# Are We Living in a Hologram?

*Paul Sutter is an astrophysicist at The Ohio State University and the chief scientist at COSI science center. Sutter is also host of Ask a Spaceman and Space Radio, and leads AstroTours around the world. Sutter contributed this article to Space.com's Expert Voices: Op-Ed & Insights.*

In the late 1990s, theoretical physicists uncovered a remarkable connection between two seemingly unrelated concepts in theoretical physics. That connection is almost inscrutably technical, but it might have far-reaching consequences for our understanding of gravity and even the universe.

To illustrate this connection, we're going to start at — of all places — a black hole. Researchers have found that when a single bit of information enters a black hole, its surface area increases by a very precise amount: the square of the Planck length (equal to an incredibly small 1.6 x 10^-35 meters on a side). [Are We Living in a 2D Hologram? Photos of Laser 'Holometer' Experiment (Gallery)]

At first blush, it may not seem all that interesting that a black hole gets larger when matter or energy falls into it, but the surprise here is that it's the surface area, not the volume, that grows in direct proportion to the infalling information, which is totally unlike most other known object in the universe. For most objects that we're familiar with, if it "consumes" one bit of information, its volume will grow by one unit, and its surface area by a only a fraction. But with black holes, the situation is reversed. It's like that information isn't inside the black hole, but instead stuck to its surface.

Thus, a black hole, a fully three-dimensional object in our three-dimensional universe, can be completely represented by just its two-dimensional surface. And that's how holograms work.

## A black hol-ogram

A hologram is a representation of a system using fewer dimensions that can still pack in all the information from the original system. For example, we live in three (spatial) dimensions. When you're posing for a selfie, the camera records a two-dimensional representation of your face, but it doesn't capture all the information; when you later examine your handiwork and choose your filter, you can't, for example, see the back of your head, no matter how you rotate the picture.

Recording a hologram would preserve all that information. Even though it's a two-dimensional representation, you would still be able to examine it from all three dimensional angles.

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Describing a black hole as a hologram might provide a solution to the so-called black-hole information paradox, the puzzle of where the information goes when matter is consumed by a black hole. But that's the subject of another article. The black-hole-as-hologram concept is also a good example to keep in your head as we make the big jump — to consider the entire universe. [The Strangest Black Holes in the Universe]

## Living on the boundary

The correspondence between the seemingly unrelated branches of physics that I teased at the beginning of this piece is another application of holographic techniques and goes by the incredibly dense name of AdS-CFT.

The AdS stands for "anti-de Sitter," a particular solution of Einstein's general relativity that describes a completely empty universe with a negative spatial curvature. It's a pretty boring universe: It contains no matter or energy, and parallel lines eventually diverge due to the underlying geometry. While it may not describe the universe we live in, it is at least some sort of universe, so that's a start — and this somewhat bland model of the universe has the necessary mathematical properties to make the connections theorists needed.

The other side of the correspondence is a framework called conformal field theory. Theoretical physics is lousy with field theories; they're the hammers that scientists use to pound a lot of quantum nails, used to describe three of the four forces of nature. Electromagnetism, the strong nuclear force and the weak nuclear force all have field-theory descriptions, and in the past half century, we've had a lot of practice in using them.

Now that we've gotten the definitions out of the way, let's dig in to why this connection is so important.

Say you're trying to solve a really hard problem, like quantum gravity, using string theory, which is an attempt to explain all the fundamental forces and particles in the universe in terms of tiny vibrating strings. It's such a hard problem, in fact, that nobody has found a solution for it despite trying for decades. The AdS-CFT correspondence tells us that it might be possible to use a holographic technique to save us a world of headaches.

Instead of trying to puzzle out quantum gravity in our three-dimensional universe, AdS-CFT allows us to switch to an equivalent problem at the boundary of the universe, which is a) only two dimensions, and b) doesn't contain gravity.

That's right: There's no gravity on the boundary. The nearly impossible-to-crack mathematics of string theory get replaced with a set of merely insanely difficult field-theory equations. Then, you can find a solution to your problems there, without any pesky gravity getting in the way, and transport your solution back into the normal three-dimensional universe and make predictions.

## Not so fast on that shortcut

This sounds like a wonderful idea, a way to cheat nature by circumventing gravitational machinations. And it just might turn out to be a brilliant way to "solve" quantum gravity. But as of right now, there are a few catches. For one, we don't live in an anti-de Sitter universe. Our universe is full of matter, radiation and dark energy, and has almost perfectly flat geometry. Is there a similar correspondence that works in our real universe? Perhaps, and theorists are working hard to find it.

Second, the "boundary" taken for the AdS-CFT correspondence is the cosmological horizon — the limit of what we can see in our observable universe. That would be fine, except that we live in a dynamic space-time with an ever-growing cosmos, and that boundary is always changing — something that's not handled very well in current theories.

Lastly, when you make the jump from a fully described anti-de Sitter universe to a simpler boundary model where conformal field theory applies, the new sets of equations are solvable only in principle. They can still be — and frequently are — fantastically, perniciously, frighteningly, heartbreakingly difficult to solve. So just because you've short-circuited gravity doesn't mean you're out of the weeds yet.

## Living in a hologram

So do we live in a hologram? Even if the AdS-CFT link proved fruitful for tackling quantum gravity, if we were able to find a way to navigate the challenges and make this technique relevant for the universe we live in, it doesn't mean that we actually live in a hologram. It's a mistake to make the jump from "AdS-CFT provides a handy way to solve gravitational problems" to "our universe with gravity in three dimensions is an illusion, and we really live in a two-dimensional boundary with no gravity."

A mathematical contrivance, as handy as it may be, doesn't necessarily dictate our views of the fundamental nature of reality. If holographic principles are useful for solving problems, it doesn't necessarily mean that we live in a hologram. And even if we did live in a hologram, we wouldn't necessarily be able to tell the difference anyway.

Learn more by listening to the episode "Do we live in a hologram?" on the Ask A Spaceman podcast, available on iTunes and on the Web at http://www.askaspaceman.com. Thanks to @kulayemnazurun and Andrew B. for the questions that led to this piece! Ask your own question on Twitter using #AskASpaceman or by following Paul@PaulMattSutter and facebook.com/PaulMattSutter.

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Paul M. Sutter is a research professor in astrophysics at SUNY Stony Brook University and the Flatiron Institute in New York City. He regularly appears on TV and podcasts, including "Ask a Spaceman." He is the author of two books, "Your Place in the Universe" and "How to Die in Space," and is a regular contributor to Space.com, Live Science, and more. Paul received his PhD in Physics from the University of Illinois at Urbana-Champaign in 2011, and spent three years at the Paris Institute of Astrophysics, followed by a research fellowship in Trieste, Italy.