Quantum explorations: from the waltz of the Pauli exclusion principle to the rock of the spontaneous collapse

The spin–statistics connection, in particular the Pauli exclusion principle (PEP), plays a very important role in our comprehension of matter and nature. Presently, the PEP violation, possible within some theories, generates a lively debate; it has given birth to a few experiments looking for tiny effects. The violation of the Pauli exclusion principle experiment put a very strong limit on the PEP violation probability by electrons, using the method of searching for PEP forbidden atomic transitions in a copper target. In this paper we present this experiment, the obtained results and future plans to upgrade the experimental setup with fast silicon drift detectors. We then present the idea of using an analogous experimental technique to search for x-rays as a signature of the spontaneous collapse of the wave function, predicted by the continuous spontaneous localization theories, and some very encouraging preliminary results.