Carlo Rovelli
6 min
Carlo Rovelli examines the foundational status of Quantum Field Theory (QFT), positioning it not merely as a collection of specific force laws, but as a general 'mechanics'—a universal scheme for describing physical systems. Drawing on a Newtonian distinction between specific laws of nature and the general theory of motion, Rovelli argues that QFT has proven remarkably resilient and effective, surviving various theoretical challenges to become the bedrock of the Standard Model.
Despite its success, QFT relies on a fixed, background space-time structure. This creates a significant conceptual friction when contrasted with general relativity, which treats space-time itself as a dynamic, physical entity. The paper explores the extent to which the notion of 'localization'—the ability to define physical states within specific regions of space-time—is compatible with our deeper understanding of gravity and geometry. The core issue is whether the mathematical formalism of QFT, which assumes a static stage, can be fully reconciled with a universe where the stage itself is a participant in the physical process.
Understanding these foundational limits is essential for researchers attempting to construct a theory of quantum gravity. If QFT is to be extended or integrated into a 'theory of everything,' the inherent assumptions about space-time localization must be scrutinized. Rovelli’s analysis highlights that while QFT is an extraordinarily powerful tool, its reliance on a non-dynamical background may be a fundamental limitation that requires a shift in how we conceptualize the relationship between quantum fields and the geometry of the universe.
How seriously should we take QFT? One of Newton's most far-reaching intuitions was to break the ‘mathematical theory of the world’ into two components. One component is given by the various specific force laws, or, in later formulations, specific Lagrangians. The other and more fundamental component is the general theory of motion, which we may denote as ‘Mechanics’. Quantum field theory (QFT) is an example of the second. It is a general scheme for treating physical theories, which is not committed to specific systems or to specific Lagrangians. As a general scheme for treating physical theories, QFT is extraordinarily successful and remarkably flexible. Its impressive effectiveness has been emphasized in this conference by Jackiw, Shankar, and others. QFT had its periods of ill-fortune, for instance in the sixties, at the time of S-matrix theory, recalled in this conference by Kaiser and by Shankar. But then it had its glorious comebacks ‘to a glory even greater than before’. Today, our understanding of the world at the fundamental level is based on the Standard Model, which is formulated within the framework of QFT, and on classical general relativity. General relativity cannot be seen as a ‘fundamental’ theory since it neglects the quantum behavior of the gravitational field, but many of the directions that are explored with the aim of finding a quantum theory of the gravitational field and/or extending the Standard Model - perhaps to a theory of everything - are grounded in QFT.
Alex: Because most attempts to quantize gravity try to adapt QFT techniques, and immediately run into the background independence problem. Without a fixed background, you lose the foundation that lets you define particles and fields in the standard way.
Sam: Right. And that's not a technical gap waiting to be filled — it's a conceptual mismatch at the level of ontology. Most quantization programs assume you can separate the geometry from the dynamics, at least perturbatively. Rovelli's point is that this separation is exactly what breaks down in the regime you care about.
Alex: So what does the alternative actually look like? If coordinate-based fields are off the table, how do you describe the physics?
Sam: The paper points toward a shift in the fundamental object of the theory. Instead of fields existing at points, you work with a relational network of quantum events — physical reality described not as values assigned to a grid, but as correlations between observable outcomes. The geometry isn't the stage; it's emergent from the relational structure.
Alex: Are there parts of QFT that survive that transition, or does the whole framework need to be rebuilt?
Sam: The S-matrix formulation is a notable survivor. Because it focuses on asymptotic states — what comes in and what goes out, far from the interaction region — it doesn't require the same rigid local coordinate structure as the full field-theoretic approach. You're abstracting away the local "where" to focus on the "what" of the interaction, and that makes it less dependent on the local geometry.
Alex: Though it's still a piece of the puzzle, not the solution.
Sam: Correct. The fundamental challenge remains: how to formulate a theory that is fully background-independent while recovering QFT's successful predictions in the appropriate limit. The S-matrix gives you a handle, but it doesn't close the gap.
Alex: I want to push on the scope of the claim here. Is this a philosophical exercise, or does it point to a concrete path forward?
Sam: It's a conceptual critique that identifies the boundary of current knowledge — and the author is explicit about that limitation. This is not a constructive proof. It diagnoses the incompatibility clearly, but it doesn't deliver the complete, non-perturbative theory of quantum gravity we're looking for. Think of it as a precise statement of what the next theory must satisfy, rather than the next theory itself.
Alex: A diagnostic rather than a prescription.
Sam: Exactly. And that's not a minor contribution. Knowing precisely why your current tools are failing is often the precondition for building better ones. The deeper implication is that our reliance on spacetime points may be a historical relic — a feature of how we first mathematized field theory, not a feature of nature. If that's right, then space and time aren't the container in which physics happens; they're emergent properties of a deeper, relational quantum structure.
Alex: We've spent decades refining the mathematics of fields on a manifold, and the argument here is that the manifold itself may be what's blocking the view.
Sam: That's the essence of it. The transition from fields on a stage to a theory of relational events is arguably the deepest conceptual hurdle in modern fundamental physics. Whether that transition is achievable — and what it would even mean to complete it — is the question that defines the next generation of work in quantum gravity. Thanks for listening to ResearchPod.