A Modal Interpretation of Quantum Spins and Its Application to Freudian Theory

Abstract

In the present paper, we aim to develop a formal quantum logic theory of the interplay between conscious and unconscious processes of the human mind, a goal that has already been envisaged in quantum cognitions; in doing so, we will show how the interplay between formal language and metalanguage allows for characterizing pure quantum states as infinite singletons: in the case of the spin observable, we obtain an equation defining a modality that is then re-interpreted as an abstract projection operator. By including a temporal parameter in the equations and by defining a modal negative operator, we derive an intuitionistic-like negation, for which the non-contradiction law is seen as an equivalent of the quantum uncertainty. Building on the psychoanalytic theory of Bi-Logic by Matte Blanco, we use modalities in interpreting the emergence of conscious representations from the unconscious one, and we demonstrate that this description fits well with Freud’s view of the role of negation in mental processes. Psychoanalysis, where affect plays a prominent role in shaping not only conscious, but also unconscious representations, is therefore seen as a suitable model to expand the domain of quantum cognition to the broader field of affective quantum cognition.

The Modal Components of Judgements in a Quantum Model of Psychoanalytic Theory

“…where indicates that a formula is closed with respect to any variable, which refers the value of the object for any thing-presentation of the object. One can prove that the equivalence defines the modal operator of S4, the necessity operator [33]. Since in S4, A = A, the operator can attribute a sharp yet undefined value to the object.…”

“…Infinite singletons were originally conceived in order to model quantum states in first-order logic (see [13,33]). One first considers the set V = {t 1 , .…”

“…Considering the collection given by the measurement of the spin for each direction, one can abstract with respect to the direction, and applying definition ( 5), find a formula A that is closed with respect to each variable for each direction, obtaining the modal operator of S4, as seen in the above Section 4. The equality A = A for every A, that holds in S4, shows that can be interpreted as an general projector, the modal projector, in an abstract space (see [33]).…”

“…This happens due to the attitude with respect to the external reality, when inner and external reality have to come in touch. Then, in physics, an initial condition of measurement for that process can be assumed, considering the Schroedinger picture as in [33]. That is, a description of the evolution of the state with respect to a fixed observable (see [34] p. 125).…”

“…In the spin model, the finitization of T can be obtained considering the temporal evolution of the spin, induced by a temporal parameter (see [33]). We have a split of the possibilities: one for each direction d of the spin.…”