invariant (ɪnˈvɛərɪənt) | |
—n | |
1. | maths an entity, quantity, etc, that is unaltered by a particular transformation of coordinates: a point in space, rather than its coordinates, is an invariant |
—adj | |
2. | maths (of a relationship or a property of a function, configuration, or equation) unaltered by a particular transformation of coordinates |
3. | a rare word for invariable |
in'variance | |
—n | |
in'variancy | |
—n |
invariance (ĭn-vâr'ē-əns) Pronunciation Key
The property of remaining unchanged regardless of changes in the conditions of measurement. For example, the area of a surface remains unchanged if the surface is rotated in space; thus the area exhibits rotational invariance. In physics, invariance is related to conservation laws. For example, conservation of angular momentum is directly related to rotational invariance (the laws of physics don't depend on the angle of the reference point), conservation of energy is related to invariance over time (the laws of physics remain the same over time), and conservation of momentum is related to invariance over translations through space (the laws of physics don't depend on the position of the reference point). A form of invariance called Lorenz invariance is fundamental to the theory of Special Relativity. Invariance is also called symmetry. See also Noether's theorem. |
invariance
in physics, the concept that the properties of particles such as atoms and molecules remain unchanged after being subjected to a variety of symmetry transformations or "operations." Since the earliest days of natural philosophy (Pythagoras in the 6th century BC), symmetry has furnished insight into the laws of physics and the nature of the cosmos. The two outstanding theoretical achievements of the 20th century, relativity and quantum mechanics, involve notions of symmetry in a fundamental way
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