Help me obi Juan whoever you are, you’re my only Ho
Unless you’ve been living under a rock, your first introduction to the concept of holograms was probably Leia’s message to Obi-Wan in Star Wars IV: A New Hope (unless your first introduction to holograms was Tupac, in which case. . . I feel old). Although to be clear, Tupac’s Coachella performance in 2012 was not actually a hologram—it was a 2D video projected on a seemingly invisible screen. We don’t actually have the technological capability yet to create real holograms—that is a 3D image projected from a 2D light source. But holograms have featured in many science fiction staples, including Star Wars where R2D2 is able to project a 3-dimensional Princess Leia onto the table so she can deliver her message to Obi-Wan (the quote above isn’t the message from the movie, of course, but a genius rewrite from Carrie Fisher’s twitter—I left out the swearing, in case any of those Tupac hologram kids are here).
As easy as R2D2 makes it look, it’s actually pretty hard to encode 3-Dimensional information onto a 2D surface. To do so, you would need to create a pseudo-dimension—a fake dimension where information about the depth of the object is stored. We do actually have something almost like this—traditional red/blue 3D glasses. A 3D movie is created by layering 2 images on top of each other—the information for the angle of that picture is encoded in the color or polarization of the light projected. When you wear the glasses, each lens filters out one of the types of light, meaning each eye sees the same image at a different angle. Even though you only perceive the image at two angles, your brain fills in the gaps and sees the image in 3-dimensions (you can actually use this trick to take 3D pictures with any camera, using stereoscopic photography). But still, this is just a trick. How could it be possible to encode a full 3-dimensional volume onto a 2-dimensional surface—like what supposedly happens on the event horizon of a black hole? What sort of pseudo-dimension could the universe use to do this? And, if the universe is a hologram, is any of this even. . . real?
Back to the Beginning: Hawking Radiation and Creating a Hologram
Let’s go back to the beginning—to the concept that started all this mess, Hawking radiation. The existence of Hawking radiation tells a lot about the behavior of black holes. We know that black holes evaporate into this radiation over very long lengths of time. This evaporation gives the black hole a measurable temperature, and it carries bits of the black hole’s “information content” back into the accessible universe. Quantum information exits the black hole through this mechanism—it is completely scrambled, but not destroyed. All of these discoveries about the nature of black holes stem from Hawking radiation, but more fundamentally, they stem from another important discovery—black hole entropy.
We’ve defined entropy roughly as the amount of disorder in a system, or more precisely, as the dispersal of energy throughout a system. To say that a black hole has entropy is to imply that it contains a certain amount of undispersed energy—and where there is energy, there is information. In 1972, Jacob Bekenstein was the first physicist to quantify the entropy of a black hole as a function of the amount of information it contains, or its mass. What he found was that each additional “bit” of information (a bit, in this case, refers to the smallest, most fundamental particles) adds a square Planck area (the smallest pixel of our universe defined as about 10-70 m2) to the surface area of the event horizon. This means you can calculate the mass, information content, and entropy of a black hole based solely on the 2-dimensional area of its surface. As the black hole evaporates, this surface area decreases, meaning the information held within the black hole is dispersed back into the universe. The entropy of a black hole represents the absolute maximum amount of information that can be packed into that amount of space. This value is called Bekenstein’s bound, and it defines the maximum amount of entropy in a given region of space as a function of the surface area of a sphere enclosing it.
This relationship between entropy and surface area may be surprising. Intuitively, we might assume that the amount of “stuff” in a given space is directly related to the volume of that space. After all, the volume is where most of that “stuff” exists . . . right? But it turns out that, at least in terms of the fundamental physics, 3-dimensional volumes can be completely described by interactions on their 2-dimensional surfaces. The implication of this is that the universe itself—a 3-dimensional volume—could be perfectly described by interactions on its surface—a distant spherical boundary. But where does the extra dimension go? How can we make a real hologram?
AdS/CFT Correspondence and The Holographic Universe
For a while, despite the revelation of the Bekenstein bound, physicists couldn’t determine how a 3D space could be encoded on a 2D surface—just like engineers couldn’t determine how to make real, practical holograms. The core problem was determining how to encode the extra dimension. A potential solution came from string theory and an Argentinian physicist, Juan Maldacena. Maldacena’s solution, called AdS/CFT (anti-de Sitter/conformal field theory) correspondence, demonstrates how the information in a 4-dimensional Anti-de Sitter space (in simplest terms, a 4D spacetime that is negatively curved) can be encoded on a 3-dimensional space with a conformal field theory (space where the physical laws are scale-invariant).
The full derivation of AdS/CFT is far too complicated to explain here, but it provides a demonstration of how a higher-dimensional space can be encoded on a lower-dimensional surface—like a hologram. The basic way it works is by taking advantage of the scale invariance of the CFT space to create a pseudo-dimension. Scale invariance means that objects at every scale interact in the same ways. You can change the scale at any point in the space, but the physical interactions between objects at that scale will still follow the same patterns as objects at another scale. If objects at different scales are mostly independent of each other, then scale invariance creates a “fake” dimension where objects can be described by both their position in the space and their relative scale. In this way, it could be possible to encode 3-dimensions (x, y, and z) on a 2-dimensional surface that records an object’s z-position as a function of its relative scale.
While this is obviously a mind-bending concept, the underlying value of AdS/CFT and the Holographic principle is that it gives physicists a mathematical basis for modeling 3-dimensional space in 2-dimensions. This is extremely valuable for physicists because, in a 2D universe, the force of gravity disappears. Without a theory of “quantum gravity” (a theory that describes how the force of gravity works on quantum scales), physicists have struggled to unify the behaviors of atomic-scale objects with that of cosmic scale objects. Despite being one of the more intuitive physical phenomena, gravity is by far the most confounding physical force. We don’t even know for sure where it comes from (physicists have pinned gravity on massless particles called “gravitons”, although they have never been practically observed). So, the mathematical consequence of AdS/CFT is that stubborn physical problems can be translated from 3D space to a 2D surface without the confounding variable of gravity. This may mean that the holographic principle is the key that could lead to a universal “Theory of Everything” that unifies general relativity with quantum field theory.
Whether this “holographic universe” is a physical reality or a mathematical artifact is almost irrelevant—there’s no way for us to know if we live in a “real” volume space or an encoded area space. In fact, the implication of AdS/CFT is that the two realities are mathematically indistinguishable. And there is no reason to believe we would be able to perceive the difference. Our perception is already a gross estimation of reality fabricated by our brains—like the Tupac “hologram” or the red-blue 3D glasses, our brains fill in the gaps automatically. If the universe is actually a 3D projection from a 2D surface, then we must exist in both universes, exactly the same, and both completely convinced that this is reality.
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