Exploring the quantum-gravity connection: theoretical insights and unprecedented experimental constraints

This thesis investigates the quantum-gravity interface from both theoretical and experimental perspectives, focusing on two complementary approaches: violations of particle statistics and spontaneous radiation. These frameworks provide sensitive probes of possible departures from standard quantum mechanics and quantum field theory. Underground X-ray experiments offer an ideal environment to detect ultra-rare events, providing a unique window into Planck-scale physics, where direct measurements are impossible due to the prohibitive energy scales. The VIP collaboration has recently devoted considerable effort to bridging theory and experiment, achieving unprecedented precision in tests of fundamental quantum principles. Small violations of Bose and Fermi statistics are predicted by several low-energy effective quantum-gravity models, while spontaneous radiation constitutes a distinctive signature of spontaneous collapse models (SCMs). Although no predicted signals have been observed, several models have been experimentally constrained and even excluded. The first part of the thesis explores deformations of statistics in models incorporating a minimal length, realized through deformations of the algebraic structure of spacetime or phase space. We present a detailed analysis of noncommutative spacetime models, focusing on the well-studied string-related Moyal plane. Previous approaches to twisted statistics $-$ required in this context to preserve covariance $-$ are generalized, and a consistent theoretical framework is developed, resulting in the first relativistic realization of the quon model, originally proposed 35 years ago as a nonrelativistic framework interpolating between bosonic and fermionic statistics. At the phenomenological level, a pivotal role is played by the investigation of superselection rules among different symmetry sectors. We demonstrate that while these rules can be consistently defined at the kinematical level, they may be violated in interacting systems. In fact, we find that such violation is necessary to prevent large deviations from the Pauli exclusion principle (PEP). Using VIP lead data and a Bayesian analysis, we set the most stringent bounds on the Moyal plane in the electromagnetic sector, providing a Planck-scale test of string theory. We further constrain a whole class of noncommutative spacetime models, ruling out a proposed quantization scheme in $\kappa$-Minkowski spacetime up to energy scales above 10$^{21}$ Planck scales, and place the first limits on cubic suppressions of PEP-violating transition $-$ $5.6\times 10^{-9}$ Planck scales $-$ which may be relevant for “triply special relativity”. We extend these studies to models based on the generalized uncertainty principle (GUP). We generalize a proposed QFT model and identify a quon-like deformation of the field-mode algebra. The model is tested using VIP copper data. We compute the relevant PEP-violating transition probabilities and obtain the strongest limits to date on the quadratic GUP model, excluding a broad class of statistics deformations associated with minimal lengths at or below the Planck length scale. Specifically, we set for this class upper bounds on the dimensionless GUP parameter of $\beta_0 = \beta/\ell_p^2 \lesssim 1$, improving on existing limits by approximately 16 orders of magnitude. The second part of the thesis focuses on SCMs. We provide an improved derivation of the spontaneous radiation emission rate, implementing an ab initio evaluation based on radial distribution functions. This allows one to perform computations for arbitrary materials which depend solely on intrinsic SCM parameters. We test then a reformulation of the pioneering gravity-related Károlyházy model, focusing on a version equivalent to a non-Markovian generalization of the continuous spontaneous localization (CSL) model, with time correlation and collapse rate fixed by the Károlyházy spacetime uncertainty. Applying a dedicated analysis using data from a High-Purity Germanium detector, we experimentally rule out the model. We also explore the implications of spacetime irreversibility associated with mass-proportional collapse models, including CSL and Diósi-Penrose models. These models suggest an induced uncertainty in the flow of time due to fluctuations in the Newtonian potential. We calculate the ultimate limit on time uncertainty and demonstrate that the resulting clock-time uncertainty remains negligible for all contemporary timekeeping devices, including atomic clocks. Finally, we present a new experimental setup based on a Broad-Energy Germanium detector, designed to simultaneously probe statistics violations and spontaneous radiation. The apparatus has been optimized to lower the energy detection threshold to a few keV, achieving sensitivity in the $(1-15)$ keV range, which is crucial for advancing experimental tests of the quantum-gravity interface. This setup is expected to improve current limits on spin-statistics violations by approximately one order of magnitude, and enable searches for spontaneous radiation that may, for the first time, discriminate between different collapse mechanisms. Overall, this work demonstrates that experimental investigations of the quantum-gravity interface have reached a precision sufficient to test fundamental theoretical predictions at relevant scales. While no deviations from standard theories have been observed, the stringent bounds obtained and the methodological advancements developed provide a roadmap for future studies at the foundations of a unified theory of quantum mechanics and gravity.