Bounds on the bizarrity of the Universe from experiments with trapped, cold, charged particles

In order to understand nature better, humans often had to expand their horizon with seemingly bizarre concepts. In the probably most targeted search for such new underlying concepts, theorists explore hypothetical concepts and make predictions which can be tested in controlled experiments. I will focus on two instances where high-precision control of trapped ions and electrons allows us to place bounds on such concepts.

In the first, S. Weinberg was wondering whether the laws of nature at the quantum scale are nonlinear (Ann.Phys. (N.Y.), 194, 336-386 (1989)). However, no indications of nonlinearities could be detected even by using high precision spectroscopy. In addition, it became apparent that nonlinearities should lead to non causal effects and thus the idea of a nonlinear quantum theory became less attractive. However, recently Kaplan and Rajendran (arXiv:2106.10576 [hep-th]) managed to add non-linear and state-dependent terms without violating causality. Interestingly this extension rendered the existing experimental tests ineffective, mainly because the quantum mechanical test objects used to exclude nonlinearities were not localized. This delocalization leads to a dilution of the self-interaction between the superposition states of the wavefunction and hence the observable energy shift. I will discuss new experiments where the quantum mechanical object is tied to a macroscopic object (such as an ion trap) leading to sufficient localization such that a self-interaction could lead to measurable non-linearities.