Image courtesy Light Field Lab, Inc.
As strange as that possibility sounds, the idea ripples through theoretical physics, enabling physicists to explore answers to the fundamental question troubling them. How can they reconcile the theories of relativity and quantum mechanics? What is the theory of everything?
“We’re trying to put together a complete picture,” says Matthew Headrick, a professor of physics at Brandeis University. “Relativity tells us that gravitation is due to the geometry of space and time. Quantum mechanics tells us that physical things fluctuate; that they don’t have definite positions and there is fuzziness.” But, the two theories of gravity and quantum mechanics don’t always play together nicely. “Things are crashing if you look at distances around the Planck Length,” Headrick says. (The miniscule Planck Length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. It’s roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.) “Planck Length is smaller than any length we’ve probed with experiments,” Headrick says. “The place things go wrong is in these very short distances, shorter than the size of an atom. We don’t know what’s going on, but we know our usual theories don’t work. Something has to change.”
Holography is the study of relationships known as dualities. A hologram, for example, is a two-dimensional image that stores information about all three dimensions of an imaged object. “The idea of holography rewrites the problem,” Headrick says. “The holographic principle basically says the world we see with its three dimensions and one dimension of time is an approximation of something more fundamental that is two dimensional. We don’t know if it’s true and, if it is, we don’t know in any detail how it would work in our universe.”
If that sounds outlandish, remember that physicists explain theories to people who don’t understand the complex underlying mathematics by using metaphors. The holographic principle is a metaphor, an analogy that captures some of the mathematics behind it. It might, in fact, be a fundamental property of quantum gravity, which theoretically describes gravity according to the principles of quantum mechanics, thus linking the two. The holographic principle has been realized mathematically, but in another theoretical universe. “The kind of physics we’re talking about is very theoretical,” Headrick says. “And since we’re theoretical, we can invent other universes. The idea that the universe is two dimensional is more amenable to the math we know how to do.”
Headrick tells a physics joke: A farmer tells his neighbor, a physicist, that his cows aren’t giving milk. The neighbor says, “Imagine a spherical cow…” What if our universe is encoded on a 2D surface with the position and velocity of physical objects around us; that is, everything 3D? What if there is another universe?
Wind back to 1935 when Albert Einstein published two papers: In March, he wrote, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” And in May, “The Particle Problem in the General Theory of Relativity.”
Theoretical physicist Leonard Susskind, professor of theoretical physics at Stanford University, talked about how the connection between these papers led to the holographic principle and other research in a recorded panel moderated by Brian Greene at the World Science Festival. Susskind explained that Einstein agreed that Quantum Mechanics provides a description of the microscopic world. Still, he thought it was a provisional theory that would be replaced by one that would not rely on probabilities. He worked to expose the qualities of quantum mechanics that would counter how the world works. Continuing with Susskind: The Achilles heel, Einstein thought, was that according to quantum mechanics math, if two objects interact and then separate widely, the measurement on one will have an instantaneous impact on the other regardless of the distance. He called it “spooky action at a distance,” and it troubled him. He couldn’t accept this quantum view of reality. We now call this non-local effect, “entanglement.”
In the second paper, Einstein and Rosen found that two regions of space could be joined with a kind of short bridge. This notion led to the idea of wormholes and to a so-called “event horizon” or “boundary” around a black hole. According to general relativity, what falls into a black hole, stays in a black hole. Any mass, compressed enough, can become a black hole where gravity is so strong that nothing can escape.
But in the 1970s, Stephen Hawking predicted that black holes emitted radiation at the event horizon. As radiation escapes over time, the black hole evaporates. Hawking’s radiation is thermal, which can’t carry information, that is, data that describes physical phenomena. So, what happens to the information? Quantum mechanics says that information is not lost, and that you can create an initial state from an object’s final state. Nothing is lost. But if information cannot be destroyed, the accepted laws of physics would need to change. This is the “black hole information paradox.”
In a recorded conversation with Sean Carroll, Raphael Bousso, a UC Berkeley theoretical physicist and cosmologist, offers an example. If you compressed a bunch of matter and turned it into a black hole, the only way that’s consistent with the principles of quantum mechanics, which says that information can’t be lost, is if the black hole could store the information about which state the matter was in. Then, it could be reversed. In other words, information such as the position and velocity of physical objects, should be preserved somewhere, but where? How? Imagining how has led to the holographic principle.
When Gerard ‘t Hooft, a theoretical physicist, professor at Utrecht University, and Nobel Prize winner in Physics (1999) analyzed the emission of Hawking radiation, he determined that when it escapes, there is a way in which incoming particles can modify the outgoing particles. And in 1994, Leonard Susskind published the paper, “The World as a Hologram,” which states: “According to 't Hooft, the combination of quantum mechanics and gravity requires the three-dimensional world to be an image of data that can be stored on a two-dimensional projection much like a holographic image.” In that paper, he uses string theory as a possible way to realize ‘t Hooft’s idea.
During the recorded panel, Susskind describes the possibility this way: The more precision you bring to bear on the measurement of a quantum string, the more you find it’s spread out over all of space. If you look at it without great resolving power, you find it localized in local space. When a particle falls into a black hole, because everything slows down, someone watching from outside sees it with more and more precision, like an airplane propeller. As he sees it with better precision, he sees it spread out in such a way that instead of falling into the black hole, it spreads out not only over the horizon but into infinity. In other words, information never really falls into the black hole. It’s stored. It’s recoverable. What falls into the black hole is a kind of image. The information is, as ‘t Hooft described in “Dimensional Reduction of Quantum Gravity,” encoded far away at the boundaries of the world. Thus, the universe is a hologram. Information that falls into a black hole remains trapped inside, but an exact copy is preserved on the horizon. The amount of information inside is related to its two-dimensional surface, not its three-dimensional volume. There is a mathematical equivalence when the holographic principle is generalized, it suggests that not just a black hole, but the entire three-dimensionality of space is the projection of a distant horizon, the horizon of the universe surrounding us.
In 2013, Maldacena and Susskind proposed a new duality, that two entangled particles are connected by a wormhole; that wormholes are equivalent to entanglement. And thus connected Einstein’s two 1935 papers. And, in Stephen Hawking’s final theory of the Big Bang, he imagines the universe as a hologram. The most cited prime example of the holographic principle is the AdS/CFT correspondence, a duality first published by Juan Maldacena in 1997, an Argentine theoretical physicist now at Princeton University. AdS/CFT is a mathematical realization of the holographic principle, but in another universe. Not our universe. Still, AdS/CFT has become useful and has led to the belief that the holographic principle should be a fundamental principle of quantum gravity.
Bousso explains: Let’s say that a star explodes in Andromeda Galaxy and that you can’t find out about that faster than the amount of time it takes light to travel from Andromeda to here. That’s been a very important principle in physics. And yet the holographic principle tells us that at some level it has to be wrong. If I can store all the information about a space time region on its boundary, in some sense I should be able to look at this boundary and read information about what’s going on in its interior instantaneously some distance away from it. And in fact, that’s literally what we’re able to do when we apply this AdS/CFT correspondence, this explicit quantum theory of gravity that we have for a class of space time. It realizes the notion of the holographic principle in a totally explicit way. You can put it on a computer and do calculations. But, as wonderful as it is, it’s not our universe.
Bousso and other physicists are trying to bring the theories into our universe and they may be getting closer. In November 2022, for example, physicists at Caltech reportedly (in Nature) simulated sending clouds of entangled particles through a simulated wormhole; through a holographic dual. That they actually created a wormhole has been challenged, but using quantum computers’ qubits and machine learning to run possible quantum gravity simulations is intriguing.
Separately, the summer of 2023 marked the end of an eight-year collaboration funded by the Simon Foundation during which computer scientists and information theorists participated along with high-energy physicists toward an understanding of quantum gravity. Headrick was a co-leader of the group, which calls itself, “It From Qubit.” (A qubit is a quantum bit; information stored in qubits and sent is quantum information.)
“What we have learned from holography and other developing theories is that the language of information theory is useful for understanding quantum gravity,” Headrick says. “When information theory and quantum people talk to each other, we understand more deeply how the hologram encodes the three-dimensional information. To understand in detail the encoding, you need sophisticated information theory.” Meanwhile, the holographic principle is still a theory, a metaphor. A theory that there is mathematical equivalence or “duality” between relativity and quantum mechanics; that general relativity and gravity are to quantum effects as a 3D hologram is to a 2D pattern.
Susskind: I think this holographic idea is permanent in the vocabulary of physicists. But how it plays out? There will be surprises.
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