IMAGINE lying in a giant bathtub when someone pulls the plug. Sliding towards a watery exit from this world, it gets worse. The fluid gathers pace to supersonic speed and you realise no one can even hear you scream. Your sounds are transported with you down the drain, lost to the bathtub for all time.
It is the stuff of surrealist nightmares – and a pretty fair description of what happens to an atom or a photon of light as it crosses a black hole’s event horizon. Black holes famously devour anything that comes too close: light, matter, information. In doing so, they cause some almighty headaches for our best theories of physical reality.
Or do they? Although we are pretty certain black holes exist, we’ve never observed one directly, let alone got up close and personal. That’s where the bathtub analogy is now coming into serious play. Get fully to grips with it, and we could have a new way not just to fathom black holes, but also to crack some of cosmology’s other toughest nuts – from why the expansion of the universe is accelerating to how it all began.
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There’s a catch, naturally. To make the analogy real, we can’t use any old water from the tap. It takes a fluid so extreme and bizarre that it was fabricated for the first time just 20 years ago, and only exists within a whisker of absolute zero, the lowest temperature there is. With that magic ingredient, you can begin to make a superfluid sonic black hole.
Black holes are the most mysterious of the many predictions made by general relativity, Einstein’s theory of gravity that he formulated just over a century ago. General relativity is a peerless guide to the workings of gravity, but puts gravity at odds with the other known forces of nature. Unlike them, gravity is not caused by the exchange of quantum particles; instead, massive bodies bend space and time around them, creating dents in the fabric of the universe that dictate how other bodies move.
The world according to general relativity contains some shady spectres – invisible dark matter to explain why galaxies whirl at the speeds they do, and dark energy to explain why the expansion of the universe is accelerating. The theory also fails completely when you wind the universe back to its first instants and the big bang. Here, it predicts a seemingly nonsensical “singularity” of infinite temperature and density.
“It is an entirely different state of matter beyond solid, liquid and gas”
Still, black holes take the biscuit. We now think these impossibly dense scrunchings of mass exist across the cosmos – where massive stars have collapsed in on themselves, and at the heart of galaxies including our own.
For all their heft, however, black holes seem strangely tenuous, at least in theory. In 1974, physicist Stephen Hawking used quantum rules to show that all black holes must eventually evaporate, apparently destroying any information they might have swallowed, a physical no-no.
According to quantum physics, space-time is a roiling broth of particles and their antiparticles that pop up spontaneously in pairs, disappearing again almost instantaneously. But when such a pair pops up at the edge of a black hole’s event horizon – the point beyond which nothing can escape its gravity – sometimes one will have the energy to whizz away, while the other falls in. By the law of conservation of energy, this second particle must have negative energy, causing the black hole to slowly lose its oomph and evaporate. The signal this is happening is a faint stream of escaping partner particles – Hawking radiation.
In theory at least, Hawking radiation has a temperature: the smaller the black hole, the warmer it is. For a black hole 30 times the mass of our sun, it is a titchy nanokelvin or so, impossible to measure in the chaotic surroundings of an astrophysical black hole. Hopes were high that the Large Hadron Collider at CERN near Geneva, Switzerland, might produce mini black holes with measurable Hawking radiation – but not a peep. “This is a pity, because if they had, I would have got a Nobel prize,” Hawking said in a BBC lecture this February.
Wind back to 1981, however, and physicist William Unruh of the University of British Columbia in Vancouver, Canada, was thinking of ways to study Hawking radiation. It led him to some strange parallels between the “metric” – a mathematical construction in general relativity that expresses the geometry of space-time – and equations used to describe superfluid flow.
Unruh showed that the equations governing such flow at supersonic speed mimicked the metric of space-time around a black hole. This implied a superfluid could create a black hole that would trap “phonons” of sound, just as an astrophysical black hole traps photons of light. It’s the surrealist nightmare, with an added twist. Just as with an astrophysical black hole, quantum fluctuations would make a sonic black hole emit Hawking radiation – but made of phonons, not photons.
Unruh realised this could be just the thing to test Hawking’s idea. Prove the radiation exists in one situation, and the mathematical mirror provides a pretty good indication that it does in the other.
He was rather ahead of the times. Although the first superfluid state was created in liquid helium in the late 1930s, for a sonic black hole the fluid had to be flowing faster than the speed of sound in that fluid – in superfluid helium, that’s hundreds of metres a second. Experimental verification of Unruh’s idea would have to wait.
Then, in 1995, came a Nobel-prizewinning development: the creation of the first Bose-Einstein condensates (BECs). This is an entirely different state of matter beyond solid, liquid and gas, made up of collections of atoms cooled down to temperatures so low, sometimes a few nanokelvin above absolute zero, that the individual atoms lose their identity. They occupy the same quantum state, and behave and flow as one.
Sonic event horizon
Creating this extreme, bizarre form of superfluid was an experimental tour de force, and came with an important detail as far as the black hole story was concerned: in a BEC, the speed of sound is just millimetres a second. Sonic black holes suddenly looked feasible.
, a theorist at the BEC Center in Trento, Italy, was initially a sceptic. But returning from holiday in 2005, he found himself sitting next to a college friend on a train who turned out to be a gravitational physicist, and the two got talking shop. The friend introduced Carusotto to , an expert on general relativity at the University of Bologna. These two started to build computer models of sonic black holes that took into account factors such as how the speed of sound varies according to how a fluid is moving, its temperature, the wavelength of the phonons and so on.
Carusotto still has the first image spewed out by the simulation in 2008 hanging on the wall in his office. “I jumped off my chair,” he says. It shows that as a Bose-Einstein condensate starts flowing at supersonic speeds, a sonic event horizon forms and phonons of Hawking radiation spontaneously appear. “To see it so precisely in agreement with theory was a great surprise, and a great success,” says Carusotto.
, an atomic physicist at the Technion-Israel Institute of Technology in Haifa, was the man who could make the analogy an experimental reality. He had developed some crucial tools: a way of measuring a condensate’s temperature to an accuracy of a nanokelvin, and complex systems of adjustable magnetic fields to stop condensates sagging and being disrupted under the effect of real gravity. By 2009, he was able to use lasers to accelerate a long, thin stretch of condensate to supersonic speed. The result was the first sonic black hole with an event horizon ().
Measuring individual phonons to verify the existence of Hawking radiation proved more tricky. In 2014, Steinhauer reached a halfway house by accelerating a thin condensate stream to supersonic speed and then allowing it to slow again. This created the equivalent of two event horizons – a black-hole horizon from which no sound could escape, and a “white-hole” horizon into which no sound could enter. In such a situation, Hawking phonons produced by the black hole bounce between the two horizons, producing more and more Hawking radiation in a similar way to how light is amplified in a laser.
And amplified radiation is certainly what Steinhauer saw. “It was very exciting to suddenly see this effect,” he says. “It was very gratifying to think that the physics Hawking predicted was creating it.” The question raised by Carusotto and others since is how to tell for certain whether the initial phonon was created by spontaneous, random quantum fluctuation rather than some classical process. Final confirmation could be coming soon: Steinhauer currently has a paper under peer review in which he reports seeing unadorned Hawking radiation from a single sonic horizon ().
Steinhauer himself wouldn’t discuss this work further, but theorist of the International School for Advanced Studies in Trieste, Italy, is excited. “If this result is confirmed, it’s definitely a major breakthrough,” he says. “It would be the first experimental detection of Hawking radiation.”
Whether it’s enough for Hawking to get his Nobel prize remains to be seen, but Liberati thinks this work is just the beginning. Not only might sonic black holes illuminate further mysteries of the real thing (see “What are black holes made of?“), but get superfluids flowing in different ways and you can create other space-time geometries that equate to other cosmological problems. One is the exponential expansion of the universe in the period known as inflation, thought to have occurred immediately after the big bang. Current cosmological theories predict that during this phase, the quantum fluctuations of space-time also got stretched, eventually giving rise to the particles we see everywhere today. We can’t test this idea directly, but Liberati and his colleagues have shown how a similar situation implemented using a condensate should give rise to phonons. “You should be able to reproduce the salient features of cosmological particle creation,” he says.
One way of doing this involves using lasers or magnetic fields to suddenly compress a condensate, thus changing the speed of sound within it. This creates an analogy to the change in light’s travel time between two points in space as the universe expands. In 2012, and his colleagues at the Charles Fabry Laboratory at the University of Paris-Sud in France did just that and saw indirect effects of phonon creation – although the experimental temperature of 200 nanokelvin was still too high to rule out thermal fluctuations as the source.
Liberati suggests that a similar analogy could provide clues to another huge cosmological conundrum, dark energy. The peculiar problem of dark energy is not so much that it exists. General relativity allows for a “cosmological constant” that represents the energy of empty space and whose effect would be to expand space ever faster, just as dark energy is thought to do. But calculating the value of this constant from observations gives a number 10120 times smaller than the value you get from quantum field theory.
Again, Bose-Einstein condensates could hold the answer. In a condensate, not all the atoms that you cool down end up in the lowest-energy condensate state: you never get a perfect condensate. What’s more, these stragglers “backreact” with the condensate, an interaction that appears in the equations in a similar way to the cosmological constant.
“The superfluid analogy might provide clues to the cosmic conundrum of dark energy“
To Liberati, this is suggestive of the real nature of dark energy, and space-time itself. What if the fabric of the universe, and hence gravity, emerge from some as-yet-unknown “atoms” of space-time, just as a superfluid state emerges from normal atoms when they are cooled? If some of these atoms are left over and do not form the basis of space-time, then their backreaction with those that do could reduce the value of the cosmological constant to match what astronomers find.
In this view, the equations of general relativity might just be a high-level picture that emerges from a more fundamental description. In fluid dynamics, the set of equations known as Euler’s equations similarly describes the flow as a whole, but not the molecular interactions that underlie it. “It’s teaching you a very important lesson,” says Liberati. “If gravity is emergent, the only way you can calculate the cosmological constant is by knowing the fundamental system from which gravity emerges.”
The quest for a more fundamental picture of gravity is central to the search for a “theory of everything” that will finally unite all the forces of nature, gravity included. So far, convincing answers have been thin on the ground – in part because we have lacked any way to test ideas experimentally. In that sense, listening carefully to sounds swirling through superfluids could be the stuff of physicists’ dreams, rather than their nightmares. “It’s a success story,” says Liberati. “It’s a case in which theoretical physics finally made connection with experiments.”
What are black holes made of?
For all we know, it could be snails and puppy-dog tails. There is no microscopic theory of a black hole’s innards, but Georgi Dvali of the Ludwig Maximilian University of Munich, Germany, thinks we might find clues in parallels between how black holes and Bose-Einstein condensates process information.
Black holes are careless stewards of information, apparently dribbling it away as they evaporate (see main story), but they are efficient stores of it. It would take about 10-5 electronvolts of energy to stuff one quantum bit of information into a cubic-centimetre box. To stuff that qubit into a black hole of the same size – which would have the mass of Earth – would take 1066 times less energy, says Dvali.
Intriguingly, Dvali and his colleagues have shown that Bose-Einstein condensates seem to process information similarly to black holes. “There is a one-to-one correspondence,” he says. “In particular, the system delivers very cheap qubits for storing information.”
Bose-Einstein condensates exist in a so-called quantum-critical state, transitioning from a normal state to one in which all the atoms act as a coherent quantum whole. Dvali speculates that the parallels indicate that black holes are quantum-critical states too – albeit not of atoms, but of quantum particles of gravity known as gravitons.
This article appeared in print under the headline “The hole story”
