What does invariance mean?
Invariance is the property of remaining unchanged under specified conditions or transformations. It is especially important in mathematics and physics, where it can describe a quantity that retains its value, an equation that remains equivalent, or a law whose form does not change when coordinates, scale, or observational perspective are altered. Concepts such as translation invariance, scale invariance, and gauge invariance are central in describing fundamental symmetries. Outside the sciences, invariance can broadly mean resistance to change, though this use is more formal and less frequent. The word is useful because it names not simply a lack of change, but a relationship between something and the transformations to which it is subjected: the object or law remains unchanged while other aspects of the situation vary.
nounThe quality of remaining unchanged, especially the property of a mathematical quantity or form under a specified transformation, operation, or set of conditions.
- The state or quality of remaining unchanged, especially under a transformation or operation.
- The quality of a physical law, quantity, or form retaining the same form or value despite a change in conditions, coordinates, or perspective.
"The symmetry of the design demonstrates its invariance under rotation."
"The equation has an important symmetry because it exhibits invariance under exchanging the two variables."
"The physicist used scale invariance to compare the behavior of the system at different levels of magnification."
Usually plural when referring to distinct mathematical or physical invariance properties.
"The model exhibits several important invariances."
In mathematics and physics, invariance reveals the structures that do not change when the world around them is transformed.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does invariance come from?
Invariance was formed in the 19th century from invariant, meaning 'unchanged', with the suffix -ance. The adjective invariant comes from Latin invarians, from invariāre, 'to remain unchanged', with in- expressing negation and variāre meaning 'to vary'. Related English forms include invariable and invariably. The Latin root is also reflected in words such as variable and variance, which express change rather than its absence.
Related word forms
How invariance is actually used
The term is most common in mathematics and physics, where it describes a quantity, law, or structure that remains unchanged under specified transformations. In general contexts, it is formal and less common than 'constancy' or 'unchangingness'.
Easily confused with invariance
Invariance is the property of remaining unchanged, whereas an invariant is a quantity or rule that remains unchanged under particular conditions.