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- Scale_invariance abstract "In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that does not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.".
- Scale_invariance thumbnail Wiener_process_animated.gif?width=300.
- Scale_invariance wikiPageID "695241".
- Scale_invariance wikiPageRevisionID "590876674".
- Scale_invariance hasPhotoCollection Scale_invariance.
- Scale_invariance subject Category:Conformal_field_theory.
- Scale_invariance subject Category:Critical_phenomena.
- Scale_invariance subject Category:Scaling_symmetries.
- Scale_invariance subject Category:Symmetry.
- Scale_invariance type Abstraction100002137.
- Scale_invariance type Attribute100024264.
- Scale_invariance type Property104916342.
- Scale_invariance type ScalingSymmetries.
- Scale_invariance type SpatialProperty105062748.
- Scale_invariance type Symmetry105064827.
- Scale_invariance comment "In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that does not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves.".
- Scale_invariance label "Invariance d'échelle".
- Scale_invariance label "Invariancia de escala".
- Scale_invariance label "Invarianza di scala".
- Scale_invariance label "Invariância de escala".
- Scale_invariance label "Scale invariance".
- Scale_invariance label "Skaleninvarianz".
- Scale_invariance label "Масштабная инвариантность".
- Scale_invariance sameAs Skaleninvarianz.
- Scale_invariance sameAs Invariancia_de_escala.
- Scale_invariance sameAs Invariance_d'échelle.
- Scale_invariance sameAs Invarianza_di_scala.
- Scale_invariance sameAs Invariância_de_escala.
- Scale_invariance sameAs m.033g2k.
- Scale_invariance sameAs Q1750766.
- Scale_invariance sameAs Q1750766.
- Scale_invariance sameAs Scale_invariance.
- Scale_invariance wasDerivedFrom Scale_invariance?oldid=590876674.
- Scale_invariance depiction Wiener_process_animated.gif.
- Scale_invariance isPrimaryTopicOf Scale_invariance.
