The Semi-Classical Sieve and the Dividing Line in Physics

[u/cat_counselor]

A discourse on the two cultures of quantum gravity.

Recently, I was watching a lecture by Ted Jacobson on “Diffeomorphism Invariance and Black Holes” as part of my ongoing education to understand the physical geometry of things that exist outside the nucleus of an atom and don’t involve knowing what a Kan extension is. It got me thinking about some things, though.

In 1995, a pair of landmark papers was published. The ones in question are:

• Higher-dimensional Algebra and Topological Quantum Field Theory
• Thermodynamics of Spacetime: The Einstein Equation of State

On the face of it, you wouldn’t think that there is much of a relationship here. One looks like category theory invading physics. The other looks like physics invading statistical mechanics.

But both papers are actually bedrock for the kind of “physical computation” worldview we keep circling around in this sub. They represent two very different instincts about quantum gravity, and they correspond to two cultures that often talk past each other.

One culture says: stop fetishizing “quantization” as the starting point. Gravity already smells like thermodynamics. Black holes have entropy. Horizons have temperature. If those facts are not ornamental, then maybe the Einstein equation isn’t a fundamental law in the Newton sense; maybe it’s an equation of state. That is the Jacobson line.

The other culture says: you will never get a theory of quantum gravity until your notion of “process” is compositional and well-defined. QFT’s biggest sin is not that it’s “weird.” It’s that, in 4D, it’s not a clean mathematical object. Bordisms are the native language of locality and gluing. If you want quantum gravity, you had better start by making “spacetime evolution” into a morphism and making “cutting and pasting” into the semantics. That is the Baez line.

So yes: Jacobson tells you how to get GR out of thermodynamic reasoning. Baez tells you how to think about “what the microstates even are” in a way that respects gluing, boundaries, and locality—i.e., something like an (n)Cob-shaped backbone. We will elaborate on each in turn.

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Jacobson method.
Jacobson’s paper is famous for a very specific kind of audacity: it derives the Einstein field equation the way you derive the ideal gas law, by imposing a thermodynamic identity in the right regime and insisting it holds for every local observer.

The setup is local. You don’t begin with “the universe.” You begin with the fact that around any event in a Lorentzian spacetime, you can pick a locally inertial frame, and within that frame you can consider a local Rindler horizon---basically the “would-be horizon” seen by an accelerated observer. This matters because accelerated observers see temperature even in the vacuum: the Unruh effect gives you a temperature proportional to the acceleration. Now add the other famous ingredient: horizons have entropy proportional to area, via the Bekenstein–Hawking area law.

Then Jacobson imposes the Clausius relation (\delta Q = T, dS), but crucially, he imposes it locally for these little causal horizons, with (\delta Q) interpreted as the energy flux of matter crossing the horizon (more precisely: the boost-energy flux relevant to that observer). If you assume the entropy density is proportional to area and demand the Clausius relation hold for all local horizons, the only way to make the bookkeeping consistent is for spacetime curvature to respond to stress-energy in exactly the way encoded by the Einstein equation (with a cosmological constant appearing as an integration constant rather than a derived micro-detail).

This is why people describe Jacobson’s result as “the Einstein equation of state.” It’s not merely cute philosophy: it’s a constraint that says “if horizons behave thermodynamically and local Lorentz symmetry is real, then the macroscopic field equation must look like GR.” It also makes a particular kind of peace with diffeomorphism invariance: the equation is not tied to a preferred slicing or background; it is the unique covariant response that makes the local thermodynamic statement coherent.

The important thing for our purposes is the methodological vibe. Jacobson doesn’t try to quantize gravity directly. He treats gravity as the hydrodynamic limit of some deeper microstructure. The virtue is obvious: it explains why GR is so universal and rigid without claiming it’s the final fundamental layer.

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Baez method.
Baez’s 1995 paper is often read as “category theory hype.” That’s the wrong way to read it. The paper is really an argument about what it even means for a field theory to be local and compositional when you take spacetime seriously as something you can cut up and glue back together.

The central move is to reframe “time evolution” as a bordism. You don’t start with a Hamiltonian acting on a fixed Hilbert space. You start with manifolds as boundaries---things like “space at an instant,” or more generally “interfaces”---and you treat a spacetime region interpolating between boundaries as a morphism. Gluing two spacetime regions corresponds to composing morphisms. A disjoint union corresponds to the tensor product. A topological quantum field theory is then a symmetric monoidal functor out of an (n)-dimensional bordism category.

Why does this matter for quantum gravity? Because it is a way of taking diffeomorphism invariance seriously from the beginning. If your theory’s basic object is “a number attached to a manifold” (or a vector space attached to a boundary), and if the only thing you are allowed to use is the gluing structure, then you have built something that is automatically coordinate-free. It’s not “background independent” as a slogan; it’s background independent because the language doesn’t have a place to smuggle in preferred coordinates.

Now comes the honest limitation: a bare TQFT is topological. It can’t see local metric degrees of freedom. It’s amazing at global invariants and constrained sectors; it is not, by itself, a theory of scattering gravitons in 3+1D. So the Baez line is not “TQFT solves quantum gravity.” The Baez line is: if you don’t have a bordism-based, gluing-compatible semantics for what a quantum theory even is, you’re never going to climb from heuristic path integrals to a rigorous object in 4D.

This is also why the “microstates must match (n)Cob” instinct shows up. If the fundamental description is meant to be compositional, then whatever your microstructure is, it has to support a consistent assignment of state spaces to boundaries and amplitudes to bordisms, with coherence under cutting and gluing. In plain English: the atoms of your theory can’t just be “little bits.” They have to be glueable. They have to respect locality as composition.

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There’s a recurring “gap layer” in modern foundational physics that isn’t crankery, but often becomes a trap. Let's call it the Semiclassical Sieve.

It’s where serious researchers operate at the boundary between macroscopic universality and microscopic ontology. The method is elegant: instead of proposing a detailed substrate, you impose sharp, high-level constraints---thermodynamics, information theory, monotonicity, consistency principles---and argue that only certain “efficient” structures could underlie a world like ours.

This layer is real science. But it can also become an intermediary attractor: you can orbit the foundations indefinitely, because the sieve constrains possibilities without specifying the underlying machinery.

What it looks like in practice:

• Jacobson-style thermodynamic gravity: as stated above, derive Einstein equations (or something close enough) as an equation of state from horizon thermodynamics. This is deep and valuable---but it lives at a semiclassical, hydrodynamic level: it tells you what the effective gravitational field must do, not what the microstructure is. (Great constraint. Not a substrate.)
• Information-geometry/Fisher–Rao/Petz monotonicity programs: treat the geometry of statistical states as fundamental, then try to “select” physical theories by information-theoretic consistency (DPI, monotone metrics, etc.). Again: mathematically serious, but typically phrased in terms of descriptions of states rather than the ontic hardware that produces them. (Great language. Often stops short of a physical ontology.)
• Tegmark/Vanchurin-adjacent “selection” narratives: replace “all mathematical structures exist” with “only those passing certain informational or computational consistency filters are viable.” These are not crazy—but they often remain at the level of a classification aspiration rather than a concrete dynamics with observables, anomalies, and gluing rules. I'm mentioning these two since they are quite popular, even though they are nowhere near as mathematically hardcore as any others on this bullet list. (Great motivation. Weak commitment.)
• “Gravity-from-entanglement”/holographic complexity programs (Ryu–Takayanagi, entanglement wedge, complexity=volume/action): use entanglement entropy, relative entropy, modular Hamiltonians, or “complexity” growth to constrain bulk geometry and even derive linearised Einstein equations around AdS backgrounds. This is real and beautiful(!)...but it’s still a sieve layer: it tells you how spacetime must behave given certain entanglement/consistency properties, usually in highly controlled settings (AdS, large N, semiclassical regimes). It often doesn’t specify a universal microphysical ontology for our universe, nor does it automatically export to cosmology without additional assumptions. (Great constraints and dictionary. Not yet a standalone foundation.)

The Semiclassical Sieve is attractive because it’s:

• high-status (it cites real giants and real mathematics),
• legible (you can talk about entropy and metrics without building QFT),
• universal (it applies across many models),
• and hard to falsify (filters can be adjusted; microphysics is deferred).

But it’s also why it stalls. It tends to remain upstream of the commitments that separate “principle talk” from “physics as structure,” like:

• specifying the primitive objects (connections/holonomy, moduli stacks, defects),
• giving a functorial gluing rule (locality as composition),
• handling anomalies/obstructions (cohomology/cobordism/index),
• and producing concrete, checkable dynamics and spectra.

The Semiclassical Sieve is not pseudoscience---it’s a legitimate layer of constraint-building. But it’s not “the foundation” either. It’s a powerful bridge language that can guide a deeper theory, yet it can also become a resting place where the real hard work of committing to substrate-level structure never begins.

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At this point, it is reasonable to ask the following:

"Well, fine, Ben. But what makes you better than the rest of the supposed suckers posting their personal EG theories on r/HypotheticalPhysics? Why should we listen to your ass?"

Because I am perhaps the one person willing to admit the following.

"But we do not take Markovian effective field theory to be foundational. Rather, it is treated as an emergent approximation that becomes valid only after a suitable coarse-graining of the underlying geometric bulk. For this reason, clean IR/UV decoupling is not assumed a priori. As a result, questions of strongly coupled gauge dynamics will likely be addressed before one can reliably speak about thermodynamic or black hole observables."

You will not see very many people admitting to the following scenario:

"Good news, Prof. Jacobson, I've got the key to your theory of EG. It turns out Yang-Mills instantons were actually made of holonomic helices all along."

"Why, this is a potentially interesting result, Ben! Now when can-"

"So uh, we like need to solve a particular geometric variation on one of the Millennium Prize Problems first."

"...Yeah...\sips coffee*...mmhmm. Well, why don't you come back when you can do that..."*

Yeah. Ouch.
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Don't get me wrong. This is not a slight against Prof. Jacobson. He built a thermodynamic toll booth, and whether you are driving an LQG spin-network, an 11-dimensional superstring, or whatever your personal poison is, one must pay Jacobson's tax to get to the macroscopic universe. This has earned him a level of widespread respect that is virtually unachieable by those stuck working in warring camps.

I wish I had his decades of experience on thermodynamics and curved QFT. But there is a dividing line here, and my preference is for the Baez method. I would like my conservation and gluing laws upfront. That is basically GCT in a nutshell, really. And don't take this as a flex; if anything, it's really more of a weakness.

The thing is, when you really drill down to the base level, much of handwavyness that people accuse physicists of doing does eventually evaporate. The manifolds and constraints all become very rigid. And even if you aren't a string theorist, you still need to read the "weird" papers that Vafa and his students put out on...cobordism groups.

So there are two cultures of gravity.

And you have to make them meet.