For as long as we have tried to figure out the nature of reality, we have grappled with the concept of empty space. Around 400 BC, when the ancient Greek philosopher Democritus conceived of small, indivisible bodies called atoms, he supposed there must also exist a void surrounding them: a featureless, unchanging vacuum in which they moved.
Today, the void remains a potent idea for understanding the universe, but we have come to realise that it is anything but featureless. More than a century ago, Albert Einstein’s theory of gravity revealed that space-time is stretched and warped by the matter it contains. Later, quantum theory introduced the idea of virtual particles, which momentarily appear and disappear in a vacuum, making pure nothingness seem like an intangible, bubbling soup.
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This alone would surely have shocked Democritus, but I believe we should go further still. I have spent four decades trying to find a way to combine Einstein’s theory of gravity and quantum mechanics. This long journey has led me to a startling conclusion: there is another rich structure hidden within the void, which can be traced to ethereal entities called virtual black holes.
The influence of these stretches across the entire cosmos, linking space-time in subtle ways that ultimately cause Einstein’s theory to fail – forming a bridge between the smallest scale of the quantum realm and the cosmic one of gravity. Enticingly, I have now begun to grasp how this hidden property of space-time may be the source of dark energy, the mysterious force that is tearing the universe apart and that has long puzzled physicists.
To begin unpacking all this, let’s begin with black holes as described by Einstein’s theory of gravity, general relativity. These behemoths form when a star exhausts its fuel and suffers a runaway collapse. All the star’s mass gets sucked to a point of infinite density around which the vacuum of space-time forms a deep pit. From this, even light cannot escape. The boundary of this dark region, called the event horizon, can be quite large: if the sun could collapse to a black hole, the horizon would be about the size of a small city.
We know plenty about black holes; we even recently took photos of one specimen’s exterior, which confirmed the shape of the boundary that is formed by the vacuum of space-time, as predicted by general relativity. But if we could look beyond the event horizon, I believe we would find that general relativity breaks down and quantum physics takes over. That is because our most cherished principles of physics are incompatible with the deep pit predicted by Einstein’s theory.
Black hole paradoxes
The chain of reasoning for this started in 1973, when Jacob Bekenstein at Princeton University posed a question: what would happen if we ? The gas has entropy, a measure of the disorder arising from the random positions of its atoms. So when the box disappears into the infinite-density centre of the black hole, he reasoned, this entropy seems to be lost. But the second law of thermodynamics, one of the fundamental principles of physics, says that entropy can’t do this.
Bekenstein suggested that the loss of entropy in the box of gas was compensated for by an increase in the overall entropy of the black hole. When the black hole swallows the box, its event horizon expands to occupy a larger area, and he argued that the entropy of the black hole is proportional to this area. But Bekenstein’s black hole entropy was puzzling in several ways. First, in general relativity, a black hole is an empty vacuum, so what is the nature of the disorder? Second, the magnitude of this entropy was surprisingly large. Third, if a black hole has entropy then, like a piece of hot coal, it must also have a temperature and consequently it radiates particles. Yet according to general relativity, nothing can escape a black hole.
Stephen Hawking was among the physicists who tried to make sense of all this. In 1974, he made an amazing discovery: when we include the effects of quantum theory, a . Hawking found that pairs of virtual particles pop into existence around the event horizon of a black hole. The stretching of space-time there, as described by general relativity, turns these into real particles. One falls into the back hole, but the other escapes in what’s known as Hawking radiation.
Alas, the excitement of his discovery was short-lived. The next year, Hawking found a . Suppose we take two black holes with the same mass, but formed from stars made up of different kinds of atoms. The shape of space-time around the horizon would be the same in each case, and so the radiation emerging from this vacuum would also be the same. Since we can’t use this radiation to differentiate between the stars, we have lost information to the black holes. This was a problem because physics works on the basis that information can’t be destroyed.
Ever since, theorists like me have desperately tried to find a way for information to escape a black hole. There have been several proposed resolutions in recent years, but I believe string theory offers the most compelling way forward. Not only can it resolve Hawking’s so-called black hole information paradox, but mulling it over more deeply has led me to some very intriguing ideas.
String theory is the idea that point-like elementary particles are, on closer inspection, extended objects made of one-dimensional strings (and “sheets” of varying dimensionalities called branes). It aims to unify quantum mechanics with gravity into a single theory of quantum gravity. In the mid-1990s, string theorists showed that a simplified general model of a of strings and branes would have the entropy predicted by Bekenstein. Soon after, in work done with , then at the Tata Institute of Fundamental Research, India, I used a similar approach to calculate that such objects would . All this suggested we were on the right track to resolve the information paradox.
But we still had no idea about the form that particular black holes made from strings would take or how exactly they would store their entropy. By now I had spent almost a decade fighting with this problem, only to come up against the same wall each time. It was generally assumed that strings only had effects at the minuscule scale of the Planck length (1.6 × 10-33 centimetres), where both quantum theory and gravity become important. So how could strings possibly describe a vast black hole?
On the night of 29 May 1997, I was at a hospital keeping watch over my newborn daughter. To while away the hours, I tried to strings and branes came together to make a black hole. The result was a shock. Its size was enormously magnified by the large number of strings and branes. Black holes made of stretchy strings were behaving very differently from black holes made of particles. When you squeeze strings, they , as general relativity tells us, but they instead fluff up. The energy goes into stretching the strings out into tangles, called fuzzballs, that extend up to the black hole’s event horizon.
Later on, with my colleague , then at The Ohio State University, we based on these ideas – work that was later extended to all kinds of black holes by at Paris-Saclay University, France, and at the University of Southern California, among others. Each one of these stringy black holes can be organised in one of many different possible fuzzball shapes. This is similar to the way that in a box of gas there are many ways to arrange the gas molecules.
There are virtual fuzzballs of all possible sizes, from zero to infinity
This seemed to answer the puzzle of where a black hole’s entropy was being stored: it lies within the multitudinous fuzzball shapes that comprise each black hole. More importantly, fuzzballs solved the information paradox by allowing information to leak out. In Hawking’s paradox, random radiation comes out of the vacuum, but in the fuzzball picture, radiation is emitted from the stringy surface. This .
But there was still a critical, unresolved question: how does a collapsing star turn into a fuzzball? According to general relativity, which has stood up to every test thrown at it so far, a collapsing star should leave a vacuum shaped like a deep pit, rather than a fuzzball. So what causes Einstein’s theory to fail – making way for a theory of quantum gravity?
How general relativity fails
The answer, coming from string theory, reveals a secret structure within the vacuum that changes our understanding of space-time in a fundamental way. What follows may sound like a just-so story, but the maths and physics underpinning this idea aren’t fiction. It has been thoroughly examined and is feasible, theoretically speaking.
To understand how it works, we need to take a closer look at virtual particles. It is often said that these ephemeral counterparts of real particles pop in and out of existence, and indeed I have used that phrasing myself for convenience. But in truth that isn’t a good way to think of them. Quantum physics paints all matter and energy as just fluctuations in the quantum fields that undergird all of reality. It is best to think of virtual particles just as very tiny disturbances in these fields. Like real particles, these virtual particles can be correlated with each other. For example, an electron and its antimatter partner the positron attract, orbiting each other as a “bound state”. Likewise, virtual electrons tend to occur closer to virtual positrons, correlated through the strange phenomenon of quantum entanglement.
In this way, bound states of real particles leave an imprint in the structure of space-time: an intricate web of virtual correlations. Most of them operate at too small a scale to have any meaningful effect on black holes. But could there be other bound states whose virtual versions affect black holes and, perhaps, the entire cosmos?
I believe so. As we saw earlier, there are good reasons to think that black holes are fuzzballs made of strings. Strings are akin to elementary particles, which means that there are also virtual versions of these stringy bundles called virtual fuzzballs – which we could call virtual black holes. As far as we know, black holes can exist in any size from zero to infinity. So there are also virtual black holes of all possible sizes. What’s more, there is a vast number of them due to the very large Bekenstein entropy. So, in the same way that virtual particles imprint a subtle web of correlations through the vacuum over very short distances, virtual fuzzballs do likewise, but across all possible distances, however large.
These correlations may be subtle but they have huge implications. To see them, let’s now apply these ideas to the question I raised earlier: how exactly does a collapsing star form a black hole?
Well, during this process, space-time stretches. This means that the correlations created by virtual fuzzballs across the cosmos must alter the strength of their entanglement to reflect their new separations. This readjustment requires physical signals to be exchanged across the black hole region. But in the area created by a collapsing star, where space-time is being radically stretched, signals can’t connect without travelling faster than light, which is forbidden by general relativity. As a result, quantum fluctuations in the pit-shaped region are unable to develop the correlations required to form a stable, low-energy vacuum. Instead, these fluctuations effectively tie space-time in knots until it shatters. The result isn’t a stretched vacuum, but a stringy fuzzball mess.
In short, general relativity fails when space-time stretches too fast. Similar reasoning suggests that Einstein’s theory should also fail across the largest spans of the expanding universe – which is like a collapsing star in reverse. It takes too long for signals to be exchanged between two points in the vacuum separated by billions of light years. So, once again, virtual fuzzballs cannot imprint space-time with the correct correlations across these distances. This means that the cosmos isn’t a perfect vacuum on these scales, but carries extra quantum energy. When I ran the maths in published in December, I found that the relevant scales are exactly those at which we observe the effects of dark energy.
The origin of dark energy
Astronomers first postulated dark energy in the late 1990s when they found that distant exploding stars called supernovae were consistently fainter than expected. They figured out that these supernovae must be much further away from us because the intervening space was stretching. In other words, there was a mysterious force pushing the universe apart ever faster at its furthest reaches. To account for this, cosmologists stuck dark energy into the equations of general relativity, but with little idea about its origin. But now it appears that the extra quantum energy generated by virtual fuzzballs could be driving this expansion.
Recent observations back up this idea further. The Hubble tension is a discrepancy between how fast the universe seems to be expanding and how fast we expect it to do so based on our best model of cosmology. The mismatch can be resolved by postulating a sudden sharp burst of additional dark energy – called early dark energy – billions of years ago when the universe changed from mostly radiation to mostly dust. Virtual fuzzballs suggest a natural explanation for early dark energy: the equations of cosmic evolution tell us that a dust universe expands faster than a radiation one, and the faster the universe expands, the harder it is to form correlations between virtual fuzzballs. Once again, this yields an extra burst of quantum energy, this time at the transition from radiation to dust, which in this case is the right size to resolve the Hubble tension.
Telescopes like the Dark Energy Spectroscopic Instrument are beginning to precisely measure dark energy and how it might change over the course of cosmic history. My hope is that soon we may be able to match these precise observations with the behaviour of dark energy that emanates from the secret structure of space-time.
