Hilbert Space Quotes

“Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.”
― Asher Peres, Quantum Theory: Concepts and Methods

“In Hilbert space, the classical states are just in one corner of the room, quantum attention functions are in the middle, and they are the matrix of cosmic functions that can collapse any other quantum wave function and transform the non-classical states into classical states in the Hilbert space.”
― Amit Ray, Quantum Attention Function Theory

“The ramifications of Pythagoras' theorem have revolutionized twentieth century theoretical physics in many ways. For example, Minkowski discovered that Einstein's special theory of relativity could be represented by four-dimensional pseudo-Euclidean geometry where time is represented as the fourth dimension and a minus sign is introduced into Pythagoras' law. When gravitation is present, Einstein proposed that Minkowski's geometry must be "curved", the pseudo-Euclidean structure holding only locally at each point. A complex vector space having a natural generalization of the Pythagorean structure (defined over functions in an abstract space rather than geometrical points in the familiar Euclidean space) is known as Hilbert space and forms the basis of quantum mechanics. It is remarkable to think that the two pillars of twentieth century physics, relativity and quantum theory, both have their basis in mathematical structures based on a theorem formulated by an eccentric mathematician over two and a half thousand years ago.”
― Peter Szekeres, A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry