# What Sonic Black Holes Can Teach Us About the Information Paradox

By now, just about everyone knows about black holes: the all-consuming regions in outer space that are so dense that not even light can escape from their mysterious interior. But those are only one kind of black hole, even if they are the most famous of the bunch.

There can be other kinds of black holes that trap other physical phenomena, like sound waves, and these kinds of black holes, known as sonic black holes, might be critical to understanding their light-consuming counterparts in the wider universe.

Most important of all, what can sonic black holes tell us about one of modern physics' most contentious debates, the so-called Information Paradox? A recent study attempted to find out, and its results seem to make the problem more complicated, not less.

## What is the Information Paradox?

One commonly-known understanding about black holes is that whatever falls into a black hole doesn't come back out, not even light. But in 1971, physicist Steven Hawking proposed an interesting theory, which set off a series of discussions that changed the way physicists looked at black holes. He predicted that the total area of a black hole’s event horizon would never decrease. This statement is similar to the second law of thermodynamics, which states that the entropy, or degree of disorder within an object, should also never decrease.

Hawking's theory suggested that black holes could behave as thermal, heat-emitting objects — in contradiction to the normal understanding of black holes as objects which never let energy escape. In 1974, Hawking proposed a solution to this contradiction by showing that, over exceptionally long timescales, black holes could have both entropy and emit radiation by taking into account their quantum effects. This phenomenon was dubbed “Hawking radiation”.

Hawking argued that black holes were actually acting as an idealized black body in space that absorbed all wavelengths of light, but which emitted energy called black body radiation, or Hawking radiation, all along the event horizon.

That is because of virtual particles — matter and anti-matter particles that momentarily spawn in space out of nothing and due to their proximity to each other — immediately annihilate each other and release the energy used to produce them in the first place. This maintains the vital law of thermodynamics that states that the energy of a closed system (the universe) must remain constant.

But, if a pair of virtual particles spawn along the edge of an event horizon, one of the two particles will get sucked into the black hole, while the remaining particle survives and flies away into space as a form of energy known as Hawking radiation.

You can see the problem, right? The universe just took some of its energy and created matter out of nothing, but didn't get that energy back.

The only way Hawking radiation could be allowed to exist mathematically is if the in-falling particle actually had negative energy equal in magnitude to the positive energy used to create the two particles, thereby preserving the universe's total energy.

This leads to another problem though, as that particle falling into the black hole is now a part of it, and so the negative energy balance of the particle is taken out of the energy of the black hole.

It might be slight, all things considered, but if a black hole doesn't accrete any additional material to itself, all of those infinitesimally small energy deductions will start reducing the black hole's mass. Given enough time, the black hole actually evaporates out of existence.

You might be asking why that's a problem — after all, that's one less black hole to accidentally run into out there — but the problem is that particles aren't just matter, they also carry quantum information, such as position, spin, and velocity.

Quantum mechanics as we know it requires that this information, just like the energy of the universe, must be preserved. It might be scrambled beyond all recognition, but there's nothing in physics that says you can't go back and undo that scrambling and reclaim that information — unless it was either inside a black hole or encoded into its event horizon when that black hole winked out of existence, thus taking that information with it.

What happens to that quantum information is the heart of the Information Paradox, and physicists and philosophers have been trying to untangle it ever since to no avail.

## What are sonic black holes?

To understand a sonic black hole, let's review the physics of a traditional black hole in space. Gravity is the warping in the fabric of spacetime that is caused by an object's mass. That warping can be envisioned as a sloped well with the object at the bottom, pulling down and stretching the fabric below the plane of unaffected space-time.

In order to climb out of that well, you need to reach a certain speed, known as escape velocity. So, in order to escape the gravity well of Earth, you need to travel about 6.95 miles per second (11.19 m/s), or a little over 25,020 mph (about 40,270 km/h). Anything less, and you'll fall back down to Earth eventually.

The only thing that makes black holes different in this sense is that a black hole's escape velocity exceeds the speed of light. So, like a rocket that is only going 6.8 miles per second, light can get very high up the slope of a relatively small black hole's gravity well, but just not enough to get fully out of it.

In effect, the light would enter into a decaying orbit as it slowly spirals back down the center, like a bit of dirt caught in the whirlpool at the bottom of a drain in a bathtub. The more massive the black hole, the higher the slope of that well, so that light might barely be able to climb it at all.

A sonic black hole then, is this exact same phenomenon, except where the escape velocity of an object exceeds the speed of sound, rather than the speed of light. Fortunately, the speed of sound is much, much lower than the speed of light, so at sea level with a temperature of 59 degrees Fahrenheit (15 degrees Celsius), sound travels at 761 miles per hour (about 1224.74 km/h).

All an object (at sea level and at 59 degrees Fahrenheit) would need is an escape velocity infinitesimally greater than 761 miles per hour and it could prevent sound from escaping its event horizon, just as sure as its space-dwelling counterparts trap light.

## How are sonic black holes and black holes in space analogous?

Since sonic black holes and light black holes both have this basic property around their escape velocities, there is a lot of interest around whether we can use sonic black holes to effectively model the light-consuming black holes we find in space.

This is especially important since it's impossible to actually measure Hawking radiation, since we'd be talking about individual photons appearing just outside an event horizon. These would be too faint to ever detect without, say, surrounding a black hole in a super-cold Dyson Sphere-like detector that blocks out any outside radiation and which emits less energy than the black hole does itself.

So, the only way to really test for Hawking radiation is to find analogies that we can actually create and measure, which is where sonic black holes come in. Since a sonic black hole with its own event horizon for sound energy *is* something that we can create in a lab, can it give us insight into Hawking radiation?

A key feature of these sonic black holes is that they are just as immersed in the quantum field of the universe as a supermassive black hole at the center of a galaxy, so virtual particles will be constantly popping in and out of existence throughout, including phonons, which are quantum units of sound equivalent to light's photons.

An Israeli research team created one such sonic black hole using about 8,000 rubidium atoms cooled to nearly absolute zero and trapped in place with a laser beam to create a Bose-Einstein Condensate (BEC), in which atoms become so densely packed they behave like one super atom.

The team then used a second laser beam to create an effective event horizon, where one half of the BEC was flowing faster than the speed of sound, while the other half moved slower.

## What do experiments with sonic black holes reveal?

What the team from Technion in Haifa, Israel, led by Jeff Steinhauer, found is that pairs of phonons (quantum sound waves) did in fact appear on either side of the sonic event horizon, with the pair in the slower half getting swept away from the "event horizon" and the phonon on the faster half became trapped by the speed of the supersonic flowing BEC, just as Hawking predicted a photon would from the event horizon of a black hole in space.

In a study the team published in January 2021 in the journal *Nature*, the team reported that they observed spontaneous Hawking radiation at six different times after the formation of the sonic black hole, and verified that the temperature and strength of the radiation remained constant. The evolution of the Hawking radiation throughout the life of the sonic black hole also compared to the predictions for real black holes. The experiment provided experimental support to Hawking’s analysis.

However, an inner horizon formed within the sonic black hole, in which the sound waves are no longer trapped. This inner horizon stimulated additional Hawking radiation, beyond the spontaneous emission. This phenomenon was not included in Hawking’s analysis.

Not everyone is convinced that the two types of black holes are truly analogous, however.

A key point of contention is that Hawking speculates that all along the event horizon of a black hole, spacetime can be considered smooth; this is essential for the creation of Hawking radiation.

If spacetime around the event horizon is not smooth, however, quantum-scale variations could be encoding information into Hawking radiation in ways we can't detect.

What's more, the fact that sonic black holes and the Hawking radiation they produce behave a certain way does not prove that the light-trapping black holes in space that they are attempting to model will also behave in the same fashion.

In the Steinhauer team's recent experiment, the sonic black hole collapsed every time they took a picture, due to the heat created in the process (the team repeated their experiment 97,000 times over 124 days to come up with the results in their paper). The rubidium atoms didn't disappear in the collapse, though; they remained, as did whatever quantum information the infalling phonon imprinted on them. This information can still, theoretically, be extracted even now.

What's more, even though a sonic black hole behaves the same way in one regard, the creation of an event horizon that produces a form of Hawking radiation, it might be too reductive to say that sharing a surface-level characteristic makes the two identical on more fundamental levels. A collection of 8,000 rubidium atoms in a BEC is not the same thing as a spacetime singularity of infinite density where physics as we know it breaks down. An analogy is just an analogy, after all.

## What does it mean if information is truly destroyed in a black hole?

Still, this recent experiment does provide some evidence that information that falls into a black hole is permanently lost when the black hole evaporates from Hawking radiation, so that raises the question of what would happen if this fundamental premise of quantum mechanics turned out to be incorrect?

A key principle of classical physics is that having a perfect knowledge of the state of all the particles of the universe should give you the ability to predict the future state of the universe at any given point in the future (at least theoretically).

Physics does *not* require that having such perfect knowledge of a current state gives you that same predictive ability about the past. If two different states (A and B) both lead to the same state (C), then you can know that having A and B will give you C and C, but having C by itself can't tell you whether you started with A, with B, or with both. That quantum information would be lost forever when A and B make the transition to state C.

Quantum mechanics forbids this loss of information, however, owing to the principle of unitarity, which essentially means that all probabilities of any given quantum state must sum to 1.

If we look at a six-sided die, the probability of getting a value between 1 and 6, inclusive, are all 1/6. But the probability of getting *any *value is 1, which is the sum of all six probabilities of 1/6.

A six-sided die can't also become a five-sided die simply because it is rolled, all six sides of the die must remain intact during the transition between quantum states, so that two quantum states cannot become the same quantum state, they must remain separate and distinct.

Losing quantum information then is like taking one of those probabilities off the board, so rather than adding six values of 1/6 together, you add five of them and end up with 5/6 rather than 1. If this were possible, then the Schrodinger equation is wrong, the wave function is wrong, essentially the entire foundation of quantum mechanics is a lie and nothing is as it appears to be, even if a century of work in quantum mechanics tells us otherwise.

This is why the Information Paradox is such a thorny problem, since even though something as simple as permanently losing the knowledge of the spin of a virtual particle as it falls into a black hole might not seem like it should matter, it alters and unbalances the probabilities of the universe that quantum mechanics relies on, turning it from science to just really good guessing, and no one likes being told that they're just making stuff up.

There have been all sorts of proposed solutions to the information paradox over the years, and none have really settled the issue. Sonic black holes aren't likely to do so either, though they're still a pretty cool attempt regardless.

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