

Inflation theory was developed in the late 1970s and early 1980s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Starobinsky, Guth, and Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation". It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation). Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.

In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically). The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. Uniform scaling happens, for example, when enlarging or reducing a photograph, or when creating a scale model of a building, car, airplane, etc.

More general is scaling with a separate scale factor for each axis direction. Non-uniform scaling (anisotropic scaling) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles). It occurs, for example, when a faraway billboard is viewed from an oblique angle, or when the shadow of a flat object falls on a surface that is not parallel to it.

In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines.

This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, point and line are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the following definition, which is more often encountered in modern textbooks.

A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to magnitude of the fluid's velocity vector.

A fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow. If the fluid is also isotropic (i.e., its mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuous shear deformation and continuous compression or expansion, respectively.

The optical properties of a material define how it interacts with light. The optical properties of matter are studied in optical physics (a subfield of optics) and applied in materials science. The optical properties of matter include:

• Refractive index
• Dispersion
• Transmittance and Transmission coefficient
• Absorption
• Scattering
• Turbidity
• Reflectance and Reflectivity (reflection coefficient)
• Albedo
• Perceived color
• Fluorescence
• Phosphorescence
• Photoluminescence
• Optical bistability
• Dichroism
• Birefringence
• Optical activity
• Photosensitivity

A basic distinction is between isotropic materials, which exhibit the same properties regardless of the direction of the light, and anisotropic ones, which exhibit different properties when light passes through them in different directions.

Snell's law (also known as the Snell–Descartes law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.In optics, the law is used in ray tracing to compute the angles of transmission or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index. (When light travels from a denser to a rarer medium, the formula is reciprocated (sin r divided by sin i) to find out refractive index)

The law states that, for a given pair of media, the ratio of the sines of angle of incidence ${\displaystyle \left(\theta _{1}\right)}$ and angle of refraction ${\displaystyle \left(\theta _{2}\right)}$ is equal to the refractive index of the second medium with regard to the first (${\displaystyle n_{2,1}}$) which is equal to the ratio of the refractive indices ${\displaystyle \left({\tfrac {n_{2}}{n_{1}}}\right)}$ of the two media, or equivalently, to the ratio of the phase velocities ${\displaystyle \left({\tfrac {v_{1}}{v_{2}}}\right)}$ in the two media.

The Friedmann–Lemaître–Robertson–Walker metric (FLRW; /ˈfriːdmən ləˈmɛtrə ... /) is a metric that describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson, and Arthur Geoffrey Walker – is variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). When combined with Einstein's field equations, the metric gives the Friedmann equation, which has been developed into the Standard Model of modern cosmology and further developed into the Lambda-CDM model.

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the very early universe. This enormous expansion supercooled the universe and ending when the energy content of the field driving inflation condensed into hot, dense particles, a process called reheating. Following the inflationary period, the universe continued to expand, but at a slower rate.

Inflation theory was developed in the late 1970s and early 1980s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Starobinsky, Guth, and Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation". It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation). Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.

A liquid crystal phase is thermotropic if its order parameter is determined by temperature. At high temperatures, liquid crystals become an isotropic liquid and at low temperatures, they tend to glassify. In a thermotropic crystal, those phase transitions occur only at temperature extremes; the phase is insensitive to concentration.

Most thermotropic liquid crystals are composed of rod-like molecules, and admit nematic, smectic, or cholesterolic phases.

A kilonova (also called a macronova) is a transient astronomical event that occurs in a compact binary system when two neutron stars (BNS) or a neutron star and a black hole collide. The kilonova, visible over the weeks and months following the merger, is an isotropically expanding luminous afterglow of electromagnetic radiation emitted by the radioactive decay of r-process nuclei synthesized by—and then ejected from—the initial cataclysmic event.

The high sphericity of kilonovae through its early epochs was deduced from the blackbody nature of the spectrum observed for the most important recorded BNS merger, GW170817 / AT2017gfo.

The Lorentz oscillator model (classical electron oscillator or CEO model) describes the optical response of bound charges. The model is named after the Dutch physicist Hendrik Antoon Lorentz. It is a classical, phenomenological model for materials with characteristic resonance frequencies (or other characteristic energy scales) for optical absorption, e.g. ionic and molecular vibrations, interband transitions (semiconductors), phonons, and collective excitations.