Singularities in Space-Time Prove Hard to Kill.pdf

Singularities are predictions of Albert Einstein’s general theory of relativity. According to this theory, clumps of matter or energy curve the space-time fabric toward themselves, and this curvature induces the force of gravity.

1. Singularities in Space-Time Prove Hard to Kill
QUANTUM GRAVITY
ByCHARLIE WOODMay 27, 2025 Black hole and Big Bang singularities break
our best theory of gravity. A trilogy of
theorems hints that physicists must go to the
ends of space and time to find a fix.
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2. At the singular point in a black
hole, time seems to grind to a
halt, and predictions become
impossible.
Mark Belan/Quanta Magazine16
T
wo blind spots torture physicists: the birth
of the universe and the center of a black
hole. The former may feel like a moment in
time and the latter a point in space, but in both
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3. cases the normally interwoven threads of space
and time seem to stop short. These mysterious
points are known as singularities.
Singularities are predictions of Albert Einstein’s
general theory of relativity. According to this
theory, clumps of matter or energy curve the
space-time fabric toward themselves, and this
curvature induces the force of gravity. Pack
enough stuff into a small enough spot, and
Einstein’s equations seem to predict that space-
time will curve infinitely steeply there, such
that gravity grows infinitely strong.
Most physicists don’t believe, however, that
Einstein’s theory says much about what really
happens at these points. Rather, singularities
are widely seen as “mathematical artifacts,” as
Hong Liu, a physicist at the Massachusetts
Institute of Technology, put it, not objects that
“occur in any physical universe.” They are
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4. where general relativity malfunctions. The
singularities are expected to vanish in a more
fundamental theory of gravity that Einstein’s
space-time picture merely approximates — a
theory of quantum gravity.
But as physicists take steps toward that truer
and more complete theory by merging general
relativity and quantum physics, singularities are
proving hard to erase. The British mathematical
physicist Roger Penrose won the Nobel Prize in
Physics for proving in the 1960s that
singularities would inevitably occur in an
empty universe made up entirely of space-time.
More recent research has extended this insight
into more realistic circumstances. One paper
established that a universe with quantum
particles would also feature singularities,
although it only considered the case where the
particles don’t bend the space-time fabric at all.
Then, earlier this year, a physicist proved that
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5. these blemishes exist even in theoretical
universes where quantum particles do slightly
nudge space-time itself — that is, universes
quite a bit like our own.
This trilogy of proofs challenges physicists to
confront the possibility that singularities may
be more than mere mathematical mirages. They
hint that our universe may in fact contain
points where space-time frays so much that it
becomes unrecognizable. No object can pass,
and clocks tick to a halt. The singularity
theorems invite researchers to grapple with the
nature of these points and pursue a more
fundamental theory that can clarify what might
continue if time truly stops.
Space-Time’s Fatal Flaws
Karl Schwarzschild first discovered an
arrangement of space-time with a singularity in
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6. 1916, just months after Einstein published
general relativity. The bizarre features of the
“Schwarzschild solution” took years for
physicists to understand. Space-time assumes a
shape analogous to a whirlpool with walls that
swirl more and more steeply as you go farther
in; at the bottom, the curvature of space-time is
infinite. The vortex is inescapable; it has a
spherical boundary that traps anything falling
inside, even light rays.
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7. It took decades for physicists to accept that
these inconceivable objects, eventually dubbed
black holes, might actually exist.
The British mathematical physicist Roger
Penrose proved that given two simple
assumptions, space-time must end at points
called singularities.
Public Domain
J. Robert Oppenheimer and Hartland Snyder
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8. calculated in 1939 that if a perfectly spherical
star gravitationally collapses to a point, its
matter will become so dense that it will stretch
space-time into a singularity. But real stars
bubble and churn, especially while imploding,
so physicists wondered whether their
nonspherical shapes would stop them from
forming singularities.
Penrose eliminated the need for geometric
perfection in 1965. His landmark proof relied on
two assumptions. First, you need a “trapped
surface” inside of which light can never escape.
If you cover this surface in light bulbs and
switch them on, their light rays will fall inward
faster than they can travel outward. Crucially,
this shell of light will shrink regardless of
whether it started out as a perfect sphere, a
dimpled golf ball, or something more
misshapen.
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9. Second, space-time should always curve in such
a way that light rays bend toward each other but
never diverge. In short, gravity should be
attractive, which is the case so long as energy is
never negative.
With these two stipulations, Penrose proved the
mortality of at least one of the trapped light
rays. Its otherwise eternal journey through
space and time must terminate in a singularity,
a point where the space-time fabric ceases to
exist, where there is no future for the light ray
to travel into. This was a new definition of a
singularity, distinct from the infinite curvature
of the Schwarzschild solution. Its generality
enabled Penrose to prove in three scant pages of
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10. math that, under his two assumptions,
singularities will inevitably form.
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11. A hand-drawn figure in Penrose’s 1965 paper
proving the singularity theorem shows the
collapse of space-time to form a singularity. The
paper has been called “the most important
paper in general relativity” since Einstein’s.
Roger Penrose, Physical Review Letters, American
Physical Society
“Penrose’s paper was probably the most
important paper in general relativity ever
written, other than Einstein’s original paper,”
said Geoff Penington, a physicist at the
University of California, Berkeley.
Stephen Hawking soon extended Penrose’s
argument to the early universe, proving that a
cosmos described by general relativity must
have sprung from a singular point during the
Big Bang. This cosmological singularity
resembles a black hole in that, if you imagine
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12. rewinding the history of the universe, light rays
will run into a wall at the beginning of time.
Over the years, physicists have accumulated
heaps of evidence that black holes exist, and
that the universe began with an event that
looks very much like a Big Bang. But do these
phenomena truly represent space-time
singularities?
Many physicists find the actual existence of
such points unthinkable. When you try to
calculate the fate of a particle approaching the
singularity, general relativity glitches and gives
impossible, infinite answers. “The singularity
means a lack of predictability,” Liu said. “Your
theory just breaks down.”
But the particle in the real world must have a
fate of some sort. So a more universal theory
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13. that can predict that fate — very likely a
quantum theory — must take over.
General relativity is a classical theory, meaning
that space-time takes on one, and only one,
shape at every moment. In contrast, matter is
quantum mechanical, meaning it can have
multiple possible states at once — a feature
known as superposition. Since space-time
reacts to the matter in it, theorists expect that
any matter particles in a superposition of
occupying two different locations should force
space-time into a superposition of two
distortions. That is, space-time and gravity
should also follow quantum rules. But
physicists haven’t yet worked out what those
rules are.
Into the Onion
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14. Theorists approach their quest for a quantum
theory of gravity the way they might peel an
onion: layer by layer. Each layer represents a
theory of a universe that imperfectly
approximates the real one. The deeper you go,
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15. the more of the interplay between quantum
matter and space-time you can capture.
The German physicist-soldier Karl
Schwarzschild calculated the shape that space-
time takes around a massive point. Years later,
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16. Penrose worked in the outermost layer of the
onion. He used the general theory of relativity
and ignored quantumness entirely. In effect, he
proved that the space-time fabric has
singularities when it is completely devoid of any
quantum matter.
Physicists aspire to someday reach the onion’s
core. In it, they’ll find a theory describing both
space-time and matter in all their quantum
glory. This theory would have no blind spots —
all calculations should yield meaningful results.
But what about the middle layers? Could
physicists resolve Penrose’s singularities by
physicists realized that this geometry contains
a singularity.
Public Domain
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17. moving to something a little more quantum,
and therefore a little more realistic?
“It was the obvious speculation, that somehow
quantum effects should fix the singularity,”
Penington said.
They first tried to do so in the late 2000s. The
assumption that had confined Penrose’s proof
to the outermost layer was that energy is never
negative. That’s true in everyday, classical
situations, but not in quantum mechanics.
Energy goes negative, at least momentarily, in
quantum phenomena such as the Casimir
effect, where (experiments show) two metal
plates attract each other in a vacuum. And
negative energies play a role in the way black
holes are thought to radiate particles, eventually
“evaporating” entirely. All the deeper, quantum
layers of the onion would feature this exotic
energetic behavior.
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18. The physicist who peeled the top layer was Aron
Wall, then based at the University of Maryland
and now at the University of Cambridge. To cut
into the quantum realm and abandon Penrose’s
energy assumption, Wall latched on to a
theoretical discovery made in the 1970s by Jacob
Bekenstein.
Bekenstein knew that for any given region of
space, the contents of the region grow more
mixed up as time goes on. In other words,
entropy, a measure of this mixing, tends to
increase, a rule known as the second law of
thermodynamics. While considering a region
that contains a black hole, the physicist realized
that the entropy comes from two sources.
There’s the standard source — the number of
ways that quantum particles in the space
around the black hole could be arranged. But
the black hole has entropy too, and the amount
depends on the black hole’s surface area. So the
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19. total entropy of the region is a sum: the surface
area of the black hole plus the entropy of nearby
quantum stuff. This observation became known
as the “generalized” second law.
Wall “made it his mission to understand the
generalized second law,” said Raphael Bousso, a
physicist at Berkeley. “He was thinking about it
in much clearer and much better ways than
everybody else on the planet.”
Reaching the quantum layers of the onion
would mean accommodating negative energy
and the presence of quantum particles. To do so,
Wall reasoned that he could take any surface
area in general relativity and add to it the
entropy of those particles, as the generalized
second law suggested. Penrose’s proof of his
singularity theorem had involved the trapped
surface. So Wall upgraded it to a “quantum
trapped surface.” And when he reworked
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20. Penrose’s singularity theorem in this way, it
held. Singularities form even in the presence of
quantum particles. Wall published his findings
in 2010.
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21. “Aron’s paper was a seminal breakthrough in
combining quantum mechanics and gravity in a
more precise way,” Penington said.
Having peeled back the classical outer layer of
the onion, where energy is always positive, Wall
reached a lightly quantum layer — a context
physicists call semiclassical. In a semiclassical
world, space-time guides the journeys of
quantum particles, but it cannot react to their
presence. A semiclassical black hole will radiate
particles, for instance, since that’s a
consequence of how particles experience a
In 2010, Aron Wall, now at the University of
Cambridge, revamped Penrose’s proof to show
that singularities exist in a world where space-
time has no quantum properties but is filled
with particles that do.
Nicole Wall
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22. space-time warped into a black hole shape. But
the space-time — the black hole itself — will
never actually shrink in size even as the
radiation leaks energy into the void for all
eternity.
That’s almost, but not exactly, what happens in
the real universe. You could watch a black hole
radiate particles for a century without seeing it
shrink a single nanometer. But if you could
watch for longer — many trillions upon
trillions of years — you would see the black
hole waste away to nothing.
The next onion layer beckoned.
Dialing Up the Quantumness
Bousso recently revisited Wall’s proof and found
that he could cut a little deeper. What about the
world where black holes shrink as they radiate?
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23. In this scenario, the space-time fabric can react
to quantum particles.
Using more refined mathematical machinery
developed by Wall and others since 2010, Bousso
found that, despite the intensified quantumness
of his scenario, singularities continue to exist.
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24. He posted his paper, which has not yet been
peer-reviewed, in January.
Raphael Bousso of the University of California,
Berkeley recently extended Wall’s singularity
proof to a universe made of space-time that
reacts to quantum particles.
Courtesy of Raphael Bousso
The world of Bousso’s new theorem still departs
from our universe in notable ways. For
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25. mathematical convenience, he assumed that
there’s an unlimited variety of particles — an
unrealistic assumption that makes some
physicists wonder whether this third layer
matches reality (with its 17 or so known
particles) any better than the second layer does.
“We don’t have an infinite number of quantum
fields,” said Edgar Shaghoulian, a physicist at
the University of California, Santa Cruz.
Still, for some experts, Bousso’s work delivers a
satisfying denouement to the Penrose and Wall
singularity story, despite its unrealistic
abundance of particles. It establishes that
singularities can’t be avoided, even in space-
times with mild reactions to quantum matter.
“Just by adding small quantum corrections, you
can’t prevent the singularity,” Penington said.
Wall and Bousso’s work “answers that pretty
definitively.”
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26. The Real Singularity
But Bousso’s theorem still doesn’t guarantee
that singularities must form in our universe.
Some physicists hold out hope that the dead
ends do somehow go away. What seems like a
singularity could actually connect to
somewhere else. In the case of a black hole,
perhaps those light rays end up in another
universe.
And a lack of a Big Bang singularity might
imply that our universe began with a “Big
Bounce.” The idea is that a previous universe, as
it collapsed under the pull of gravity, somehow
dodged the formation of a singularity and
instead bounced into a period of expansion.
Physicists who are developing bounce theories
often work in the second layer of the onion,
using semiclassical physics that exploits
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27. negative-energy quantum effects to get around
the singularity required by the Penrose and
Hawking theorems. In light of the newer
theorems, they will now need to swallow the
uncomfortable truth that their theories violate
the generalized second law as well.
One physicist pursuing bounces, Surjeet
Rajendran of Johns Hopkins University, says he
is undaunted. He points out that not even the
generalized second law is gospel truth.
Rejecting it would make singularities avoidable
and continuations of space-time possible.
Singularity skeptics can also appeal to the
theory at the core of the onion, where space-
time behaves in truly quantum ways, such as
taking on superpositions. There, nothing can be
taken for granted. It becomes hard to define the
concept of area, for instance, so it’s not clear
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28. what form the second law should take, and
therefore the new theorems won’t hold.
Bousso and like-minded physicists, however,
suspect that a highly quantum arena with no
notion of area is tantamount to a dead-end for a
light ray, and therefore that something Penrose
would recognize as a singularity should persist
in the core theory and in our universe. The
beginning of the cosmos and the hearts of black
holes would truly mark edges of the map where
clocks can’t tick and space stops.
“Inside of black holes, I am positive there is
some notion of singularity,” said Netta
Engelhardt, a physicist at MIT who has worked
with Wall.
In that case, the still-unknown fundamental
theory of quantum gravity would not kill
singularities but demystify them. This truer
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29. theory would allow physicists to ask questions
and calculate meaningful answers, but the
language of those questions and answers would
change dramatically. Space-time quantities like
position, curvature and duration might be
useless for describing a singularity. There,
where time ends, other quantities or concepts
might have to take their place. “If you had to
make me guess,” Penington said, “whatever
quantum state describes the singularity itself
does not have a notion of time.”
Correction: May 28, 2025
The final section have been edited to correctly
explain the role that the generalized second law
plays in the debate about the existence of
singularities.
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