Macroscopic aspects of Spin-Networks

A short discussion about the work on Quantum Gravity that I did for D.Phil. thesis, regarding some ideas about the macroscopic phenomenology of spin-networks, within the context of Loop Quantum Gravity.

Quantum gravity is considered, by many, as the holy grail of theoretical physics. For several years people have investigated different approaches, each with their own limitations and advantages. Unfortunately, the quest for a coherent quantum theory of gravity, with a semiclassical regime in agreement with General Relativity, is still ongoing. Among all approaches, String Theory and Loop Quantum Gravity (LQG) are certainly the most advanced ones. While I believe that LQG provides a useful framework to think about the quantum aspects of spacetime, I remain skeptical about String Theory and how its use can inform the quest for quantum graviy.

My approach is based on the use of Information Theory, which was originally developed as a theory of communication. Since its inception, an increasing number of physicists has used its tools and concepts to study the behaviour of physical systems. The interaction between physics and information theory has been especially enlightening in the context of quantum mechanics. Indeed, the inherently statistical nature of quantum theory makes Information Theory particularly suitable to investigate the behaviour of quantum systems. The large body of results developed in the last 50 years gave rise to Quantum Information Theory (QI): a well developed research field which, at its core, tries to describe how quantum systems share or store information and “what they do with it” (Lloyd 1988). For this reason, I believe QI provides a good set of ideas and techniques to study the behavior of quantum systems, beyond the standard tools of analysis inherited from classical mechanics. Nowadays, ideas from QI, such as the entanglement entropy, are part of the standard tools of analysis in various fields: from condensed matter systems to the more fundamental topics such as understanding the emergence of thermal equilibrium in quantum mechanics.

In more recent years, techniques and tools from QI have played an increasingly central role also in quantum gravity. Such interplay has proved particularly insightful both in the context of the holographic duality in AdS/CFT, as well as for the current background independent approaches to quantum gravity, including Loop Quantum Gravity (LQG), the related spin-foam formulation and group field theory. Interestingly, many background-independent approaches today share a microscopic description of space-time geometry given in terms of discrete, pre-geometric degrees of freedom of combinatorial and algebraic nature, based on spin-network Hilbert spaces. In this context, the behaviour of quantum correlations provides a new tool to characterise the quantum texture of space-time in terms of the structure of microscopic correlations of the spin networks states. For example, several recent works have considered the possibility to use specific features of the short-range entanglement (area law, thermal behaviour) to select states which may eventually lead to smooth spacetime geometry classically. These analyses usually focus on states with few degrees of freedom, leaving open the question of whether a statistical characterisation may reveal new structural properties. 

During my Ph.D., I tackled the problem from a slightly different perspective. I was interested in understanding how some quantum degrees of freedom give rise to the smooth structure that we perceive as spacetime. To pursue this ambitious goal, I used the information-theoretical notion of quantum typicality as a tool to investigate and characterise universal local features of quantum geometry, going beyond the physics of states with few degrees of freedom. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon, at the macroscopic scale. Thus, I focused on studying the emergence of typical behavior in the local aspects of spin-networks, together with their thermodynamic behaviour and interplay with the semiclassical limit. The ultimate goal of this line of research is to give a quantum description of a black hole which is consistent with the expected semiclassical behaviour. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why a horizon exhibits thermal properties.