What does incommutability mean?
Incommutability is a technical noun meaning that two operations, measurements, or mathematical quantities cannot be exchanged or reordered without changing the result. A familiar example occurs in quantum mechanics, where measuring position before momentum does not generally give the same result as measuring momentum before position. The term is also used more broadly in mathematics and theoretical physics for systems whose order of operations matters. It is the opposite of commutativity, which describes operations that can be reordered freely. Although incommutability has a specialized history in quantum theory, the word follows the ordinary English pattern of forming a noun from the property expressed by an adjective, “incommutable,” and is chiefly encountered in academic and scientific writing. Its usefulness lies in naming a precise distinction that ordinary words such as “order” or “sequence” do not convey.
nounThe property of an operation or pair of quantities being incommutable, meaning that their order cannot be interchanged without changing the result or outcome. In physics, it is especially associated with quantum mechanical observables whose order of measurement matters.
- The property of an operation or mathematical relation not being commutative.
- In quantum mechanics, the property of two observables not commuting, so that their order of measurement affects the outcome.
"The incommutability of position and momentum is a defining feature of quantum mechanics."
"The theory relies on the incommutability of certain quantum observables."
"This result demonstrates the incommutability of the relevant operations."
The plural is used when referring to several distinct instances of the property.
"The model compares the incommutabilities of different pairs of observables."
In quantum mechanics, changing the order in which you measure two properties can change the result: nature refuses to commute.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does incommutability come from?
The word is formed from the Latin prefix in-, meaning “not,” together with commutability, a noun derived from commute. In its mathematical sense, it ultimately refers to operations that do not commute, meaning that swapping their order changes the result. The concept became especially prominent in the development of quantum mechanics during the early twentieth century, where the failure of certain observables to commute has fundamental physical significance.
How incommutability is actually used
This is a technical term used chiefly in mathematics and quantum physics. It is uncommon in ordinary English, where its general sense may be expressed more simply as the inability to change order without consequence.
Easily confused with incommutability
Commutativity is the property of an operation that gives the same result when its factors or terms are reordered, whereas incommutability means that reordering does not generally preserve the result.