What does scale invariance mean?

Definitions for scale invariance
scale invari·ance

This dictionary definitions page includes all the possible meanings, example usage and translations of the word scale invariance.


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Wiktionary

  1. scale invariancenoun

    a feature of objects or laws that do not change if length scales (or energy scales) are multiplied by a common factor.

Wikidata

  1. Scale invariance

    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, 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.

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Numerology

  1. Chaldean Numerology

    The numerical value of scale invariance in Chaldean Numerology is: 9

  2. Pythagorean Numerology

    The numerical value of scale invariance in Pythagorean Numerology is: 1


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"scale invariance." Definitions.net. STANDS4 LLC, 2024. Web. 19 Mar. 2024. <https://www.definitions.net/definition/scale+invariance>.

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