GRS for Einstein-Cartan Gravity

Gravity is an everyday force. Nevertheless we are surprised that one single mathematical equation describes all observation well both at distances at the very small and distances at the very large principally applying to the universe as a whole. The equation has been named Einsteins General Relativity in 1915. Einstein missed out some possibilities nature is offering. A bit later in 1922 Ellie Cartan suggested that gravity can be generalized by adding a direction of rotation. So the question arises whether there exists a spin contribution to gravity. Mathematically speaking, we added a minus sign in one of the equations. The descripting is becoming more symmetric and fits in nicely with our ideas of modern physics. The aim of this work is to test this theory, which is nowadays known as Einstein-Cartan gravity. For that purpose we use elementary particles with spin. We allow neutrons to fall in the gravity potential of the earth and measure very precisely. It might be that a falling object, in this case a neutron, starts rotating and adapts other energy levels, in contrast current experience. We have developed a quantum interference techniques for gravity experiments linked to resonance spectroscopy. Quantum objects so far provide the most precise measuring techniques. Examples are atomic clocks or magnetic resonance techniques, which deliver accurate time standards or fanciful images of the body at the doctors office for medical services. We adapt these techniques to ultra-cold neutrons within the experiment.

Exploring Gravity at the Quantum Frontier: The qBounce Experiment The qBounce experiment explores one of the most fundamental questions in physics: how gravity behaves at the quantum level. Using ultra-cold neutrons bouncing above a mirror in Earth's gravitational field, qBounce has established a unique laboratory for studying gravity where quantum mechanics and gravitation meet directly. A central innovation of qBounce is the development of gravity resonance spectroscopy. In this technique, quantum states of neutrons bound by gravity are excited and probed with unprecedented precision, allowing direct measurements of their energy splittings. Unlike conventional gravitational experiments, this approach is intrinsically quantum and free from electromagnetic background effects, making it exceptionally clean and sensitive to new physics. Building on this foundation, qBounce successfully implemented Ramsey spectroscopy with gravitational quantum states. By coherently manipulating superpositions of neutron states over time, the experiment achieved a dramatic increase in precision, analogous to the methods that revolutionized atomic clocks. This advance opened the door to precision tests of gravity in a regime that had never been accessible before. A major scientific focus of qBounce is the experimental investigation of Einstein-Cartan gravity, an extension of general relativity that includes spacetime torsion and allows new couplings between gravity and intrinsic spin. Within this framework, qBounce has produced the world's most stringent limits on several parameters describing possible deviations from standard Riemannian gravity. These results directly improve upon and, in several cases, surpass the constraints discussed in Searches for Beyond-Riemann Gravity (Phys. Rev. D 104, 044054, 2021), establishing qBounce as a leading experiment in this field. Beyond Einstein-Cartan gravity, the sensitivity of gravity resonance and Ramsey spectroscopy enables tests of other foundational ideas. Notably, qBounce has provided experimental statements on Verlinde's entropic gravity, a theory proposing gravity as an emergent, thermodynamic phenomenon rather than a fundamental interaction. By probing gravity at micrometer length scales and pico-electron-volt energy levels, qBounce places both strong constraints on but also possibilities for such emergent-gravity scenarios. Altogether, qBounce demonstrates that precision quantum experiments with neutrons are powerful tools for exploring gravity beyond classical general relativity. The combination of gravity resonance spectroscopy and Ramsey techniques establishes a new benchmark for testing fundamental physics, offering some of the best existing limits on novel gravitational interactions and opening new perspectives on the quantum nature of spacetime itself.