  This is an article written in a popular science style, in which I will
explain: (1) the famous Heisenberg uncertainty principle, expressing the
experimental incompatibility of certain properties of micro-physical entities;
(2) the Compton effect, describing the interaction of an electromagnetic wave
with a particle; (3) the reasons of Bohr's complementarity principle, which
will be understood as a principle of incompatibility; (4) the Einstein,
Podolski and Rosen reality (or existence) criterion, and its subsequent
revisitation by Piron and Aerts; (4) the mysterious non-spatiality of the
quantum entities of a microscopic nature, usually referred to as non-locality.
This didactical text requires no particular technical knowledge to be read and
understood, although the reader will have to do her/his part, as conceptually
speaking the discussion can become at times a little subtle. The text has been
written having in mind one of the objectives of the Center Leo Apostel for
Interdisciplinary Studies (CLEA): that of a broad dissemination of scientific
knowledge. However, as it also presents notions that are not generally
well-known, or well-understood, among professional physicists, its reading may
also be beneficial to them.
