A new theoretical framework proposes that gravity may arise from entropy, offering a fresh perspective on the deep connections between geometry, quantum mechanics and statistical physics. Developed by Ginestra Bianconi, a mathematical physicist at Queen Mary University of London, UK, and published in Physical Review D, this modified version of gravity provides new quantum information theory insights on the well-established link between statistical mechanics and gravity that is rooted in the thermodynamic properties of black holes.
Quantum relative entropy
At the heart of Bianconi’s theory is the concept of quantum relative entropy (QRE). This is a fundamental concept of information theory, and it quantifies the difference in information encoded in two quantum states. More specifically, QRE is a measure of how much information of one quantum state is carried by another quantum state.
Bianconi’s idea is that the metrics associated with spacetime are quantum operators that encode the quantum state of its geometry. Building on this geometrical insight, she proposes that the action for gravity is the QRE between two different metrics: one defined by the geometry of spacetime and another by the matter fields present within it. In this sense, the theory takes inspiration from John Wheeler’s famous description of gravity: “Matter tells space how to curve, and space tells matter how to move.” However, it also goes further, as it aims to make this relationship explicit in the mathematical formulation of gravity, framing it in a statistical mechanics and information theory action.
Additionally, the theory adapts QRE to the Dirac-Kähler formalism extended to bosons, allowing for a more nuanced understanding of spacetime. The Dirac-Kähler formalism is a geometric reformulation of fermions using differential forms, unifying spinor and tensor descriptions in a coordinate-free way. In simpler terms, it offers an elegant way to describe particles like electrons using the language of geometry and calculus on manifolds.
The role of the G-field
For small energies and low values of spacetime curvature (the “low coupling” regime), the equations Bianconi presents reduce to the standard equations of Einstein’s general theory of relativity. Beyond this regime, the full modified Einstein equations can be written in terms of a new field, the G-field, that gives rise to a non-zero cosmological constant. Often associated with the accelerated expansion of the universe, the cosmological constant contributes to the still-mysterious substance known as dark energy, which is estimated to make up 68% of the mass-energy in the universe. A key feature of Bianconi’s entropy-based theory is that the cosmological constant is actually not constant, but dependent on the G-field. Hence, a key feature of the G-field is that it might provide new insight into what the cosmological constant really is, and where it comes from.
The G-field also has implications for black hole physics. In a follow-up work, Bianconi shows that a common solution in general relativity known as the Schwarzschild metric is an approximation, with the full solution requiring consideration of the G-field’s effects.
What does this mean for quantum gravity and cosmology?
The existence of a connection between black holes and entropy also raises the possibility that Bianconi’s framework could shed new light on the black hole information paradox. Since black holes are supposed to evaporate due to Hawking radiation, the paradox addresses the question of whether information that falls into a black hole is truly lost after evaporation. Namely, does a black hole destroy information forever, or is it somehow preserved?
The general theory predicts that the QRE for the Schwarzschild black hole follows the area law, a key feature of black hole thermodynamics, suggesting that further exploration of this framework might lead to new answers about the fundamental nature of black holes.
Unlike other approaches to quantum gravity that are primarily phenomenological, Bianconi’s framework seeks to understand gravity from first principles by linking it directly to quantum information and statistical mechanics. When asked how she became interested in this line of research, she emphasizes the continuity between her previous work on the topology and geometry of higher-order networks, her work on the topological Dirac operator and her current pursuits.
“I was especially struck by a passage in Gian Francesco Giudice’s recent book Before the Big Bang, where a small girl asks, ‘If your book speaks about the universe, does it also speak about me?’” Bianconi says. “This encapsulates the idea that new bridges between different scientific domains could be key to advancing our understanding.”
Future directions
There is still much to explore in this approach. In particular, Bianconi hopes to extend this theory into second quantization, where fields are thought of as operators just as physical quantities (position, momentum, so on) are in first quantization. Additionally, the modified Einstein equations derived in this theory have yet to be fully solved, and understanding the full implications of the theory for classical gravity is an ongoing challenge.
Though the research is still in its early stages, Bianconi emphasizes that it could eventually lead to testable hypotheses. The relationship between the theory’s predicted cosmological constant and experimental measurements, for example, could offer a way to test it against existing data.
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