Toy model of quantum mechanics modified by gravity

This thesis contributes to the debate on the outstanding issue of quantum gravity, fitting into the context of the upcoming related experimental era. We part ways with the conventional view of effective field theory, where General Relativity adapts to quantum laws, in favour of a transitional approach from quantum to classical regime at low energies. In the first part we challenge the implications of a framework imposing quantization on the non-linear specificity of gravity. A stream of research about gravitation preventing massive objects to fluctuate and violating quantum mechanics is examined afterwards. In line with this argumentation, we introduce a recent alternative to standard quantum gravity, the Correlated WorldLine (CWL) theory by Stamp, with the new perspectives it brings to the table. In the core part we perform numerical analysis on toy models inspired by Stamp's approach with simplified method. Our goal is to mimic the above models to evaluate their reliability by heuristically predicting what kind of effects might surface and at what mass scales. The last part is dedicated to briefly summarize results and identify possible development of related research.