Experimental tests of Quantum Mechanics: from Pauli Exclusion Principle Violation to spontaneous collapse models

The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the q violation parameter translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the q-parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (Violation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter and as probability of PEP violation, we briefly discuss the results and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopic fast Silicon Drift Detectors. We mention as well the possibility of using a similar experimental technique to search for eventual X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continuous spontaneous localization type theories.