February 2023

Quantum nonlocality, generated by strong correlations between entangled systems, defies the classical view of nature based on standard causal reasoning plus physical assumptions. The new frontier of the research on entanglement is to explore quantum correlations in complex networks, involving several parties and generating new striking quantum effects. We present recent advances on the realization of photonic quantum networks.

This paper is a transcript of the dialogue between Carlo Rovelli and Mike Jackson after Rovelli’s delivery of the 2021 Annual Mike Jackson Lecture, hosted by the Centre for Systems Studies at the University of Hull. The dialogue covers a range of topics, including how Rovelli developed a sense of curiosity in his youth; the connection between his interests in science and politics; the pathology of disciplinary divisions in academia; the value of Bogdanov’s transdisciplinarity; Rovelli’s theory of quantum gravity; the notions of granularity, indeterminism and relationality underpinning quantum mechanics; the role of the observer; mistaken uses of quantum mechanics; relational and network views of the world; how the discipline of Physics is becoming more systemic; the concept of levels of analysis in relation to nature and human inquiry; and the future for humanity.

In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to define the approach. This core is the quantum character of its geometrical observables: space and spacetime are built up out of Planck-scale quantum grains. The interrelations between these grains are described by spin networks, graphs whose edges capture the bounding areas of the interconnected nodes, which encode the extent of each grain. We explain how quantum Riemannian geometry emerges from two different approaches: in the first half of the chapter we take the perspective of continuum geometry and explain how quantum geometry emerges from a few principles, such as the general rules of canonical quantization of field theories, a classical formulation of general relativity in which it appears embedded in the phase space of Yang-Mills theory, and general covariance. In the second half of the chapter we show that quantum geometry also emerges from the direct quantization of the finite number of degrees of freedom of the gravitational field encoded in discrete geometries. These two approaches are complimentary and are offered to assist readers with different backgrounds enter the compelling arena of quantum Riemannian geometry.

We introduce a strategy to compute EPRL spin foam amplitudes with many internal faces numerically. We work with texttt{sl2cfoam-next}, the state-of-the-art framework to numerically evaluate spin foam transition amplitudes. We find that uniform sampling Monte Carlo is exceptionally effective in approximating the sum over internal quantum numbers of a spin foam amplitude, considerably reducing the computational resources necessary. We apply it to compute large volume divergences of the theory and find surprising numerical evidence that the EPRL vertex renormalization amplitude is instead finite.