Wormholes in the laboratory

One example is a scenario in which two black holes are connected by the laws of quantum mechanics. This means that whatever happens to one of the two collapsed stars immediately affects the other — regardless of how far apart they are. If such a connection exists, it could solve one of the greatest mysteries of cosmology.

When information enters a black hole, for example by a quantum particle falling into it, it is distorted beyond recognition extremely quickly. This circumstance has been causing scientists’ stomach ache for decades. After all, the laws of quantum mechanics state that information, just like energy, cannot be destroyed.

AT A GLANCE

1. If a particle falls into a black hole, all information about its properties such as mass, charge, or velocity seems to disappear forever.

2 However, if the black hole was connected to another wormhole, the information could slip through the connection and escape from the second collapsed star.

3. Physicists now want to recreate such a situation in the laboratory using ultracold atoms.

Some researchers have suggested a way out: the information about a quantum particle could, after a certain time, escape from another black hole that is connected to the first one. In this case, it would appear as if the particle had traveled through spacetime via a shortcut. The quantum mechanical connection between the collapsed stars then corresponds to a wormhole.

Of course, such an event is pure speculation so far. Today’s technology is far from being able to prove such phenomena. But physicists around Sepehr Nezami from Stanford University have now worked out a proposal to observe the described processes experimentally. This would not require the use of real black holes. The researchers claim that only a few ions and lasers are needed. If their prediction is confirmed, they could answer one of the most fundamental questions in cosmology, namely whether black holes do destroy information irretrievably.

It follows from quantum mechanics that the total amount of information in the universe always remains the same. However, black holes are described by general relativity and therefore follow different laws. They are formed by massive stars that collapse under the influence of their gravity so that they only fill a tiny area of space. When a particle of light passes the so-called event horizon (see glossary) of a black hole, it can never escape again — the information it carried seems to have disappeared forever.

In search of the lost information

This apparent contradiction arises because there is as yet no theory that unites the microcosm with the macrocosm. The laws of gravity on large scales are based on general relativity, while quantum mechanics explains the behavior of the smallest particles. For more than 100 years, researchers have tried to unite both theories, but so far they have failed.

In the 1970s, the British physicist Stephen Hawking addressed the problem of the disappearing information in black holes. By applying the laws of thermodynamics and quantum mechanics to curved space-time, as the general theory of relativity suggests for black holes, he achieved astonishing results: He calculated that the galactic monsters would emit radiation and slowly evaporate.

Hawking assumed that a black hole is surrounded by a vacuum. However, this does not mean that the space is empty (see “Spectrum” December 2019, p. 12). In reality, particle-antiparticle pairs are constantly being created, and they destroy each other again within a very short time. Because of the large gravitational energy of a black hole, there are particularly many such short-lived pairs. This leads to a strange effect: When particles and antiparticles form near the event horizon, a particle may pass the horizon — and thus disappears forever — while its associated partner escapes. At some point it collides with an abandoned antiparticle, causing the two to annihilate each other and produce a photon, which leads to so-called Hawking radiation.

This has important consequences for the black hole: because it emits energy in the form of photons and energy can be created from nothing, the collapsed star must lose mass. This cannot be proven with today’s technology, but the phenomenon is accepted among physicists. Even though Hawking’s work has had a significant impact on modern cosmology, it does not solve the original problem. The black hole does emit photons, but they contain no information about the particles that have fallen into it. Once it has completely evaporated, the information it contains would also be lost forever.

In 1997 the Argentine physicist Juan Maldacena found a possible solution. He postulated the so-called AdS/CFT correspondence, from which it follows, for example, that Hawking radiation contains information about the interior of the black hole.

The AdS/CFT correspondence is regarded as one of the most promising directions in string theory — an approach that aims to unite quantum mechanics with gravity. String theorists assume that the smallest threads (English: strings) generate all known elementary particles and fundamental forces through their oscillations. The theory is extremely complicated and has been in a tight spot for years. Among other things, it predicts several particles that have not been observed so far. When Maldacena developed the AdS/CFT correspondence, it seemed like a glimmer of hope. She says that certain models of space-time are related to quantum systems.

If such a connection existed, it would be extremely useful for physicists. For example, if one wanted to predict certain properties of a complicated quantum mechanical process, one could instead perform a — possibly simpler — cosmological calculation and then transfer the results back to the quantum world according to the AdS/CFT correspondence.

The AdS/CFT correspondence is like a dictionary that translates cosmological processes into quantum phenomena and vice versa. If one takes the connection seriously, it follows that the completely different physical systems are two sides of the same coin. On one side is a space-time with a certain type of curvature known as anti-de-sitter space. This is the ADS part of the correspondence. On the other side is what is known as conformal field theory (CFT), which occurs in one dimension less than spacetime. This means: The mathematical description of an anti-de-Sitter space in d dimensions is equal to that of a conformal field theory in d-1 dimensions.

Anti-de-Sitter Universe

Albert Einstein shook our understanding of the universe in 1915 when he published his general theory of relativity. As he worked out, time and space are not static, but change their form: Energy bends space-time.

Initially, physicists tried to solve Einstein’s equations in a simplified form by studying empty universes without matter, which are curved in the same way everywhere. For such a case, general relativity allows three possible forms of spacetime: it is either flat (Minkowski space), positively curved like a spherical surface (de Sitter space) or negatively curved like a saddle (anti-de Sitter space, or AdS for short) — with the difference that the universe is not a two-dimensional surface, but rather the four-dimensional counterpart to the examples mentioned.

While physicists wondered which of the three solutions best described our cosmos, mathematicians tried to find out whether the solutions were stable at all. In other words: If you insert a tiny mass into a universe, does space-time retain its shape as far as possible or does it create a black hole that distorts it completely?

As soon as a mass-bearing object — such as a particle — is created in an empty universe, gravitational waves are formed and propagate through spacetime. Similar to waves in a body of water, they can become weaker and silt up over time; this happens in a stable solution like our universe. Or, in the unstable case, they could build up into a kind of tsunami, which would create a black hole.

The physicist Helmut Friedrich from the Max Planck Institute for Gravitational Physics in Potsdam proved in 1986 that the positively curved de Sitter space is stable. Although small amounts of matter influence this type of space-time, they do not change it significantly. Seven years later, a publication by the mathematicians Demetrios Christodoulou and Sergiu Klainerman followed, in which they showed that even the flat Minkowski space retains its coarse form when small masses are added. However, how the anti-de-Sitter space behaves remained a mystery for a long time.

Only recently, the mathematician Georgios Moschidis was able to prove what numerous physicists already suspected: that an anti-de Sitter universe is not stable. As soon as even the smallest bit of mass appears black holes form.

This is no problem for the AdS/CFT correspondence, a promising area of string theory that links anti-de-sitter universes with quantum systems (conformal field theories, CFT). Black holes are needed in the correspondence on the AdS side to find a quantum physical analog at all. Moschidis’ work suggests that black holes in the AdS universe are created faster than previously thought.

Moreover, physicists already knew that AdS universes do not correspond to our spacetime. Nevertheless, the correspondence could help to look at cosmological puzzles in a new light and perhaps even answer them. It is often helpful to examine problems in a simpler environment and then consider how they could be solved in a more realistic context.

The strange connection works like a hologram — all information of a cosmos is contained in quantum systems in a lower dimension. This so-called holographic principle was first proposed by Nobel Prize winner Gerardus ‘t Hooft in 1993. Maldacena’s work provided the first concrete example of this four years later.

Here, the continuous space in the AdS universe corresponds to numerous interlaced qubits (see glossary) on the CFT side, which interacts with each other incessantly. Some physicists see the holographic principle as a mathematical tool that simplifies calculations. However, some go further and conclude that entangled quantum-mechanical systems create space-time with gravity. This would mean that gravity is made up of quantum effects.

So far, however, both the holographic principle and the AdS/CFT correspondence are only guesses. Maldacena has shown in his work that some properties of quantum systems have a cosmological analog. We are still far away from a complete dictionary that assigns a corresponding variant to each phenomenon on the one hand and each phenomenon on the other. Moreover, our space-time is very different from an ADS universe (see “Anti-de-Sitter universe”).

Information exits black holes in a flash

Nevertheless, the mysterious connection fascinates many physicists. Among other things, it could solve the information paradox of black holes. To do so, one must translate the scenario of a particle falling into a black hole to the CFT side. In the quantum physics picture, the information is not lost. This was not a big surprise at first since quantum mechanics says that information is retained. However, by studying the corresponding quantum system more closely and then transferring it back to the AdS page, physicists were able to track what happens to the information: it is encoded into the Hawking radiation. If the correspondence is correct, the information would not be irrevocably lost, but would slowly escape from the black hole.

In practice, however, it would hardly be possible to recover it. As Hawking found out, one would have to capture every single photon emitted by a black hole during its entire lifetime. “If somehow it were possible to collect all of Hawking’s rays, then in principle there is a calculation that could be used to extract the swallowed information,” says Norman Yao of the University of California at Berkeley. But it is unclear what such a calculation looks like.

Another difficulty is that, according to the theory, black holes do not emit information from the beginning, but only after half of them have evaporated. The reason for this is the particle-antiparticle pairs from which Hawking radiation is generated. The pairs are entangled with each other so that there is a quantum mechanical connection between the black hole into which one of the particles falls and the photons emitted.

Shortly after its formation, only a small area of the black hole is entangled with Hawking radiation. The area continues to grow over time until half of the collapsed star has evaporated. From then on, the entire black hole is connected to the emitted radiation. The photons, therefore, contain information about the interior of the galactic monster. However, black holes only evaporate very slowly — a specimen of the Sun’s mass survives for about 1067 years.

Until 2007, physicists assumed that the swallowed information would seep out at a constant speed after the half-life period. However, Patrick Hayden from Stanford University and John Preskill from the California Institute of Technology refuted this idea. They were able to show that the information would not escape evenly but extremely quickly. “As soon as a black hole has half evaporated, any further information bounces back immediately, like a mirror,” Yao said.

Hayden and Preskill came to their conclusion when they discovered that black holes and certain quantum systems had something in common. This is because galactic monsters behave like an extremely efficient coding system (see glossary): As soon as a particle passes the event horizon, its properties such as mass, charge, momentum, and so on are suddenly mixed with those of all other matter trapped inside. This effect is similar to the way heat in a system is evenly distributed over time when equilibrium is reached — only it happens much faster. As a result, it seems impossible from the outside to ever get the information back. “It’s like a deck of cards,” says physicist Adam Brown of Stanford University. “It is assumed to be shuffled as soon as there is no obvious pattern to the order of the cards. However, this does not mean that the cards are completely randomly arranged.”

Nearly every many-body quantum system will be scrambled at some point, physicists call this phenomenon quantum encryption. One of the most important properties of the process is that it is reversible: it is in principle possible to recover the information in a mixed-up quantum system.

How long it takes for a system to be encrypted depends on how the particles it contains interact with each other. To determine the encryption rate, scientists use a so-called Hamilton operator, from which the most important physical properties of a system can be calculated. Black holes stand out: Their Hamilton operator means that they encode quantum information as quickly as possible (“Spectrum” June 2019, p. 24).

This led Hayden and Preskill to their conclusion. If a particle falls into a black hole, the associated information is mixed with the information inside almost instantly. The resulting Hawking radiation is therefore almost instantaneously entangled with the new state of the black hole so that it also contains the new information.

If the AdS/CFT correspondence is correct, the physicists’ results will provide a solution to the information paradox. However, to get the information from a particle that has passed through an event horizon, one would have to wait until it has half evaporated — a period that far exceeds the previous age of our universe.

Entangled black holes

Therefore, some scientists were not satisfied with the solution. They looked for another way to get the swallowed information — and found it. In 2016, Ping Gao and Daniel Jafferis from Harvard University, together with Aron Wall from the Institute for Advanced Study, wondered what would happen if a black hole were to become entangled with something other than Hawking radiation, for example, a second black hole. According to their calculations, this would allow the information that falls into the first collapsed star to be read out of the second. If all the matter of the galactic monsters is entangled, researchers say that a qubit swallowed by the first black hole would be registered almost immediately in the second.

When Gao and his colleagues examined the hypothetical process in more detail, they noticed that under certain circumstances it resembles teleportation. As early as 1997, physicists succeeded in teleporting a particle successfully in the laboratory for the first time. To do so, they exploited the properties of entanglement: They created two entangled particles and transferred the quantum state of the first to the second. Afterward, the second particle is no longer distinguishable from the original first particle. Such an event is identical to the one in which the first particle is destroyed at one location and instantly appears at a different location — teleportation.

If a particle falls into a black hole that is entangled with another, it is teleported into the second collapsed star as quickly as possible. This is because the information in the first black hole is shared at maximum speed by all the particles in it. But because the black hole is coupled to the second, the latter receives almost instantaneously all the information about the swallowed particle.

This is how quantum information theorists interpret the process. However, if the AdS/CFT correspondence is taken seriously, the channel between the entangled collapsed stars corresponds to a wormhole. In this view, the qubits travel through a shortcut in spacetime.

Quantum mechanical circuit of entangled, ultracold ions

Although wormholes are consistent with the general theory of relativity, it was previously assumed that they could not be traversed: If they existed, nothing could be sent through them. In their work, however, Gao, Jafferis, and Wall were able to show that the AdS/CFT correspondence allows passable wormholes.

If the correspondence is correct, there is no need to deal directly with entangled black holes in the AdS image. Instead, researchers can use quantum systems on the CFT side that are completely equivalent. Nezami and Brown have now worked with the renowned string theorist Leonard Susskind from Stanford University, among others, to devise a way to implement such an experiment.

To do this, they have been looking for a quantum system whose Hamilton operator corresponds to that of a black hole into which a qubit of information falls. Because collapsed stars mix information as quickly as possible, a comparable quantum coding system would have to be created in the laboratory.

Physicists demonstrated such a mixing of qubits in the laboratory in early 2019. At the suggestion of Yao and his colleague Beni Yoshida, Christopher Monroe and his team in Maryland created a quantum mechanical circuit of entangled, ultracold ions. The researchers used electromagnetic traps to trap the particles so that the ions were arranged in a row.

One of the greatest challenges of the experiment was to distinguish quantum encryption from other processes. Because it is impossible to completely seal off a system from the external environment, decoherence always occurs in experiments with microscopic particles, for example. Like encryption, this effect occurs when particles interact with each other. In the case of decoherence, the particles interact with particles from the environment, whereby the information of the quantum system slowly escapes and is thus irretrievably lost.

This is the big difference between decoherence and encryption: the latter can be reversed. In practice, decoherence can never be completely avoided, which makes it the specter of quantum computers. To ensure that the results delivered are correct, every calculation must, therefore, be completed before the phenomenon sets in.

Ultracold quantum systems as wormholes

Normally, a quantum system begins to interact with its environment before encryption can occur. This makes it so difficult to detect the latter within a system. But Monroe’s team found out that both effects can be distinguished from each other through quantum teleportation.

To do this, the researchers used a circuit consisting of seven entangled ytterbium ions arranged in a row. They split the system into two parts with three ions each; the remaining particle was later used for teleportation. By deliberately disturbing both subsystems in different ways, they mixed the information contained in them. Now all they had to do was prove that the quantum states of the subsystems were encoded — and that they had not caused decoherence.

To do this, they teleported the remaining particle from one end of the ion series to the other and back again. At the beginning of the experiment, all particle states were entangled with each other, so at that time teleportation was possible. The perturbation, however, mixed up the states — if decoherence had started, some of the information would have disappeared. In this case, therefore, the particle could not be teleported. If, on the other hand, the information is still present in the system, but only mixed up, the process can succeed because all states are intertwined. The researchers were able to teleport the ytterbium ion successfully in 80 percent of cases. This enabled them to experimentally demonstrate quantum encryption for the first time.

Brown and his team now suggest that similar quantum-mechanical circuits could be used to recreate a passable wormhole that teleports a qubit from one black hole to another. The black holes would consist of entangled ions. A qubit would then have to be introduced into one of the systems, which would encrypt it. After a certain period, the information would reappear unencrypted in the second quantum system. It is not surprising that the qubit is transmitted across the systems — after all, the ions are coupled together. What is surprising, however, is that the information in the second system does not need to be decrypted, even though the first black hole had completely mixed it.

When the theoretical physicist Brian Swingle from the University of Maryland talked to his colleague Monroe about such an experiment in October 2019, the latter realized that the setup required for it was more or less the same as the one he and his team had used to prove the quantum encryption. The experiment described by Swingle could thus be realized.

However, as impressive as such an experiment would be, it could not currently imitate the space-time of our universe. Instead, the quantum systems would correspond to a simplified model of the cosmos, namely an anti-de-Sitter space. “To simulate a realistic universe governed by Einstein’s equations, you need systems that are very difficult to build in the laboratory,” says Maldacena.

If the results of the proposed experiment confirm the researchers’ predictions, it does not necessarily follow that the AdS/CFT correspondence is correct. This is because such an experiment can just as well be viewed from a purely quantum-physical perspective — one does not necessarily have to use the holographic principle to predict the outcome of the experiment. Nevertheless, some of the predicted phenomena are easier to describe through the correspondence, for example, the teleportation of a particle, than a passage through a wormhole. “While it would be possible to deduce all this using the Schrödinger equation, there is a much simpler explanation based on black holes,” says Brown.

It’s hard to believe that the collapsed stars are related to a handful of cooled ions. However, if the AdS/CFT correspondence proves to be correct, then the quantum systems would be more than the analog of a black hole — they would be completely equivalent.

Glossary

Microscopic particles can be entangled with each other. This means that the state of one depends directly on the state of the other. Thus, entangled systems influence each other almost instantaneously.

The event horizon of a black hole corresponds to a distance at which an object can no longer escape the collapsed star. Even massless photons are irretrievably sucked into the black hole at this point.

When information — for example in the form of a qubit — falls into a black hole, it is encoded: Properties such as mass, energy, or charge mix so strongly with those of the rest of matter that it seems impossible to ever get at the information again.

Decoherence occurs when a quantum system interacts with its environment. The original state of the system changes as a result, and the information initially contained in it is irretrievably lost.