Does the Vacuum Gravitate? Rydberg Atoms Say "Probably Not!"

One of the least understood features of our Universe is the existence of a small cosmological constant. The initial impulse was to ascribe the cosmological constant to the gravitating effects of the quantum energy of the vacuum. This seems to be wrong. We need a more detailed investigation of the quantum vacuum and its gravitating properties. Excited Rydberg atoms provide just such a laboratory. The exquisite precision attainable and the relatively large size of excited Rydberg atoms enable us to measure the gravitating properties of the vacuum. It does not gravitate as naively expected. We find an upper limit to the energy scale of gravitating vacuum energy to be $(7 \ \text{GeV})^4$, considerably lower than the scale of the Standard Model $(100 \ \text{GeV})^4$. This provides important limitations on how to incorporate gravity into our understanding of Quantum Field theory.