Is Quantum Space-Time a Scale-Free Network Like Facebook?
Researchers from Queen Mary University of London and Karlsruhe Institute of Technology have developed a model that applies ideas from the theory of complex networks, such as the brain or the Internet, to the fundamental quantum geometry of space-time.
The research is published in Scientific Reports with the title “Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free.” The research paper is freely available online.
“We hope that by applying our understanding of complex networks to one of the fundamental questions in physics we might be able to help explain how discrete quantum spaces emerge,” said author Ginestra Bianconi.
What we can see is that space-time at the quantum-scale might be networked in a very similar way to things we are starting to understand very well like biological networks in cells, our brains and online social networks.
The Mathematics of Online Social Networks Could Shed Light on Quantum Gravity
Current understanding of fundamental physics is based on general relativity, essentially developed by Einstein alone, and quantum mechanics, developed by a handful of physicists including Einstein in the first 30 years of the 20th century.
General relativity describes gravity and the warped geometry of space-time, with deviations from pre-Einstein physics that are especially evident in large-scale cosmology and strong gravitational fields.
Quantum mechanics describes the behavior of matter and fields, with important and “mysterious” deviations from classical (pre-quantum) physics at subatomic scales.
Both theories, which of course have been further explored and clarified since their formulation, have been thoroughly validated experimentally.
The problem is that it has been difficult to put general relativity and quantum mechanics together. We don’t have yet a theory of quantum gravity able to describe the quantum behavior of the gravitational field in warped geometries. Space-time at quantum scales might not have a geometry, but only a “pregeometry” substrate.
“In the apparently unrelated field of quantum gravity, pregeometric models, where space is an emergent property of a network or of a simplicial complex, have attracted large interest over the years,” wrote the researchers in a previous paper.
Whereas in the case of quantum gravity the aim is to obtain a continuous spacetime structure at large scales, the underlying simplicial structure from which geometry should emerge bears similarities to networks.
The researchers developed a pregeometry model describing the evolution of quantum network states, dubbed Complex Quantum Network Manifolds (CQNMs), and applied techniques developed for the study of networks, such as computer networks, biological networks, and social networks, an interdisciplinary field that combines ideas from mathematics, physics, biology, computer science, the social sciences, and many other areas.
The researchers demonstrated that CQNMs of dimension higher than two are scale-free networks characterized by large fluctuations of the degree (connectivity) of the nodes. Scale-free networks, which are known to be robust to random perturbations, have “hubs” with a number of connections much bigger than the average degree, like a particularly popular Facebook user. In fact, Facebook is thought to be a scale-free network.
The researchers’ work shows that CQNMs exhibit many statistical features of quantum mechanics, indicating that the model could be useful to physicists working on quantum gravity.
Images from Ginestra Bianconi, Christoph Rahmede, and Wikimedia Commons.