From Fuzzy Spacetime to Classical Reality

This thesis investigates the interplay between quantum mechanics and gravity, focusing on how gravitational effects may influence quantum state reduction and decoherence. The work proceeds along two complementary directions: gravitational decoherence (Károlyházy model) and gravity-induced collapse (Diósi–Penrose model), representing two distinct pathways through which classicality might emerge from quantum theory. On the decoherence side, we developed a generalized stochastic model of spacetime fluctuations that refines Károlyházy’s original idea of metric-induced decoherence. The model overcomes inconsistencies in earlier formulations, aligns with current experimental bounds, and quantifies how stochastic gravitational potentials degrade quantum coherence without invoking wave-function collapse. By introducing generalized correlation functions, it restores consistency with known limits, narrows the viable parameter space, and identifies the conditions under which gravitational decoherence may become experimentally accessible. On the collapse side, we analyzed the Diósi–Penrose (DP) model, which links spontaneous wave-function localization to gravitational self-energy. Using analytic and numerical methods, we derived theoretical upper bounds on the model’s parameters by requiring that the collapse effectively suppress macroscopic superpositions. We explored scaling laws for the collapse time as a function of mass, geometry, and dimensionality, and extended the framework to include non-Markovian (memory) effects. More broadly, the thesis addresses one of modern physics’ central challenges: reconciling quantum theory, which governs the microscopic world, with general relativity, which describes spacetime and gravitation. Collapse and decoherence models provide promising frameworks to study this interface. The DP model introduces genuinely non-unitary dynamics, offering an experimentally testable link between quantum mechanics and gravity, while the Károlyházy approach preserves unitarity but attributes decoherence to stochastic spacetime fluctuations. Together, these studies provide tighter theoretical constraints on gravitationally induced quantum effects and delineate experimentally relevant regimes. The combined results clarify under which conditions gravity could account for the quantum-to-classical transition and guide the design of future precision experiments probing the quantum–gravitational boundary.

This thesis investigates the interplay between quantum mechanics and gravity, focusing on how gravitational effects may influence quantum state reduction and decoherence. The work proceeds along two complementary directions: gravitational decoherence (Károlyházy model) and gravity-induced collapse (Diósi–Penrose model), representing two distinct pathways through which classicality might emerge from quantum theory. On the decoherence side, we developed a generalized stochastic model of spacetime fluctuations that refines Károlyházy’s original idea of metric-induced decoherence. The model overcomes inconsistencies in earlier formulations, aligns with current experimental bounds, and quantifies how stochastic gravitational potentials degrade quantum coherence without invoking wave-function collapse. By introducing generalized correlation functions, it restores consistency with known limits, narrows the viable parameter space, and identifies the conditions under which gravitational decoherence may become experimentally accessible. On the collapse side, we analyzed the Diósi–Penrose (DP) model, which links spontaneous wave-function localization to gravitational self-energy. Using analytic and numerical methods, we derived theoretical upper bounds on the model’s parameters by requiring that the collapse effectively suppress macroscopic superpositions. We explored scaling laws for the collapse time as a function of mass, geometry, and dimensionality, and extended the framework to include non-Markovian (memory) effects. More broadly, the thesis addresses one of modern physics’ central challenges: reconciling quantum theory, which governs the microscopic world, with general relativity, which describes spacetime and gravitation. Collapse and decoherence models provide promising frameworks to study this interface. The DP model introduces genuinely non-unitary dynamics, offering an experimentally testable link between quantum mechanics and gravity, while the Károlyházy approach preserves unitarity but attributes decoherence to stochastic spacetime fluctuations. Together, these studies provide tighter theoretical constraints on gravitationally induced quantum effects and delineate experimentally relevant regimes. The combined results clarify under which conditions gravity could account for the quantum-to-classical transition and guide the design of future precision experiments probing the quantum–gravitational boundary.