Physicists
have wondered for decades whether infinitely dense points known as
singularities can ever exist outside black holes, which would expose the
mysteries of quantum gravity for all to see. Singularities — snags in the
otherwise smooth fabric of space and time where Albert Einstein’s classical
gravity theory breaks down and the unknown quantum theory of gravity is needed
— seem to always come cloaked in darkness, hiding from view behind the event
horizons of black holes. The British physicist and mathematician Sir Roger
Penrose conjectured in 1969 that visible or “naked” singularities are actually
forbidden from forming in nature, in a kind of cosmic censorship. But why
should quantum gravity censor itself?

Now, new
theoretical calculations provide a possible explanation for why naked
singularities do not exist — in a particular model universe, at least. The
findings indicate that a second, newer conjecture about gravity, if it is true,
reinforces Penrose’s cosmic censorship conjecture by preventing naked
singularities from forming in this model universe. Some experts say the
mutually supportive relationship between the two conjectures increases the
chances that both are correct. And while this would mean singularities do stay
frustratingly hidden, it would also reveal an important feature of the quantum
gravity theory that eludes us.

“It’s
pleasing that there’s a connection” between the two conjectures, said John Preskill of the California Institute of Technology, who in 1991 bet Stephen
Hawking that the cosmic censorship conjecture would fail (though he actually
thinks it’s probably true).

The new
work, reported in May in Physical Review Letters by Jorge Santos and his
student Toby Crisford at the University of Cambridge and relying on a key
insight by Cumrun Vafa of Harvard University, unexpectedly ties cosmic
censorship to the 2006 weak gravity conjecture, which asserts that gravity must
always be the weakest force in any viable universe, as it is in ours. (Gravity
is by far the weakest of the four fundamental forces; two electrons
electrically repel each other 1 million trillion trillion trillion times more
strongly than they gravitationally attract each other.) Santos and Crisford
were able to simulate the formation of a naked singularity in a
four-dimensional universe with a different space-time geometry than ours. But
they found that if another force exists in that universe that affects particles
more strongly than gravity, the singularity becomes cloaked in a black hole. In
other words, where a perverse pinprick would otherwise form in the space-time
fabric, naked for all the world to see, the relative weakness of gravity
prevents it.

Santos and
Crisford are running simulations now to test whether cosmic censorship is saved
at exactly the limit where gravity becomes the weakest force in the model
universe, as initial calculations suggest. Such an alliance with the
better-established cosmic censorship conjecture would reflect very well on the
weak gravity conjecture. And if weak gravity is right, it points to a deep relationship
between gravity and the other quantum forces, potentially lending support to string theory over a rival theory called loop quantum gravity. The
“unification” of the forces happens naturally in string theory, where gravity
is one vibrational mode of strings and forces like electromagnetism are other
modes. But unification is less obvious in loop quantum gravity, where
space-time is quantized in tiny volumetric packets that bear no direct
connection to the other particles and forces. “If the weak gravity conjecture
is right, loop quantum gravity is definitely wrong,” said Nima Arkani-Hamed, a
professor at the Institute for Advanced Study who co-discovered the weak
gravity conjecture.

The new work
“does tell us about quantum gravity,” said Gary Horowitz, a theoretical
physicist at the University of California, Santa Barbara.

**The Naked Singularities**

In 1991,
Preskill and Kip Thorne, both theoretical physicists at Caltech, visited
Stephen Hawking at Cambridge. Hawking had spent decades exploring the
possibilities packed into the Einstein equation, which defines how space-time
bends in the presence of matter, giving rise to gravity. Like Penrose and
everyone else, he had yet to find a mechanism by which a naked singularity
could form in a universe like ours. Always, singularities lay at the centers of
black holes — sinkholes in space-time that are so steep that no light can climb
out. He told his visitors that he believed in cosmic censorship. Preskill and
Thorne, both experts in quantum gravity and black holes (Thorne was one of
three physicists who founded the black-hole-detecting LIGO experiment), said
they felt it might be possible to detect naked singularities and quantum
gravity effects. “There was a long pause,” Preskill recalled. “Then Stephen said,
‘You want to bet?’”

The bet had
to be settled on a technicality and renegotiated in 1997, after the first
ambiguous exception cropped up. Matt Choptuik, a physicist at the University of
British Columbia who uses numerical simulations to study Einstein’s theory,
showed that a naked singularity can form in a four-dimensional universe like
ours when you perfectly fine-tune its initial conditions. Nudge the initial
data by any amount, and you lose it — a black hole forms around the
singularity, censoring the scene. This exceptional case doesn’t disprove cosmic
censorship as Penrose meant it, because it doesn’t suggest naked singularities
might actually form.

Nonetheless, Hawking conceded the original bet and paid
his debt per the stipulations, “with clothing to cover the winner’s nakedness.”
He embarrassed Preskill by making him wear a T-shirt featuring a nearly-naked
lady while giving a talk to 1,000 people at Caltech. The clothing was supposed
to be “embroidered with a suitable concessionary message,” but Hawking’s read
like a challenge: “Nature Abhors a Naked Singularity.”

The
physicists posted a new bet online, with language to clarify that only
non-exceptional counterexamples to cosmic censorship would count. And this
time, they agreed, “The clothing is to be embroidered with a suitable, truly
concessionary message.”

The wager
still stands 20 years later, but not without coming under threat. In 2010, the
physicists Frans Pretorius and Luis Lehner discovered a mechanism for producing
naked singularities in hypothetical universes with five or more dimensions. And
in their May paper, Santos and Crisford reported a naked singularity in a
classical universe with four space-time dimensions, like our own, but with a
radically different geometry. This latest one is “in between the ‘technical’
counterexample of the 1990s and a true counterexample,” Horowitz said. Preskill
agrees that it doesn’t settle the bet. But it does change the story.

**The Tin Can Universe**

The new
discovery began to unfold in 2014, when Horowitz, Santos and Benson Way found
that naked singularities could exist in a pretend 4-D universe called “anti-de
Sitter” (AdS) space whose space-time geometry is shaped like a tin can. This
universe has a boundary — the can’s side — which makes it a convenient testing
ground for ideas about quantum gravity: Physicists can treat bendy space-time
in the can’s interior like a hologram that projects off of the can’s surface,
where there is no gravity. In universes like our own, which is closer to a “de
Sitter” (dS) geometry, the only boundary is the infinite future, essentially the
end of time. Timeless infinity doesn’t make a very good surface for projecting
a hologram of a living, breathing universe.

Despite
their differences, the interiors of both AdS and dS universes obey Einstein’s
classical gravity theory — everywhere outside singularities, that is. If cosmic
censorship holds in one of the two arenas, some experts say you might expect it
to hold up in both.

Horowitz,
Santos and Way were studying what happens when an electric field and a
gravitational field coexist in an AdS universe. Their calculations suggested
that cranking up the energy of the electric field on the surface of the tin can
universe will cause space-time to curve more and more sharply around a
corresponding point inside, eventually forming a naked singularity. In their
recent paper, Santos and Crisford verified the earlier calculations with
numerical simulations.

But why would naked singularities exist in 5-D and in 4-D when you change the geometry, but never in a flat 4-D universe like ours? “It’s like, what the heck!” Santos said. “It’s so weird you should work on it, right? There has to be something here.”

**Weak Gravity to the Rescue**

In 2015,
Horowitz mentioned the evidence for a naked singularity in 4-D AdS space to
Cumrun Vafa, a Harvard string theorist and quantum gravity theorist who stopped
by Horowitz’s office. Vafa had been working to rule out large swaths of the
10500 different possible universes that string theory naively allows. He did
this by identifying “swamplands”: failed universes that are too logically
inconsistent to exist. By understanding patterns of land and swamp, he hoped to
get an overall picture of quantum gravity.

Working with
Arkani-Hamed, Luboš Motl and Alberto Nicolis in 2006, Vafa proposed the weak
gravity conjecture as a swamplands test. The researchers found that universes
only seemed to make sense when particles were affected by gravity less than
they were by at least one other force. Dial down the other forces of nature too
much, and violations of causality and other problems arise. “Things were going
wrong just when you started violating gravity as the weakest force,”
Arkani-Hamed said. The weak-gravity requirement drowns huge regions of the
quantum gravity landscape in swamplands.

Weak gravity
and cosmic censorship seem to describe different things, but in chatting with
Horowitz that day in 2015, Vafa realized that they might be linked. Horowitz
had explained Santos and Crisford’s simulated naked singularity: When the
researchers cranked up the strength of the electric field on the boundary of
their tin-can universe, they assumed that the interior was classical —
perfectly smooth, with no particles quantum mechanically fluctuating in and out
of existence. But Vafa reasoned that, if such particles existed, and if, in
accordance with the weak gravity conjecture, they were more strongly coupled to
the electric field than to gravity, then cranking up the electric field on the
AdS boundary would cause sufficient numbers of particles to arise in the
corresponding region in the interior to gravitationally collapse the region
into a black hole, preventing the naked singularity.

Subsequent
calculations by Santos and Crisford supported Vafa’s hunch; the simulations
they’re running now could verify that naked singularities become cloaked in
black holes right at the point where gravity becomes the weakest force. “We
don’t know exactly why, but it seems to be true,” Vafa said. “These two
reinforce each other.”

**Quantum Gravity**

The full
implications of the new work, and of the two conjectures, will take time to
sink in. Cosmic censorship imposes an odd disconnect between quantum gravity at
the centers of black holes and classical gravity throughout the rest of the
universe. Weak gravity appears to bridge the gap, linking quantum gravity to the
other quantum forces that govern particles in the universe, and possibly
favoring a stringy approach over a loopy one. Preskill said, “I think it’s
something you would put on your list of arguments or reasons for believing in unification of the forces.”

However, Lee Smolin of the Perimeter Institute, one of the developers of loop quantum
gravity, has pushed back, arguing that if weak gravity is true, there might be
a loopy reason for it. And he contends that there is a path to unification of the forces within his theory — a path that would need to be pursued all the
more vigorously if the weak gravity conjecture holds.

Given the
apparent absence of naked singularities in our universe, physicists will take
hints about quantum gravity wherever they can find them. They’re as lost now in
the endless landscape of possible quantum gravity theories as they were in the
1990s, with no prospects for determining through experiments which underlying
theory describes our world. “It is thus paramount to find generic properties
that such quantum gravity theories must have in order to be viable,” Santos
said, echoing the swamplands philosophy.

Weak gravity
might be one such property — a necessary condition for quantum gravity’s
consistency that spills out and affects the world beyond black holes. These may
be some of the only clues available to help researchers feel their way into the
darkness.

This article
was reprinted on Wired.com.

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