Complementarity Transformed

Arkady Plotnitsky, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

This paper examines the transformation of Bohr's interpretation of quantum phenomena and quantum mechanics, known as complementarity, from the version presented in his famous Como lecture (1927), which introduced complementarity, to a new version that was developed by Bohr shortly thereafter, in part under the impact of his intervening exchanges with Einstein. While the existence of more than one version of Bohr's complementarity (and of still different versions of the Copenhagen interpretation by others) has been noted, Bohr's rethinking itself of complementarity has rarely been adequately addressed. Apart from refining and indeed correcting the Como argument, the transformation in question was, I argue, defined by a shift from a more philosophical to a more experimental argument. My aim is to explore both this shift and the complexity of the relationships between physics and philosophy in Bohr's thinking in order to understand better the beginnings and the ends, also in the sense of aims, of Bohr's complementarity.

Jacob Neusner

Samira Saidani, Sid-Ahmed Yahiaoui

We investigate in this paper the concept of complementarity, introduced by Bagchi and Quesne [Phys. Lett. A 301, 173 (2002)], between pseudo-Hermiticity and weak pseudo-Hermiticity in a rigorous mathematical viewpoint of coordinate transformations when a system has a position-dependent mass. We first determine, under the modified-momentum, the generating functions identifying the complexified potentials V±(x) under both concepts of pseudo-Hermiticity η̃+ (respectively, weak pseudo-Hermiticity η̃−). We show that the concept of complementarity can be understood and interpreted as a coordinate transformation through their respective generating functions. As a consequence, a similarity transformation that implements coordinate transformations is obtained. We show that the similarity transformation is set up as a fundamental relationship connecting both η̃+ and η̃−. A special factorization η+=η−†η− is discussed in the constant mass case, and some Bäcklund transformations are derived.

Sid-Ahmed Yahiaoui, M. Bentaïba

The complementarity between the twin concepts of pseudo-Hermiticity and weak pseudo-Hermiticity, established by Bagchi and Quesne [Phys. Lett. A 301 (2002) 173-176], can be understood in terms of coordinate transformations.

Arkady Plotnitsky