### The Heisenberg uncertainty principle

The Heisenberg uncertainty principle is one of the most famous elements of quantum theory, not only mentioned in academic papers and described in quantum mechanics textbooks, but also present in popular treatises. Well, the fact is that " Heisenberg uncertainty principle " is a misnomer because it is neither a principle nor about uncertainties. Brian Randolph Greene, a leading theoretical physicist, mathematician, and string theorist, often mentions the Heisenberg uncertainty principle. He does so in his popular books and he did again in a recent tweet . The " Heisenberg uncertainty principle " is usually abbreviated as HUP and the first thing to clarify about it is that it is not a principle, but a theorem derived from the postulates of quantum mechanics. A derivation of this theorem can be found in book [1]. The result for two arbitrary quantum operators \( \hat{A} \) and \( \hat{B} \) associated to the observables \( A \) and \( B \) is \[ \sigma(A) \cdot \si