The Wigner–Araki–Yanase theorem, also known as the WAY theorem, is a result in quantum physics establishing that the presence of a conservation law limits the accuracy with which observables that fail to commute with the conserved quantity can be measured.
[1][2][3] It is named for the physicists Eugene Wigner,[4] Huzihiro Araki and Mutsuo Yanase.
[5][6] The theorem can be illustrated with a particle coupled to a measuring apparatus.
is conserved implies that, in a suitably quantified sense, the particle's position itself cannot be measured.
The Wigner–Araki–Yanase theorem generalizes this to the case of two arbitrary observables
[8][9] Mikko Tukiainen gave a generalized version of the WAY theorem, which makes no use of conservation laws, but uses quantum incompatibility instead.
[10] Yui Kuramochi and Hiroyasu Tajima proved a generalized form of the theorem for possibly unbounded and continuous conserved observables.