Observables in Terms of Antonymous and Observable Functions

Gertjan J. Burghouts, Jan‐Mark Geusebroek, Arnold W. M. Smeulders

Andreas Doering

Antonymous functions are real-valued functions on the Stone spectrum of a von Neumann algebra R. They correspond to the self-adjoint operators in R, which are interpreted as observables in quantum physics. Antonymous functions turn out to be generalized Gelfand transforms, related to de Groote's observable functions.

Francesco Galofaro, Zeno Toffano, Bich-Liên Doan +1 more

A lexeme can be represented as a vector in a Hilbert space. Each element of the vector represents the weight of a semantic relation with a second vector: the context of a second lexeme. Two query operators are defined in a way that they attribute the value +1 to the component of the state that corresponds to the word meaning we are interested in, and -1 in the orthogonal direction. Entangled states have been used to detect semantic relationships in Information Retrieval (IR). In particular, since the first operator corresponds to negation and the conditional gate corresponds to an implication in classical logic, they can represent two basic semantic relationships : hyponymy (e.g. genus-species) and antonymy (e.g. masculine-feminine). In fact, according to Semantics, if A and B are antonymic terms, then A is an hyponym of (i.e. implies) not-B as in the Gremias semiotic square. We underline how the relations of a given semantic universe, and the corresponding result of our operators, depends only on the considered text. Among others, this analogy suggests the application of quantum-based models to language and IR.

Sadri Hassani

Quantum physics and relativity are the two pillars of modern physics. Often in this context, the word “modern” is misused as an antonym of “classical.” The abstract and mathematical nature of both quantum and relativity theories makes them easy target for abuse in the hands of the purveyors of mysticism. We shall see some detailed examples of the abuse of quantum theory in Chapter 35. It will be shown there how New Age authors misrepresent quantum physics to their readers and use some twisted interpretation of the theory to advocate a parallel between quantum physics and Eastern mysticism.

Lev Deych