# A Link Between Wormholes and Quantum Entanglement

2 December 2013 7:15 pm

This advance is so meta. Theoretical physicists have forged a connection between the concept of entanglement—itself a mysterious quantum mechanical connection between two widely separated particles—and that of a wormhole—a hypothetical connection between black holes that serves as a shortcut through space. The insight could help physicists reconcile quantum mechanics and Einstein's general theory of relativity, perhaps the grandest goal in theoretical physics. But some experts argue that the connection is merely a mathematical analogy.

Entanglement links quantum particles so that fiddling with one can instantly affect another. According to the bizarre quantum laws that govern the subatomic realm, a tiny particle can be in two opposite conditions or states at once. For example, an atom can spin in one direction or the other—up or down—or both ways at once. That two-way state lasts only until the atom's spin is measured, however, at which point it "collapses" into either the up or down state. Two atoms can then be entangled so that both spin two ways at once but their spins are completely correlated, so that, for example, they point in opposite directions. Then, if the first atom is measured and found to be spin up, the second atom will instantly collapse into the down state, even if it's light-years away.

Wormholes, on the other hand, are a prediction of Albert Einstein's general theory of relativity, which describes how massive objects warp space and time, or spacetime, to create the effects we call gravity. If an object is massive enough, it can create a funnellike hole in spacetime so steep that not even light can escape from it—a black hole. In principle, two widely separated black holes can connect like back-to-back trumpet horns to make a shortcut through spacetime called a wormhole.

At first glance, entanglement and wormholes both seem to offer a way around Einstein's dictum that nothing can travel faster than light. But in both cases, that hope is dashed. Entanglement cannot be used to send signals faster than light because one cannot control the output of the measurement on the first atom and thus willfully set the state of the distant one. Similarly, one can't zip through a wormhole because it's impossible to escape the black hole on the other end. Still, there is a connection. In June, Juan Maldacena, a theorist at the Institute for Advanced Study in Princeton, New Jersey, and Leonard Susskind, a theorist at Stanford University in Palo Alto, California, imagined entangling the quantum states of two black holes. They then imagined pulling the black holes apart. When that happens, they argued, a bona fide wormhole forms between the two black holes.

That was perhaps not so surprising, because the researchers started with black holes. But now two independent teams of scientists say that it should also be possible to create a wormhole connection between two ordinary quantum particles, such as quarks that make up protons and neutrons.

Kristan Jensen of the University of Victoria in Canada and Andreas Karch of the University of Washington, Seattle, start by imagining an entangled quark-antiquark pair residing in ordinary 3D space, as they described online on 20 November in

*Physical Review Letters*. The two quarks rush away from each other, approaching the speed of light so that it becomes impossible to pass signals from one to the other. The researchers assume that the 3D space where the quarks reside is a hypothetical boundary of a 4D world. In this 3D space, the entangled pair is connected by a kind of conceptual string. But in the 4D space, the string becomes a wormhole.
Julian Sonner of the Massachusetts Institute of Technology in Cambridge then builds upon Karch’s and Jensen’s work. He imagines a quark-antiquark pair that pops into existence in a strong electric field, which then sends the oppositely charged particles accelerating in opposite directions. Sonner also finds that the entangled particles in the 3D world are connected by a wormhole in the 4D world, as he also reported online on 20 November in

*Physical Review Letters*.
To arrive at this result, Jensen, Karch, and Sonner use the so-called holographic principle, a concept invented by Maldacena that states that a quantum theory with gravity in a given space is equivalent to a quantum theory without gravity in a space with one less dimension that makes up the original space's boundary. In other words, black holes inside the 4D space and a wormhole between them are mathematically equivalent to their holographic projections existing on the boundary in 3D. These projections are essentially elementary particles that function according to the laws of quantum mechanics, without gravity, and a string connecting them. “The wormhole and entangled pair don't live in the same space,” Karch says. But, he adds, mathematically they are equivalent.

But how big an insight is this? It depends on whom you ask. Susskind and Maldacena note that in both papers, the original quantum particles reside in a space without gravity. In a simplified, gravity-free 3D model of our world, there can’t be any black holes or wormholes, Susskind adds, so the connection to a wormhole in a higher dimensional space is mere mathematical analogy. The wormhole and entanglement equivalence “only makes sense in a theory with gravity,” Susskind says.

However, Karch and colleagues say that their calculations are an important first step toward verifying Maldacena and Susskind’s theory. Their toy model without gravity, Karch says, “gives a concrete realization of the idea that wormhole geometry and entanglement can be different manifestations of the same physical reality."

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