Heisenberg cut Heisenberg cut In quantum mechanics, a Heisenberg cut is the hypothetical interface between quantum events and an observer's information, knowledge, or conscious awareness. Below the cut everything is governed by the wave function; above the cut a classical description is used. The Heisenberg cut is a theoretical construct; it is not known whether actual Heisenberg cuts exist, where they might be found, or how they could be detected experimentally. However, the concept is useful for analysis. The cut is named after Werner Heisenberg's work on the Copenhagen interpretation of quantum mechanics in which it is associated with wave function collapse.
Heisenberg group connection with the theta functions. If , are integers (in the ring Z) then one has the discrete Heisenberg group H(Z). It is a non-abelian nilpotent group. It has two generators, and relations where is the generator of the center of H. (Note that the inverses of "x", "y", and "z" replace the 1 above the diagonal with −1.) By Bass's theorem, it has a polynomial growth rate of order 4. One can generate any element through If one takes "a, b, c" in Z/"p" Z for an odd prime "p", then one has the Heisenberg group modulo p. It