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The Math of Consciousness: Q&A with Kobi Kremnitzer
A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

Can We Feel What It’s Like to Be Quantum?
Underground experiments in the heart of the Italian mountains are testing the links between consciousness and collapse theories of quantum physics.

The Thermodynamic Limits of Intelligence: Q&A with David Wolpert
Calculating the energy needed to acquire and compute information could help explain the (in)efficiency of human brains and guide the search for extra-terrestrial intelligence.

Gambling Against the Second Law
Using precision thermometry to make mini heat engines, that might, momentarily, bust through the thermodynamic limit.

Mind and Machine: What Does It Mean to Be Sentient?
Using neural networks to test definitions of 'autonomy.'

May 26, 2022

Fuzzballs v Black Holes
A radical theory replaces the cosmic crunchers with fuzzy quantum spheres, potentially solving the black-hole information paradox and explaining away the Big Bang and the origin of time.
by Sophie Hebden
FQXi Awardees: Samir Mathur
May 11, 2018
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Samir Mathur
Ohio State University
They sound like cuddly cartoon characters. But "fuzzballs"—hypothetical quantum objects posited by physicist Samir Mathur, of Ohio State University, in Columbus—could solve some serious paradoxes about the nature of black holes, and even the Big Bang.

Under the current paradigm, the core of a black hole is a tantalising mystery, where an incredibly dense, infinitesimally small, and poorly understood "singularity" is believed to lurk. Our universe is also thought to have burst forth from such a singularity, some 13.8 billion years ago, although it’s not clear how. Physicists have struggled to explain exactly what happens inside a singularity for decades. Both quantum effects, which play an important role in the behaviour of tiny objects, and gravity, which governs the motion of immensely heavy things, should be at play. However, attempts to combine the two theories into a model of "quantum gravity" have so far failed and new physics to describe what is happening is desperately needed.

If the core of a black hole isn’t confusing enough, things get worse when you consider its surface—or "event horizon"—which marks an imaginary boundary surrounding the black hole. Anything that crosses the event horizon, even light, will be sucked in towards the black hole’s core and crushed into the singularity. At first it was thought that nothing that falls in to a black hole can ever escape. But in 1974, Stephen Hawking calculated that, thanks to quantum effects, black holes can slowly radiate energy from their horizon. As they do so, they gradually shrink, until eventually they will evaporate entirely. The trouble is, if they vanish from the universe, so too does all the information about the objects that they swallowed over their lifetimes. This, Hawking realized, would violate a fundamental rule of quantum theory, which states that information can never be completely destroyed. He had hit upon the now famous, and still unresolved, black-hole information paradox.

A Fuzzball Compared to a Conventional Black Hole
Fuzzballs (left) contain a tangle of quantum matter and energy throughout,
while matter is concentrated in the core of a conventional black hole (right),
with a featureless event horizon at its surface.

Credit: Fuzzball image courtesy of Samir Mathur
Mathur’s fuzzball proposal, however, could solve all these conundrums. Firstly, it eradicates the puzzle of what happens at the centre of a black hole by replacing the singularity and surrounding invisible vacuum with a fuzzball—an impenetrable, fuzzy bramble of quantum matter and energy that stretches to the event horizon. The more massive the black hole, Mathur’s thinking goes, the bigger the fuzzball.

The idea behind fuzzballs goes back to 1997, when Mathur was working as an assistant professor at MIT. He was considering the scales at which quantum gravity acts using string theory—a theoretical framework that makes gravity more compatible with quantum theory, and describes elementary particles as one-dimensional strings that can join onto one another to form new particles.

The ability to form new types of particles is particularly helpful if you are dealing with something as exotic as a black hole. Mathur noted that a black hole must be made of not just one or two particles, but a billion particles colliding. Remarkably, his calculations revealed that when these particles come together, the resulting object does not have a smooth surface, but a fluffy, textured one. By contrast, conventional black holes are thought to be featureless at the horizon. Hence, Mathur coined the name "fuzzball." Unlike mysterious singularities, where conventional physics appears to breakdown, the goings-on within fuzzballs can be understood using string theory. Mathur’s formulation also seems to match well with physical reality; his early calculations show that fuzzball sizes always corresponded to the exact size of the black hole event horizons, computed using Einstein’s theory of gravity, which depend on their mass.

Astronauts and Fuzzballs

But what about the other major problem with black holes, the information paradox? To solve this, Mathur imagined the fate of an astronaut falling on to a fuzzball, rather than a conventional black hole. In the traditional view, the astronaut is pulled to the heart of the black hole, where she and all information about her are crushed into the singularity. But in the fuzzball picture, Mathur conjectured, information about the astronaut is absorbed into the fuzzball in the form of vibrations. The fuzzball perfectly encodes her information content and motion. "Even though the astronaut has actually been broken up into the fuzzball vibrations, you can reassemble those vibrations in a certain way to make her think that she’s still smoothly moving through the horizon into the interior of the black hole," says Mathur.

Cosmic Ripples
Could gravitational waves reveal whether fuzzballs are real?
Credit: LIGO Caltech/MIT
This information does not have to be sucked to the fuzzball’s core, but can vibrate back out of the fuzzball’s surface in the form of Hawking radiation as the fuzzball evaporates. This solves the information paradox because information about objects swallowed by the fuzzball is never lost from the universe.

Although still a contentious idea, the fuzzball paradigm has gained a prominent platform at international conferences, and fans say that it has the potential to have a remarkable impact on physics long-term. "If the fuzzball proposal is true, it would revolutionize quantum gravity and the way we think about black holes and spacetime in general," says string theorist Iosif Bena, of the IPHT, in France. Ironically, Bena had set out to prove fuzzballs wrong, a dozen years ago, but after conducting a series of consistency checks, he became convinced that the idea has real merit.

Likewise, Nicholas Warner, a string theorist at the University of Southern California, originally set out to kick fuzzballs into the metaphorical long grass, hoping to show that you couldn’t solve the problem in the black hole context using current mathematical techniques. "I ended up proving the exact opposite," says Warner. "It turned out to be much simpler than I ever had a right to believe, so I moved from being a sceptic to a convert."

By providing a mechanism for structure at the horizon of a black hole, says Warner, there’s even a faint possibility of an observational test that could distinguish between traditional black holes and fuzzballs. When black holes collide, they produce ripples in spacetime, or gravitational waves, such as those recently detected by LIGO. These ripples could be subtly different for fuzzballs compared to conventional black holes. Although, Warner notes, LIGO may not be sensitive enough to pick up fuzzball signatures, this is something to watch out for in the future.

Softening the Big Bang

Recently, Mathur has been applying his fuzzball picture to an even more challenging frontier in physics: the Big Bang. With the help of two FQXi grants, totalling over $100,000, and working with Ali Musomi at Tufts University, in Medford, Massachusetts, he has applied the fuzzball calculations in reverse. This enables him to track the universe backwards in time to its birth from a small object. No one knows what initiated the Big Bang, but the general view is that it started from some sort of singularity, which marks the origin of both space and time. Out of this singularity, spacetime exploded into existence. But the fuzzball paradigm paints a different picture.

If the fuzzball
proposal is
true, it would
quantum gravity.
- Iosif Bena
If you start with a large fuzzball representing the whole universe and push it backwards in time towards the Big Bang, it starts breaking up into smaller fuzzballs. "It appears that it just keeps fragmenting into small local regions that don’t talk among each other, so you get a completely different picture of the singularity," says Mathur.

So, does this mean that time didn’t originate at the Big Bang? Rather, mini fuzzballs have always existed—and what we interpret as the beginning of time at the Big Bang explosion is just the result of their collision? "This is indeed a deep question," says Mathur. Their preliminary studies suggest that we should be thinking of the Big Bang as a softer sort of process, where smaller fuzzballs coalesce into larger ones to ultimately make the universe we see today.

Applying the fuzzball picture to the Big Bang is extremely ambitious, according to Warner. He "jibbers" to think of the complexity of the calculations Mathur and Musomi are undertaking: this requires hundreds of pages of meticulous algebra in string theory. But, if anyone can do it, Mathur can, says Warner: "Mathur is a remarkable guy, probably one of the deepest thinkers around and most respected in the field."

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Recent Comments

It is the premise of the topology/'fabric' of spacetime that all events exist out there on the fourth dimension and are every bit as real as what is experienced as the present moment and that the sense of the present point in time is as subjective as one's point in space. The monumental logical fallacy of this is the effect of time is being created by stuff moving around and thus changing configuration. It directly contradicts another basic physical premise, that energy is conserved,...

It is the premise of the topology/'fabric' of spacetime that all events exist out there on the fourth dimension and are every bit as real as what is experienced as the present moment and that the sense of the present point in time is as subjective as one's point in space. The monumental logical fallacy of this is the effect of time is being created by stuff moving around and thus changing configuration. It directly contradicts another basic physical premise, that energy is conserved, since...

The supertranslations filling in the new vacuum left behind after a black hole has passed, reflect a different angle to surrounding galaxies' relation to the absence of the black hole.

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