✨ The Universe Written on the Night Sky: What Celestial Holography Tells Us About Reality's Hidden Architecture

Please take a look at the corresponding Substack episode.

There's something profoundly disorienting about learning that the universe might be fundamentally two-dimensional. Not in the sense that we're living in Flatland, but in the way information itself might be organized—like a cosmic hard drive where everything that happens in our three-dimensional space (plus time) is somehow encoded on a distant boundary, written across the night sky itself.

This isn't science fiction. It's celestial holography, and it represents one of the most ambitious attempts in modern physics to reconcile what we see—particles colliding, black holes merging, gravity bending light—with the deeper mathematical structures that seem to govern reality.

The story begins, as so many revolutionary ideas do, with something nobody expected: infinite symmetries lurking in Einstein's equations.

Celestial Holography Initiative

Celestial Amplitudes Program Review talk

Celestial Holography

44 results for author: Pasterski, S

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We hope you continue exploring our other podcasts, responding to the content, and checking out our related articles on the Heliox Podcast on Substack. 

Transcript

0:25

This is Heliox, where evidence meets empathy. Independent, moderated, timely, deep, gentle, clinical, global, and community conversations about things that matter. Breathe easy. We go deep and lightly surface the big ideas. Welcome back to the Deep Dive. Today we are strapping in for... Well, for one of the most ambitious conceptual shifts in modern theoretical physics… It's a big one.…we've been looking at sources program review talks, institutional overviews, and a bunch of technical papers, all detailing what is known as celestial holography. Right. Get ready for a massive shift in perspective, because we are diving into the effort to encode our entire universe, specifically its gravitational dynamics, as a hologram written on the night sky. That's it, exactly. Our mission here is to rapidly, but, you know, thoroughly unpack an incredibly dense research process. program. It really is. Celestial holography tries to establish this powerful duality, mapping four-dimensional physics, specifically gravitational scattering in flat space-time. Right, I'm space-time. Onto a 2D conformal field theory, a CFT that lives on that spherical boundary we call the celestial sphere. And we need to extract the surprisingly exotic dictionary that connects our 4D reality to these 2D field theory correlators. Yeah, and exotic is the right word. So the core definition here, this is what separates this from, say, the giants of string theory, right? We are applying the holographic principle, but we are applying it to space times where the cosmological constant vanishes. Exactly. The famous ad SCFT correspondence needs anti-de-sitter space, a negatively curved space time, kind of like a saddle. Which gives you a nice, tidy, finite boundary to work with. It does. But our universe, at least over large scales, looks flat. Asymptotically flat. The things we measure, like black hole collisions, they happen in flat space. So celestial holography needs a method to translate the standard 4D scattering matrix cell which tells us the probability of particles changing state after a collision and translate that into correlators on that 2D sphere at infinity. And that's the challenge. It is huge because flat space time doesn't naturally have a tidy boundary to project things onto, not like anti-decedor space time. does. Okay, so let's unpack this immediately. Why even attempt this? It sounds incredibly difficult. What was the original conceptual hook that suggested we could shove all of 4D physics onto a 2D sphere? It all started with finding an excess of symmetries. Symmetries that nobody expected. Ah, okay. It did. The entire program is rooted in exploring what are called asymptotic symmetries. And this work goes way back, back to the 1960s. With Bondi, Vandenberg, Metzner, and Sachs. Right, the BMS group. They were analyzing solutions to Einstein's equations, but specifically near null infinity, the boundary where light and gravity waves travel out to the edge of spacetime. And they expected to find the standard symmetries of flat space time, which is the Poincaré group. That's the one. Translations in space and time, rotations, boosts, standard quantum field theory stuff. And that's not what they found. Not at all. What they found was utterly unexpected. The class of allowed solutions had a residual symmetry group, the BMS group, which are these large coordinate changes that still preserve the physics at infinity. And the truly surprising fact is that this BMS group is infinitely larger than the Poincaré group. It includes everything we expect, plus an infinity of new symmetries. Infinite symmetries. Doesn't that usually make a physicist, you know, a little bit terrified? It did. For decades, many physicists treated it as a mathematical curiosity, maybe an artifact of defining the boundary too loosely. A bug, not a feature. Exactly. It took a long time for people to realize this infinite symmetry was a deep physical feature of gravity, and that infinite size... That's the hint of holography. It suggests that 2D surface is encoding way more information than you'd think. Okay, let's break down the two key types of infinite symmetry they found, because I think they hint directly at this 2D conformal field theory we're aiming for. Absolutely. Two main enhancements. First, Super translations. Super translations. These are large dipheomorphisms that let you shift the retarded time coordinate independently at every single point on the night sky. So wait, normally if you shift time, you shift it everywhere at once. This lets you sort of warp the time surface locally across the sky. That's a perfect way to put it. It reflects the fact that radiation arrives at different times depending on its angle. Okay. What's the second one? The second one, and this is where the CFT hint becomes undeniable, are super rotations. Super rotations. These are the symmetries that take global rotations and turn them into local conformal transformations of the celestial sphere. Whoa. So you can locally rescale a patch of the night sky or change its shape, but you have to preserve the angles. Which is the definition of a conformal transformation. That is the language of 2D CFTs. You just wouldn't have those infinite local conformal symmetries unless the dynamics were governed by a conformal field theory. You wouldn't. But the crucial bridge, the thing that turned this from a math finding into a research program, was the realization... cemented by people like Strominger. Right. That the mathematical constraints from these symmetries called word identities are mathematically equivalent to the various Sock theorems in the S matrix. Sock theorems. The physics are extremely low energy particles, right? Yeah. Like zero energy photons or gravitons. Yes. Soft theorems describe their universal behavior. And this showed the infinite symmetry wasn't abstract. It was physically realized in the infrared. Suddenly it wasn't a curiosity anymore. It was a powerful physical constraint on gravity. So if the symmetries line up, the infinite asymptotic symmetry is in 4D matching the conformal symmetries of a 2D surface. How do you do the translation? How do you take an S-matrix element calculated with momentum and turn it into a CFT correlator? This is the core technical step, and it requires a complete change of basis for the scattering states. But we stop using momentum eigenstates. We have to. The standard S-matrix uses them, but to see the conformal symmetry, we have to transform those states into a basis where the particles are in boost eigenstates. states. That's a huge shift. Instead of defining a particle by its momentum, you define it by how it transforms under a Lorentz boost. Why? Well, think of it this way. Momentum measures the literal energy, E. But to see the conformal structure, we need to focus on how the particle scales when you change your reference frame. Boost eigenstates are eigenstates of the boost generator, and that's deeply connected to the dilation operator in a CFT. The thing that tells you how an object scales? That's the one. Okay, so how do you perform this mathematical surgery? It's done with a crucial operation called the Mellon Transform. You integrate the S-matrix element over the energies of all the particles with a specific weighting factor. It's like you're stripping away the specific energy momentum coordinates and just keeping the fundamental geometric structure. And the trade-off is where the magic happens. It is. The Mellon Transform trades the particle's energy, E, for its conformal dimension, delta. And that's what a CFT cares about. So the output is something new. The output is the celestial amplitude. And it's guaranteed to transform correctly as a correlator of quasi-primaries under Lorentz transformations, which become 2D Mubius transformations on the sphere. The output is the celestial amplitude. This confirms the mathematical viability of a whole 4D to 2D idea. Okay, here's where it gets really interesting for me, because this duality, it doesn't just spit out some nice, tidy CFT from a textbook. The sources describe this dual theory as... highly unusual, exotic, even painful to work with. That's putting it mildly. It's exotic because the mapping just completely reorganizes how physics is constrained. The key difference is that the resulting correlators are often singular. Singular. You're taking an object, the S matrix, that has a rigid global momentum conservation law built into it. it. When you melon transform that, the constraint doesn't just vanish. So because the total incoming momentum has to equal the total outgoing momentum in 4D, what happens to that rule on the 2D sphere? It translates into delta functions in the celestial basis. So the correlation functions aren't smooth. They're singular. They're distributional, especially for amplitudes with fewer than five particles. That sounds like a nightmare for doing consistency checks. It's a major, major challenge. But let's look at how the infrared physics gets encoded, because that part is incredibly clean. The soft theorems, right. The zero energy particle behavior. Yes, and this is one of the program's greatest successes. The low-frequency physics is cleanly separated. The low-energy part of the Mellon integral resolves the various soft factorization theorems into these beautiful distinct poles in the complex conformal dimension plan. What about high energy structures? How does it reorganize high energy scattering? Good question. That also gets reorganized elegantly. When particles travel almost parallel to each other, what we call the collinear limits, that relationship is interpreted in the 2D framework as an operator product expansion. an OPE. Meaning you can take two operators that are close on the sphere and expand their product as a series of other simpler operators. Exactly. And this is a massive simplification because symmetry becomes the key to solving the dynamics, the infinite symmetries we talked about. translation invariants, soft theorems other new global symmetries they provide these powerful recursion relations so you can actually solve for the OPE coefficients the symmetry dictates the physics it does, it could potentially make the high energy limit solvable in this new basis that's the real power of it

Okay, but then there's the most conceptually jarring feature mentioned in the sources: 10:43

UV-IR mixing. Wait, are you telling me that this framework, which is designed to separate physics by energy scale, ends up mixing the high-energy UV and low-energy IR domains? It feels like cheating, doesn't it? It does. It feels like you're breaking the rules of quantum field theory. It's entirely counterintuitive, but it's a necessary consequence of the definition itself. To get the celestial amplitude, the Mellon transform has to integrate the S-matrix over all energy scales, from zero to infinity. So the final object is inherently sensitive to both low and high energy behavior at the same time. The information is compressed together. It is. And studies of simple 2-to-2 scattering show this amazing result. The analytic structure in the complex plane holds a distinct... An imprint of the UV completion of the theory. An imprint of the UV completion. Yes. If the underlying theory of quantum gravity that takes over at high energies involves, say, logarithmic runnings or some other specific high energy behavior, those show up directly as higher order poles in the analytic structure of the celestial amplitude. So the geometry of the correlators in the night sky, it carries a memory of what the final fundamental theory of gravity has to be, even though that theory only dominates at insane energies. It connects everything. The celestial sphere acts as this window where the infinite past, the infinite future, and all energy scales are visible at once, just through the analytic structure of these amplitudes. Yes. So what does this all mean then? We have a revolutionary framework that makes these infinite symmetries of gravity visible. It manifests them as this complex, powerful 2D hologram. But the CFT itself is really weird. What are the next big steps? Well, the framework is already powerful because it uses gravity's own symmetries to constrain scattering. The ongoing research is aimed at two fronts. First, expanding the dictionary to include more complex particles and interactions. And second. Second, and this is maybe the harder part, finding an intrinsic construction of the celestial CFT itself. So instead of deriving the 2D theory by transforming the 4D one, You just write down the rules for the 2D CFT from scratch and it would automatically spit out 4D gravity. That's the dream. We know what the output should look like, but we don't have the rule book yet. And to move forward, we have to tackle the really hard questions around consistency. Like unitarity and crossing symmetry. Exactly. Imposing constraints like unitarity, making sure probabilities add up to one and crossing symmetry on these strange, non-smooth distributional correlators is a massive technical. challenge. And you mentioned this is all connected to IR divergences, one of the biggest headaches in QFT. It is. The soft theorems are tied directly to IR divergences. This leads to the idea of dressings for operators, basically modifying the scattering states to account for all the mandatory soft radiation. I see. And researchers have found that the soft charges that resolve these divergences are in the same mathematical multiplet as the asymptotic partner modes. It shows this profound connection between IR divergences and the geometric structure of this new conformal basis. It suggests this holographic framework might just be the natural way to handle this. them. This has been a true deep dive. We started with the infinite symmetry group of gravity, mapped it onto this complex 2D hologram on the celestial sphere, and revealed these deep connections between low energy physics, symmetries, and the ultimate high energy completion. It's a remarkable synthesis. The goal is to use gravity's inherent symmetries to unify our understanding of space-time with quantum theory. It's using gravity's own constraints to define the quantum theory it must obey, hopefully leading us to a better picture of quantum gravity. And that leads us to our final provocative thought for you to chew on. Since the UV behavior of a gravitational theory leaves a distinct imprint on the analytic structure of these celestial amplitudes, this implies that the very structure of correlators on the night sky is sensitive to physics at all energy scales. So, if this framework is correct, does the structure of gravity already carry an inherent measurable memory of its eventual ultraviolet completion? Thanks for listening today.

Four recurring narratives underlie every episode: 14:50

boundary dissolution, adaptive complexity, embodied knowledge, and quantum-like uncertainty. These aren't just philosophical musings, but frameworks for understanding our modern world. We hope you continue exploring our other podcasts, responding to the content, and checking out our related articles at helioxpodcast.substack.com. Music