Investigations of possible violations of the Pauli exclusion principle represent critical tests of the microscopic space-time structure and properties. Space-time noncommutativity provides a class of universality for several quantum gravity models. In this context the VIP-2 lead experiment sets the strongest bounds, searching for the Pauli exclusion principle violating atomic transitions in lead, excluding the $\theta$-Poincaré noncommutative quantum gravity models far above the Planck scale for nonvanishing ${\theta }_{\mu \nu }$ electriclike components, and up to $6.9\times {10}^{-2}$ Planck scales if ${\theta }_{0i}=0$.

About a hundred years ago, the Russian biologist A. Gurwitsch, based on experiments with onion plants by measuring their growth rate, hypothesized that plants emit a weak electromagnetic field that somehow influences cell growth. This interesting observation remained fundamentally ignored by the scientific community; only in the 1950s the electromagnetic emission from some plants was measured using a photomultiplier used in single counting mode. Later, in the 1980s, several groups around the world started extensive work to understand the origin and role of this ultraweak emission, now called biophotons, coming from living organisms. Biophotons are an endogenous very small production of photons in the visible energy range in and from cells and organisms, and this emission is characteristic of living organisms. Today, there is no doubt that biophotons exist, this emission has been measured by many groups and for many different living organisms, from humans to bacteria. However, the origin of biophotons and whether organisms use them to exchange information is not yet well understood; no model proposed to date is capable of reproducing and interpreting the great variety of experimental data coming from the many different living systems measured so far. In this brief review, we present our experimental work on the biophotons coming from germinating seeds, the main experimental results, and some new methods we are using to analyze the data to open the door for interpretative models of this phenomenon clarifying its function in the regulation and communication between cells and living organisms. We also discuss ideas on how to increase the signal-to-noise ratio of the measured signal to open up new experimental possibilities that allow the measurement and the characterization of currently unmeasurable quantities.

We study the emission of photons from germinating seeds using an experimental technique designed to detect light of extremely small intensity. We analyze the dark count signal without germinating seeds as well as the photon emission during the germination process. The technique of analysis adopted here, called diffusion entropy analysis (DEA) and originally designed to measure the temporal complexity of astrophysical, sociological and physiological processes, rests on Kolmogorov complexity. The updated version of DEA used in this paper is designed to determine if the signal complexity is generated either by non-ergodic crucial events with a non-stationary correlation function or by the infinite memory of a stationary but non-integrable correlation function or by a mixture of both processes. We find that dark count yields the ordinary scaling, thereby showing that no complexity of either kinds may occur without any seeds in the chamber. In the presence of seeds in the chamber anomalous scaling emerges, reminiscent of that found in neuro-physiological processes. However, this is a mixture of both processes and with the progress of germination the non-ergodic component tends to vanish and complexity becomes dominated by the stationary infinite memory. We illustrate some conjectures ranging from stress induced annihilation of crucial events to the emergence of quantum coherence.

Kaonic atoms measure the antikaon-nucleus interaction at almost zero relative energy, allowing one to determine basic low-energy quantum chromodynamics (QCD) quantities, namely, the antikaon-nucleon ( $\overline{K}$ N) scattering lengths. The latter are important for extracting the sigma terms which are built on the symmetry breaking part of the Hamiltonian, thereby providing a measure of chiral and SU(3) symmetries breaking. After discussing the sigma terms and their relations to the kaonic atoms, we describe the most precise measurement in the literature of kaonic hydrogen, performed at LNF-INFN by the SIDDHARTA experiment. Kaonic deuterium is still to be measured, and two experiments are planned. The first, SIDDHARTA-2 at LNF-INFN was installed on DA $\mathsf{\Phi }$ NE in spring 2019 and will collect data in 2020. The second, E57 at J-PARC, will become operative in 2021.

The VIolation of Pauli (VIP) experiment (and its upgraded version, VIP-2) uses the Ramberg and Snow (RS) method (Phys. Lett. B 1990, 238, 438) to search for violations of the Pauli exclusion principle in the Gran Sasso underground laboratory. The RS method consists of feeding a copper conductor with a high direct current, so that the large number of newly-injected conduction electrons can interact with the copper atoms and possibly cascade electromagnetically to an already occupied atomic ground state if their wavefunction has the wrong symmetry with respect to the atomic electrons, emitting characteristic X-rays as they do so. In their original data analysis, RS considered a very simple path for each electron, which is sure to return a bound, albeit a very weak one, because it ignores the meandering random walks of the electrons as they move from the entrance to the exit of the copper sample. These complex walks bring the electrons close to many more atoms than in the RS calculation. Here, we consider the full description of these walks and show that this leads to a nontrivial and nonlinear X-ray emission rate. Finally, we obtain an improved bound, which sets much tighter constraints on the violation of the Pauli exclusion principle for electrons.

Biophotons are an ultra-weak emission of photons in the visible energy range from living matter. In this work, we study the emission from germinating seeds using an experimental technique designed to detect light of extremely small intensity. The emission from lentil seeds and single bean was analyzed during the whole germination process in terms of the different spectral components through low pass filters and the different count distributions in the various stages of the germination process. Although the shape of the emission spectrum appears to be very similar in the two samples used in our experiment, our analysis can highlight the differences present in the two cases. In this way, it was possible to correlate the various types of emissions to the degree of development of the seed during germination.