🌌 Celestial Holography: Who, What, Why, & How

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The night sky isn't just beautiful. According to the latest theoretical physics, it might be the fundamental computational substrate of reality itself—a two-dimensional screen on which the entire four-dimensional universe performs its calculations. We're only beginning to learn how to read what's written there.

This work demonstrates that fundamental problems—problems that have stumped brilliant minds for generations—can yield to new perspectives. The solution wasn't found by working harder within the existing framework. It was found by questioning the framework itself.

Celestial Holography Initiative

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Celestial Holography

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Transcript

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Welcome back to the Deep Dive. Today we are peering through one of the most exciting theoretical physics telescopes available. We're tackling a problem so fundamental it touches everything from particle scattering to, well, the black hole information paradox. That really does. The problem at its core is, how do you finally quantize gravity in the universe we actually live in? That's the crux of it. We are diving into a monumental new program called celestial holography. Our mission today is to explore this revolutionary idea that originated largely from the Perimeter Institute's initiative. Which is... The radical proposal that the entire four-dimensional gravitational reality of flat space-time can be perfectly mapped onto a two-dimensional quantum theory... living right on the night sky. The audacity of that concept. I mean, the physics of the entire 4D cosmos is encoded on the 2D sphere of the night sky. It just sounds like pure science fiction. It does, but the sources we're looking at show it's rooted in decades of extremely difficult work. And specifically, we're addressing this core mystery of quantum gravity in flat space time. That's the kind of space-time we believe describes our universe, right? Where the cosmological constant is nearly zero. Exactly. And to understand why this is such a huge undertaking, we have to start with its conceptual parent, the holographic principle. Right. Fundamentally, this principle suggests that the maximum information content of a volume of space, which is governed by gravity in, say, D dimensions, is... can be described by a simpler quantum theory living on its boundary. So a d-minus-one-dimensional boundary. A d-minus-one-dimensional boundary. It's this wild idea that a 3D reality is somehow painted onto a 2D screen. And we've talked about the one place where this actually works, the famous precedent for a functional holographic dictionary. That would be the Ad SCFT correspondence anti-decedor conformal field theory. This correspondence is, without a doubt, the most successful and well-explored realization of the holographic principle. It gives you a full working dictionary. A dictionary between what and what? Between gravity in this negatively curved anti-de-sitter space and a conformal field theory living on its boundary. The key there is that anti-de-sitter space is like a... It looks flat when you look far enough away. The walls of our universe are, you know, infinitely far apart. They're not a simple bowl. And that's the challenge that stumped physicists for decades. Applying this same duality to space times with a vanishing cosmological cost to our universe is incredibly hard because the boundary is just structurally different. Celestial holography is precisely this ambitious attempt to create that dictionary for flat space. So the goal is to establish a working duality between what happens inside. Between the gravitational S matrix which describes how particles scatter in 4D space and something on the boundary. And that something is. Correlators in a 2D conformal field theory, a CFT, living on that boundary sphere which we call the celestial sphere. It sounds like taking the most successful tool physics has for describing gravity, AASCFT, and trying to adapt it to the real world despite all the structural differences. That's the high-level view. And the stakes are enormous. I mean, not just for theoretical completeness, but for probing the deepest connections between forces. And this work has been heavily centered around the Perimeter Institute's Celestial Holography Initiative. Yes, which has really functioned as a vital collaborative research hub. pulling together all these disparate ideas from gravity, gauge theory, and even string theory. But as with all great scientific leaps, the sources gave us insight into the key people, the human journey behind this work. And we are specifically introduced to Sabrina Pestierski, who is, I mean, truly an inspirational figure in this field. She really is. She represents the kind of intense, almost singular focus required for these theoretical leaps. The sources detail her inspiring personal journey, starting with this childhood fascination with aerospace, It's an amazing story. and,- She designed, built, and flew a single engine aircraft.- A proper aircraft.- Before she was old enough to drive a car.- It's incredible. And this background perhaps of deeply understanding engineering and physical systems from such a young age, it must have given her a unique lens when she moved into dense theoretical physics.- That real world kinetic understanding of gravity and motion is just a fantastic counterpoint to the abstract mathematics. isn't it? Absolutely. And her academic trajectory, supported by fellowships at Princeton and Harvard, led her to foundational work on the universal properties of low energy particles, the soft graviton dirhams. Her PhD dissertation focused squarely on the implications of the infinite symmetries of flat space. specifically something called super rotations, which are now completely central to the Perimeter Initiative. We also have to stress the foundational role of Andrew Strominger. Oh, absolutely. His prior work alongside his collaborators kicked off a series of insights, as the sources put it, into connecting the infrared structure of gravity with gauge theory. So what does infrared structure mean here? It's the physics of very low energy particles. It was their collective realization that the long ignored asymptotic symmetries of flat space, the symmetries at infinity, were actually the key to a holographic program. And the sources also acknowledge other key contributors. Yes, people like Daniel Capek, Piyoslav Lisov, Monica Peite, and Anna Maria Riclerio. Their foundational papers contributed to proving the key symmetry results. They built the mathematical backbone that allowed this whole framework to stand up. So it wasn't a sudden invention. Not at all. It was a gradual realization that flat space wasn't as simple as everyone thought. The journey involved confronting this difficulty of flat space holography and identifying these hidden structural yet fundamental symmetries that had been largely missed or just ignored by previous generations of physicists. Why were they ignored? Because most were focused solely on particle interactions in the interior of space-time, not on what was happening at the boundary. Okay, so if we define the mission of this deep dive clearly, celestial holography maps 4D scattering matrix elements to 2D CFD correlators on the night sky. What are the genuinely astonishing consequences of this map? Well, the map is a revelation. First, it completely unearths these infinite dimensional symmetry enhancements that were entirely hidden in standard descriptions. Okay, infinite new symmetries. What else? Second, it provides radical simplification. Complicated 4D physics, specifically particle interactions where two paths nearly overlap, we call those collinear limits, are translated into the straightforward rules of CT operator product expansions, OPEs. And the third feature, which sounds like something that should just break physics as we know it It radically mixes ultraviolet and infrared behavior UV and IR, so high energy and low energy Exactly In quantum field theory, we usually separate these scales UV for high energy, short distance physics IR for low energy, long distance physics Celestial holography reveals that they are intimately connected. This lets us make powerful general claims about scattering that are not obvious if you only use perturbation theory. That mixing suggests a deep underlying unity in physics that respects no scale. It's truly wild. Okay, let's untack this. Before we get to the map itself, we have to start with the hidden structures of flat space-time that make this reorganization even possible. So our story begins at the very edges of spacetime in regions known as asymptotically flat spacetimes, or AFS. And conceptually, what does that mean? It just means these are spacetimes that look flat at extremely large distance scales. It's the description of our own universe. When physicists study gravitational scattering, they track incoming particles from a place called past null infinity. Which is like the beginning of time at the edge of space. In a sense. And then they track outgoing states at future null infinity. So this null infinity, which you called I plus or I minus, is essentially the place where radiation finally leaves or enters the universe. That's a great way to put it. It's the boundary of the space time itself. where all massless particles like photons and gravitons eventually go. And the celestial sphere is part of this. Precisely. We define null infinity as this downdry. And critically, the mathematical surface that defines how light rays converge or diverge here is the celestial sphere, the physical night sky you look up at. That 2D surface is embedded within this boundary. Now, in standard empty 4D Minkowski space, the expected symmetries are the Poincaré group. Right. Simple translations and Lorentz transformations, rotations, and boosts. For decades, people assumed that any scattering process must respect only these finite 10-dimensional symmetries. Why did that assumption turn out to be wrong once gravity was properly included? This is the genius discovery by Bondi, Metzner, and Sachs in the early 1960s. And it's a finding so subtle, its true implications took half a century to be fully appreciated. What did they find? When gravity is properly accounted for, when you allow gravitational waves to propagate, the asymptotic symmetry group enlarges dramatically from the expected Poincaré group to the infinite dimensional BMS group. The Bondi-Metzner-Sachs group. Exactly! Infinite dimensions. That sounds chaotic. What do these extra symmetries look like physically? Well, they fall into two main types. First you have super translations. Okay, a super translation, a normal translation shifts everything equally. Right. A super translation is an infinite dimensional large gauge transformation that corresponds to a position dependent translation on the celestial sphere. So imagine the surface of the nice sky. A super translation wiggles different points on that sphere by different independent amounts. They act non-trivially, only out at null infinity. So the gravitational field at the boundary allows for infinitely many ways to translate the space-time structure, depending on the angle you're looking at it from. That's a core idea. And the second type is the superrotations. These are rotations. These are an enhancement of the Lorentz group, the boosts and rotations we know. Super rotations include the global SL2C group, which is just mathematically identical to the Lorentz group, as a finite subgroup. But they're more than that. Much more. Super rotations are parameterized by arbitrary conformal killing vectors on the sphere, giving us infinitely many ways to rotate and boost the boundary structure. So the discovery of this infinite BMS group with both super translations and super rotations is the necessary prerequisite for celestial holography. Exactly. Without this rich, infinite structure at the boundary, there would be no 2D structure capable of supporting a rich 2D conformal field theory. Because a 2D CFT itself has infinite symmetry. Precisely. A 2D CFT is defined by its ability to maintain scale invariance and rotational invariance locally, which is often summarized by the infinite dimensional Virasoro algebra. The BMS group gives 4D gravity the necessary structural complexity to support this Virasoro symmetry on its boundary. But this connection goes deeper than just shared structure. Right, because these abstract symmetries have deeply physical and measurable consequences. They do. And this is where the physics really connects to reality. Let's explore the IR triangle, this tripartite equivalence that unifies symmetry, particle scattering, and observable shifts in spacetime. This relationship is one of the most elegant discoveries in modern physics. The infinite-dimensional asymptotic symmetries, the BMS group, are mathematically proven to be equivalent to universal factorization properties of scattering amplitudes known as soft theorems. Okay, and those are in turn equivalent to? Observable gravitational memory effects. It's a perfect triangle. Symmetry, scattering, and memory. Let's break down the soft theorems. What do we mean by soft? Soft refers to particles, specifically massless ones like photons or gravitons. whose energy, which we'll call omega, approaches zero. The core idea is that when a very low energy particle is involved in a collision, its contribution to the overall probability, the amplitude, should factorize universally, regardless of what the other particles in the collision are. What are the two key theorems we need to know about? First, the leading soft theorem discovered by Steven Weinberg in the mid-1960s. This concerns a factor that scales like one over omega. One over the energy. Right. So as the soft particles energy goes to zero, the term diverges. This leading dominant divergence is directly tied to the super translations. And the second one, which proved the existence of the super rotations. That's the sub-leading soft graviton theorem. This was discovered much later and is arguably the more surprising one. It has a term that is constant in energy. So it doesn't vanish as the energy goes to zero. It doesn't. It's an O of omega to the zero term. This non-vanishing universal constant factor is what is mathematically equivalent to the existence of super rotations. So we have the infinite symmetries and their influences codified in these soft particle scattering laws. Now the final corner, what are the real world observable consequences? the memory effects. Right. If a symmetry is conserved, its associated charge must be conserved, and its action must leave a measurable imprint. The leading soft graviton theorem, the one associated with super translations, translates into the displacement memory effect. And that is? This is the permanent non-zero displacement or kick of free test masses caused by the passage of gravitational waves. So it's not the wave itself which oscillates back and forth, but the final permanent shift in the background geometry is after the wave has left the area. Exactly. That permanent displacement is sourced by the net energy flux through null infinity. The vacuum state itself has changed due to the super translation charge carried away by the radiation. And what about the subtler spin memory associated with the subleeding theorem in super rotation? The spin memory effect is much more complex and was discovered more recently. It provides an operational definition for the super rotational symmetry. How would you measure it? You can't measure it with simple distance changes. Instead, it involves measuring time delays between light rays that repeatedly orbit the source. This effect is sourced by the angular momentum flux through null infinity. And because angular momentum has handedness, the effect has a chiral or spin structure. So here's the key takeaway for you, the listener. These aren't just three separate facts. They are intrinsically linked aspects of 4D gravity. Yes. The structure of our flat space-time boundary forces this deep connection between hidden infinite symmetries, how particles scatter, and how space-time shifts dynamically. And this realization leads to a huge conceptual shift, particularly concerning the vacuum. A huge shift. The sources emphasize that the leading memory effect implies that typical scattering processes induced dynamical vacuum transitions. Meaning the vacuum state can change? It's not unique. The vacuum is a vast landscape defined by these symmetries. And the soft theorems are essentially selection rules enforcing charge conservation between the initial and final asymptotic vacua. The vacuum is an active landscape of potential charges, not just nothing. Exactly. Okay, so if flat space gravity is defined by this infinite complex BMS structure and we want to map it to a neat, predictable 2D CFT, we need a mathematical tool to bridge that gap. We need the dictionary. So the structure we just discussed, the BMS symmetries, super translations, and super rotations, is the core structure we need to map onto the 2D CFT. But as we noted, these symmetries are almost completely obscured in the traditional description of 4D scattering. Right. Let's elaborate on the challenge of momentum space. Why does the traditional physics description using momentum eigenstates fail to see the symmetry? Well, standard scattering amplitudes, the S matrix, are calculated using plane wave basis states, momentum eigenstates. States of definite momentum, prodigals. Right. And these are excellent for manifesting translation symmetry. If you shift the entire collision spatially, the physics remains the same. It's obvious. But when you use these plane waves... The enhanced SL2C symmetry, the boosts and rotations, and the full super rotation group are messy, awkward, or just hidden. You can't easily see how a particle transforms under a rotation when you define it by its momentum vector. It's like trying to navigate the globe using a flat Mercator map. It's useful for local directions, but the global symmetry of the sphere, its ability to be rotated freely, is badly distorted at the poles. That's a perfect analogy. Exactly. So the solution of celestial holography is therefore to completely change the basis for external particles. Throw out the old map. Throw it out. We must move away from momentum eigenstates. and define our particles using boost eigenstates, which are specifically designed to transform correctly as 2D CFT operators on the celestial sphere. So we're trading one quantum number for another. We're trading fixed momentum for a new quantum number that respects the boundary's geometry. Yes. What is the mathematical machinery that executes this transformation? The core technical linchpin is the Mellon transform. It acts as the mathematical bridge, converting a function of energy into a function of a new variable, a conformal variable. Okay, tell us what this transformation actually does. The Mellon transform is applied to the energy, omega, of each external particle in the 4D scattering amplitude.

The formula is an integral. You integrate over the particle's energy, but you weight it by a specific power: 18:00

omega to the power of delta minus 1. Okay, so rather than scattering states defined by a fixed momentum, which includes energy, we are scattering states defined by this new variable, this delta. Precisely. And the result is the celestial amplitude. It's an observable living purely on the celestial sphere, defined by the angles of scattering. The transformation defines that variable delta as the conformal dimension and another variable j as the spin of the resulting 2d CFT operator This is the first crucial piece of the dictionary then energy in the 4d bulk physics Translates directly into the conformal dimension a fundamental property of the operator in the 2d boundary theory Why does that specific weighting omega to the delta minus 1 link energy to conformal dimension? dimension. It's because the resulting states, what we call conformal primary wave functions, are designed to diagonalize boosts. To make boosts look simple. As simple as possible. Boosts are the transformations that move you relative to a fixed origin. And in the celestial sphere context, they are the transformations that define the SL2C global conformal symmetry. By choosing this specific integral, we ensure that the wave functions transform in the simplest possible way under the 4D Lorentz group. Okay, let's clarify the connection between the 4D and 2D symmetry again. How does that work? Well, the 4D Lorentz group, which is called SO13, is mathematically isomorphic to SL2C. They're the same group, just written differently. When you project scattering onto the 2D celestial sphere, this SL2C group acts exactly as the global conformal group on the 2D plane. So the symmetry was there all along. It was there all along. The Mellon transform just makes it manifest. It ensures that the celestial operators we build transform correctly as what we call quasi-primaries under these transformations. This is how the 2D theory inherently respects the 4D physics. And this change of basis immediately provides conceptual clarity to those soft theorems we were talking about earlier. It's magnificent. The existence of those universal soft theorems, the 1 over omega and the constant term, corresponds exactly to the celestial amplitudes taking on critical dimensions. Special values of delta. Yes, special values. And these critical dimensions correspond to shortened representations of the symmetry group, which are well-known simple features in CFTs. So those seemingly complicated poles and zeros in momentum space that caused the IR catastrophe were just... They were just the momentum basis failing to resolve the true conformal symmetry. Once you switch basis, those messy limits become simple integer or half integer conformal dimensions. It's just a much cleaner way to see the physics. Infinitely cleaner. For a particle with integer spins s, the soft theorems occur as specific simple values like delta equals 1 minus s, 1 minus s plus 1, and so on. The Mellon transform unifies the UV and the IR behavior in one mathematical object, showing their intimate link. By focusing on boost symmetry, we've suddenly made the infrared physics, these soft limits, look like elegant, high symmetry objects in the conformal dimensions. The dictionary is being built. But 2D CFTs have much larger, truly infinite dimensional symmetry structures beyond this global SL2C. We need to see that full structure in 4D gravity if the holography is real. We've established the global conformal symmetry inherent in flat space, but the hallmark of a true 2D CFT is the infinite dimensional Vier-Sauro algebra. Is there conclusive evidence that 4D gravity has that much symmetry at its boundary? Yes, and this was one of the most significant breakthroughs of the initiative, consolidating the work of Westerwski, Strominger, Capek and others. The crucial finding is that gravity in 4D flat space possesses exactly this infinite structure. How did they make that link? The link between an algebra named after a Russian physicist and the behavior of a soft graviton? They identified the mathematical signatures. The sub-leading soft graviton theorem that's... surprise constant term that corresponds to super rotations, is precisely identified as a consequence of the Virasoro Ward identity of a 2D stress tensor insertion in the celestial correlator. Wait, hold on. The Virasoro algebra is defined by the stress tensor of the 2D boundary theory. And the sub-leading soft theorem is mathematically the same thing as the Ward identity for that stress tensor. So you're saying the two concepts are identical? They are structurally identical. This means the full asymptotic symmetry group of 4D flat spacetime is enhanced to include a full infinite dimensional virasaurosymmetry, which acts locally on the conformal sphere at null infinity. So it's not just an analogy. It's a duality. This confirms that the boundary theory, the celestial CFT, is a true high symmetry 2D CFT. This means we can stop trying to invent new 4D rules and instead apply the enormous existing toolbox of 2D CFTs to solve 4D quantum gravity problems. What's the most powerful tool this grants us? Well, one of the most powerful is the Operator Product Expansion, or OPE. For those unfamiliar, the OPE determines how two operators fuse together when they are brought close. In physics, this describes particle interactions. That's right. And celestial holography provides a direct translation. Collinear limits inform. So that's the physical scenario where two particles scatter, exiting the collision almost identically close to each other on the celestial sphere. Yes. That scenario is translated into a 2D operator product expansion. The OPE determines the series expansion of how two operators fuse into a new channel. Why is that a massive computational advantage? Because calculating culinary limits in momentum space, especially with gravitons, involve the complicated case-by-case calculations. It's a mess. By translating them into OPEs, we use the rigorous constraints imposed by CFT. This framework forms the backbone of the celestial bootstrap program, which lets researchers constrain the 4DS matrix using purely 2D algebraic techniques. You can generate an entire scattering amplitude just from knowing how the symmetry limits behave. In principle, yes. So we have the symmetries and we have a method to simplify scattering physics. The next step is organizing all these newfound modes, the memory effects, the super rotations, the soft theorems, into a coherent structure. This is where the concept of celestial diamonds comes in. These are organizing diagrams illustrating nested primary descendant operators, classifying how these different modes relate to each other. They provide a geometric way to understand the spectrum of the 2D boundary theory. Let's focus on the crucial components within the diamond. The Goldstone Modes. What are they physically and where do they sit in the spectrum? Goldstone Modes are a key feature of broken symmetries. They are radiative conformal primary wave functions whose corresponding large gauge symmetry is spontaneously broken, In the celestial basis, they appear at specific, beautiful, simple, conformal dimensions. Give us some examples of these simple dimensions. For massless particles, the Goldstone mode for the large U1 symmetry, so for the photon field, is found at delta equals 1. Delta equals 1. For super translations, the Goldstone mode associated with the graviton field is found at delta equals 0. Delta equals zero. It's a fundamental identification. The symmetry generator for gravity sits right at the simplest possible conformal dimension. That makes the structure immediately clear. Delta equals zero for gravity's simplest symmetry. Delta equals one for electromagnetism's simplest symmetry. And this pattern generalizes. The source material notes the existence of a spin-32 conformal primary that reduces to a Goldstino-Goldstone mode at delta equals three halves for local supersymmetry transformations. The diamond structure clearly classifies these generators. And these Goldstone modes are inherently linked to their physical effect, the memory modes. They are symplectically paired. The Goldstone modes... the degenerators of the symmetry, are paired with their corresponding memory modes, the physical response.- So an example.- For instance, the super rotation Goldstone mode is paired with the memory-like mode. This structure confirms the deep connection we identified in the IR triangle between symmetry generators and observable physical shifts.- Only now it's encoded purely in the 2D operator structure. We've moved from abstract, hard to see 4D gravity calculations to an elegant, structured, 2D language. Now, let's see the practical benefits. How does this unified framework solve the longstanding, stubborn problems of physics? We mentioned the unification of scales, and that leads us directly to the decades-old problem that has plagued quantum field theory. The infrared catastrophe. This is a monumental problem. Traditional quantum field theory struggles with infrared divergences caused by massless particles. Photons in QED. Gravitons in gravity running in loops. Why is that a problem? Because these particles are massless, you could emit an infinite number of them with arbitrarily small energy. Mathematically, this caused calculated scattering probabilities to just diverge. They blew up. So the answers were infinite, which means they were useless. Useless. For decades, physicists like Feynman had to employ clever mathematical tricks like resuming the infinite series of soft exchanges to cancel out these infinities and arrive at a finite answer. It felt like a mathematical pathology, not physics. A fudge factor. A very sophisticated fudge factor. But that's the key distinction. Celestial holography doesn't just offer a mathematical workaround, it offers a profound new physical interpretation. IR divergences are now interpreted as a direct result of violating charge conservation for the corresponding asymptotic symmetry. So the problem wasn't a flaw in the math itself, but a flawed initial assumption about the physical system. states. Precisely. We were assuming that the initial and final states of a scattering experiment were the same flat space vacuum. But, as we established, the leading memory effect implies that typical scattering processes induce dynamical vacuum transitions. The vacuum itself is shifted during the collision. If the vacuum changes, the initial and final states inherently possess different supertranslation charges. Exactly. Therefore, if you calculate an S-matrix element assuming the initial and final soft charges are the same, the probability must vanish or diverge because charge is not conserved. The soft theorems are now understood as selection rules. They are simply enforcing the conservation of the infinite family of asymptotic charges between your initial and in final states. So you have to include the change in the vacuum state in your calculation. You must. And this moves the problem from a mathematical pathology to a physical necessity of charge conservation. That's incredibly powerful. The boundary physics clarifies the physical meaning of what was previously a mathematical nuisance.

Now, let's pivot to the most famous problem in gravity: 28:30

the black hole information paradox. How does this celestial framework connect to black holes and soft hair? This initiative feeds directly into one of the most exciting theoretical proposals of

the last decade, pioneered by Hawking, Perry, and Strominger: 28:45

the concept of soft hair on black holes. The black hole information paradox suggests that since information is destroyed when it crosses the event horizon, it violates the rules of quantum mechanics. Soft hair is proposed as the mechanism to save that information. Correct. Soft hair suggests that black holes are not smooth. Bald objects defined only by mass, charge, and angular momentum, as classical physics suggests. The mechanism proposes that the infinite dimensional asymptotic charges specifically the supertranslation charge, are measurable features of the black hole, encoded right outside the horizon in the geometry. So the information isn't inside, it's encoded on the outside. It's encoded as hair. These charges are part of the black hole entropy, potentially carrying the information that fell in. And what are the implications for the controversial firewall concept, the idea that a high-energy zone exists at the horizon that violates the equivalence principle? Well, this framework offers a potential resolution to the firewall dilemma. One proposal is that an infalling observer, as they approach the horizon, automatically measures the classical value of the soft mode before crossing. This measurement implements a crucial quantum mechanical procedure, called a code subspace projection. And this projection helps resolve the high energy conflict for the infalling observer. So it might dissolve the firewall concept without violating established quantum laws. It's a promising path forward. So the infinite symmetries defined at the cosmic boundary inform the quantum state of the black hole horizon. That's a fundamental link between the very large and the very small.

Let's look at another profound connection supported by this new basis: 30:22

the classical double copy. The double copy principle suggests a deep structural link between gravity and gauge theory which describes forces like electromagnetism. The fundamental idea is that the gravitational fields can be conceptually related to the square of the gauge field. It's a remarkable mathematical connection. Gravity is gauge theory squared. Traditionally, this is seen in the relationship between the gravitational field tensor and the gauge field tensor. But in the celestial basis, this connection becomes elegantly and algebraically simple. How does the celestial map make this explicit? It organizes the fields by spin and conformal dimension, making the relationship clear. The spin2 gravitational conformal primary wave function is shown to be proportional to the square of the spin1 electromagnetic primary, the photon. The structure of the wave functions themselves reveals that the spin2 particle is composed of two spin1 components. The relationship is just manifest when all fields are transformed into the boost eigenbasis. This suggests the connection between gauge theory and gravity is not just a computational shortcut, but is intrinsically embedded in how the physics is encoded on the celestial sphere. It gives massive credence to the idea that these theories are intrinsically linked through their asymptotic behavior. It's pushing us towards unification. We've seen the power of this new dictionary in solving old problems. Finally, where is the field heading next? Where are researchers like Sabrina Pestursky, who helped pioneer this, focusing their efforts now? The field is rapidly expanding in several critical directions. One major focus is connecting this framework to higher energy theories. specifically constraining string theory amplitudes. They are checking if string theories are the only consistent theories of AFS quantum gravity by mapping their amplitudes into this celestial framework and seeing if they adhere to the necessary symmetry structures. And moving beyond the classical tree-level interactions, what about quantum corrections? That's the other big push. Researchers are actively exploring loop corrections in quantum symmetries. Loop corrections involve quantum particles running in closed paths, which is necessary to transition to a truly quantum theory of gravity. And perhaps the most ambitious goal. That would be the development of an intrinsic, non-perturbative definition of celestial CFT. Meaning? Right now, we define the CCFT by mapping known 4D solutions onto the 2D sphere. The ultimate goal is to reverse this. to start only with the rules and constraints of the 2D CFT, its spectrum, its OPEs, its symmetries, and use those rules to define the physics of the 4D bulk. That would be the full realization of the holographic dream, defining gravity not by the rules of 4D space-time but by the rules of its 2D boundary. The view from the celestial sphere is proving far more revealing than we ever imagined. This has been an incredibly deep dive, revealing that the night sky is not just a passive backdrop, but potentially the holographic screen for four-dimensional gravity, governed by these deep, hidden symmetries. If we summarize the key structural shift. Flat space-time isn't simple. It's governed by infinite BMS symmetries. And the critical change of basis, the Mellon Transform, revealed that these symmetries are mathematically equivalent to the Verocero symmetry of a 2D CFT. And this celestial holography dictionary is already providing breakthroughs in solving the IR catastrophe, illuminating black hole information. and unifying forces through the double-copy principle. It's compelling to follow the journey from a scientist's initial fascination with flight and engineering, through years of confronting what seems like intractable problems in gravity, to defining a radical new map of the universe. The success has been the recognition that seemingly accidental mathematical properties of scattering are in fact the universal signature of a fundamental infinite symmetry at the very edge of space-time. We're finally learning how to read the language of the boundary. Exactly. And that leads us to our final provocative thought for you to take away. The celestial sphere provides a new horizon for physics because it turns the physics of scale inside out, We know the standard memory effect is sourced by energy flux and spin memory by angular momentum flux. That is the lowest order multipole moments. Right. But given the infinite family of soft theorems and the corresponding Goldstone memory mode pairings in this celestial tower, the deeper question is this. If super translations and super rotations are just the first two infinite sets of symmetries, what are the corresponding, more exotic, higher multiple moments of matter that our celestial fear observations can theoretically measure? What even deeper, subtler memory effects are waiting to be revealed by this map that are associated with these infinite higher symmetries? A profound question to end on. If the universe is a hologram, the revolution has just begun. Thank you for guiding us through this complex and revolutionary field.