Warner Bros. Entertainment/Paramount Pictures
Black holes such as the one depicted in Interstellar (2014) can be connected by wormholes, which might have quantum origins.
In early 2009, determined to make the most
of his first sabbatical from teaching, Mark Van Raamsdonk decided to
tackle one of the deepest mysteries in physics: the relationship between
quantum mechanics and gravity. After a year of work and consultation
with colleagues, he submitted a paper on the topic to the
Journal of High Energy Physics.
In
April 2010, the journal sent him a rejection — with a referee’s report
implying that Van Raamsdonk, a physicist at the University of British
Columbia in Vancouver, was a crackpot.
His next submission, to
General Relativity and Gravitation, fared little better: the referee’s report was scathing, and the journal’s editor asked for a complete rewrite.
Quantum‘spookiness’passes toughest test yet
But by then, Van Raamsdonk had entered a
shorter version of the paper into a prestigious annual essay contest run
by the Gravity Research Foundation in Wellesley, Massachusetts. Not
only did he win first prize, but he also got to savour a particularly
satisfying irony: the honour included guaranteed publication in
General Relativity and Gravitation. The journal published the shorter essay in June 2010.
Still,
the editors had good reason to be cautious. A successful unification of
quantum mechanics and gravity has eluded physicists for nearly a
century. Quantum mechanics governs the world of the small — the weird
realm in which an atom or particle can be in many places at the same
time, and can simultaneously spin both clockwise and anticlockwise.
Gravity governs the Universe at large — from the fall of an apple to the
motion of planets, stars and galaxies — and is described by Albert
Einstein’s general theory of relativity, announced 100 years ago this
month. The theory holds that gravity is geometry: particles are
deflected when they pass near a massive object not because they feel a
force, said Einstein, but because space and time around the object are
curved.
Both theories have been abundantly
verified through experiment, yet the realities they describe seem
utterly incompatible. And from the editors’ standpoint, Van Raamsdonk’s
approach to resolving this incompatibility was strange. All that’s
needed, he asserted, is ‘entanglement’: the phenomenon that many
physicists believe to be the ultimate in quantum weirdness. Entanglement
lets the measurement of one particle instantaneously determine the
state of a partner particle, no matter how far away it may be — even on
the other side of the Milky Way.
Einstein loathed the idea of entanglement, and famously derided it as “spooky action at a distance”. But it is central to quantum theory.
And Van Raamsdonk, drawing on work by like-minded physicists going back
more than a decade, argued for the ultimate irony — that, despite
Einstein’s objections, entanglement might be the basis of geometry, and
thus of Einstein’s geometric theory of gravity. “Space-time,” he says,
“is just a geometrical picture of how stuff in the quantum system is
entangled.”
“I had understood something that no one had understood before.”
This idea is a long way from being proved,
and is hardly a complete theory of quantum gravity. But independent
studies have reached much the same conclusion, drawing intense interest
from major theorists. A small industry of physicists is now working to
expand the geometry–entanglement relationship, using all the modern
tools developed for quantum computing and quantum information theory.
Einstein was no lone genius
“I would not hesitate for a minute,” says
physicist Bartłomiej Czech of Stanford University in California, “to
call the connections between quantum theory and gravity that have
emerged in the last ten years revolutionary.”
Gravity without gravity
Much of this work rests on a discovery
2
announced in 1997 by physicist Juan Maldacena, now at the Institute for
Advanced Study in Princeton, New Jersey. Maldacena’s research had led
him to consider the relationship between two seemingly different model
universes. One is a cosmos similar to our own. Although it neither
expands nor contracts, it has three dimensions, is filled with quantum
particles and obeys Einstein’s equations of gravity. Known as anti-de
Sitter space (AdS), it is commonly referred to as the bulk. The other
model is also filled with elementary particles, but it has one dimension
fewer and doesn’t recognize gravity. Commonly known as the boundary, it
is a mathematically defined membrane that lies an infinite distance
from any given point in the bulk, yet completely encloses it, much like
the 2D surface of a balloon enclosing a 3D volume of air. The boundary
particles obey the equations of a quantum system known as conformal
field theory (CFT).
Maldacena discovered that
the boundary and the bulk are completely equivalent. Like the 2D
circuitry of a computer chip that encodes the 3D imagery of a computer
game, the relatively simple, gravity-free equations that prevail on the
boundary contain the same information and describe the same physics as
the more complex equations that rule the bulk.
“It’s
kind of a miraculous thing,” says Van Raamsdonk. Suddenly, he says,
Maldacena’s duality gave physicists a way to think about quantum gravity
in the bulk without thinking about gravity at all: they just had to
look at the equivalent quantum state on the boundary. And in the years
since, so many have rushed to explore this idea that Maldacena’s paper
is now one of the most highly cited articles in physics.
Quantum weirdness:What's really real?
Among the enthusiasts was Van Raamsdonk,
who started his sabbatical by pondering one of the central unsolved
questions posed by Maldacena’s discovery: exactly how does a quantum
field on the boundary produce gravity in the bulk? There had already
been hints
that the answer might involve some sort of relation between geometry
and entanglement. But it was unclear how significant these hints were:
all the earlier work on this idea had dealt with special cases, such as a
bulk universe that contained a black hole. So Van Raamsdonk decided to
settle the matter, and work out whether the relationship was true in
general, or was just a mathematical oddity.
He
first considered an empty bulk universe, which corresponded to a single
quantum field on the boundary. This field, and the quantum
relationships that tied various parts of it together, contained the only
entanglement in the system. But now, Van Raamsdonk wondered, what would
happen to the bulk universe if that boundary entanglement were removed?
He was able to answer that question using mathematical tools
introduced in 2006 by Shinsei Ryu, now at the University of Illinois at
Urbana–Champaign, and Tadashi Takanagi, now at the Yukawa Institute for
Theoretical Physics at Kyoto University in Japan. Their equations
allowed him to model a slow and methodical reduction in the boundary
field’s entanglement, and to watch the response in the bulk, where he
saw space-time steadily elongating and pulling apart (see ‘The entanglement connection’).
Ultimately, he found, reducing the entanglement to zero would break the
space-time into disjointed chunks, like chewing gum stretched too far.
NIK SPENCER/NATURE
The geometry–entanglement relationship was
general, Van Raamsdonk realized. Entanglement is the essential
ingredient that knits space-time together into a smooth whole — not just
in exotic cases with black holes, but always.
“I
felt that I had understood something about a fundamental question that
perhaps nobody had understood before,” he recalls: “Essentially, what is
space-time?”
Entanglement and Einstein
The origins of space and time
Quantum entanglement as geometric glue —
this was the essence of Van Raamsdonk’s rejected paper and winning
essay, and an idea that has increasingly resonated among physicists. No
one has yet found a rigorous proof, so the idea still ranks as a
conjecture. But many independent lines of reasoning support it.
In 2013, for example, Maldacena and Leonard Susskind of Stanford published
a related conjecture that they dubbed ER = EPR, in honour of two
landmark papers from 1935. ER, by Einstein and American-Israeli
physicist Nathan Rosen, introduced
what is now called a wormhole: a tunnel through space-time connecting
two black holes. (No real particle could actually travel through such a
wormhole, science-fiction films notwithstanding: that would require
moving faster than light, which is impossible.) EPR, by Einstein, Rosen
and American physicist Boris Podolsky, was the first paper to clearly
articulate what is now called entanglement.
Maldacena
and Susskind’s conjecture was that these two concepts are related by
more than a common publication date. If any two particles are connected
by entanglement, the physicists suggested, then they are effectively
joined by a wormhole. And vice versa: the connection that physicists
call a wormhole is equivalent to entanglement. They are different ways
of describing the same underlying reality.
No
one has a clear idea of what this underlying reality is. But physicists
are increasingly convinced that it must exist. Maldacena, Susskind and
others have been testing the ER = EPR hypothesis to see if it is
mathematically consistent with everything else that is known about
entanglement and wormholes — and so far, the answer is yes.
Hidden connections
Theoretical physics: Complexity on the horizon
Other lines of support for the
geometry–entanglement relationship have come from condensed-matter
physics and quantum information theory: fields in which entanglement
already plays a central part. This has allowed researchers from these
disciplines to attack quantum gravity with a whole array of fresh
concepts and mathematical tools.
Tensor
networks, for example, are a technique developed by condensed-matter
physicists to track the quantum states of huge numbers of subatomic
particles. Brian Swingle was using them in this way in 2007, when he was
a graduate student at the Massachusetts Institute of Technology (MIT)
in Cambridge, calculating how groups of electrons interact in a solid
material. He found that the most useful network for this purpose
started by linking adjacent pairs of electrons, which are most likely to
interact with each other, then linking larger and larger groups in a
pattern that resembled the hierarchy of a family tree. But then, during a
course in quantum field theory, Swingle learned about Maldacena’s
bulk–boundary correspondence and noticed an intriguing pattern: the
mapping between the bulk and the boundary showed exactly the same
tree-like network.
“You can think of space as being built from entanglement.”
Swingle wondered whether this resemblance might be more than just coincidence. And in 2012, he published
calculations showing that it was: he had independently reached much the
same conclusion as Van Raamsdonk, thereby adding strong support to the
geometry–entanglement idea. “You can think of space as being built from
entanglement in this very precise way using the tensors,” says Swingle,
who is now at Stanford and has seen tensor networks become a frequently
used tool to explore the geometry–entanglement correspondence.
Another
prime example of cross-fertilization is the theory of quantum
error-correcting codes, which physicists invented to aid the construction of quantum computers.
These machines encode information not in bits but in ‘qubits’: quantum
states, such as the up or down spin of an electron, that can take on
values of 1 and 0 simultaneously. In principle, when the qubits interact
and become entangled in the right way, such a device could perform
calculations that an ordinary computer could not finish in the lifetime
of the Universe. But in practice, the process can be incredibly fragile:
the slightest disturbance from the outside world will disrupt the
qubits’ delicate entanglement and destroy any possibility of quantum
computation.
That need inspired quantum
error-correcting codes, numerical strategies that repair corrupted
correlations between the qubits and make the computation more robust.
One hallmark of these codes is that they are always ‘non-local’: the
information needed to restore any given qubit has to be spread out over a
wide region of space. Otherwise, damage in a single spot could destroy
any hope of recovery. And that non-locality, in turn, accounts for the
fascination that many quantum information theorists feel when they first
encounter Maldacena’s bulk–boundary correspondence: it shows a very
similar kind of non-locality. The information that corresponds to a
small region of the bulk is spread over a vast region of the boundary.
Nature special: General relativity at 100
“Anyone could look at AdS–CFT and say that
it’s sort of vaguely analogous to a quantum error-correcting code,” says
Scott Aaronson, a computer scientist at MIT. But in work published in
June
9,
physicists led by Daniel Harlow at Harvard University in Cambridge and
John Preskill of the California Institute of Technology in Pasadena
argue for something stronger: that the Maldacena duality is itself a
quantum error-correcting code. They have demonstrated that this is
mathematically correct in a simple model, and are now trying to show
that the assertion holds more generally.
“People
have been saying for years that entanglement is somehow important for
the emergence of the bulk,” says Harlow. “But for the first time, I
think we are really getting a glimpse of how and why.”
Beyond entanglement
That
prospect seems to be enticing for the Simons Foundation, a
philanthropic organization in New York City that announced in August
that it would provide US$2.5 million per year for at least 4 years to
help researchers to move forward on the gravity–quantum information
connection. “Information theory provides a powerful way to structure our
thinking about fundamental physics,” says Patrick Hayden, the Stanford
physicist who is directing the programme. He adds that the Simons
sponsorship will support 16 main researchers at 14 institutions
worldwide, along with students, postdocs and a series of workshops and
schools. Ultimately, one major goal is to build up a comprehensive
dictionary for translating geometric concepts into quantum language, and
vice versa. This will hopefully help physicists to find their way to
the complete theory of quantum gravity.
Still,
researchers face several challenges. One is that the bulk–boundary
correspondence does not apply in our Universe, which is neither static
nor bounded; it is expanding and apparently infinite. Most researchers
in the field do think that calculations using Maldacena’s correspondence
are telling them something true about the real Universe, but there is
little agreement as yet on exactly how to translate results from one
regime to the other.
Another challenge is that
the standard definition of entanglement refers to particles only at a
given moment. A complete theory of quantum gravity will have to add time
to that picture. “Entanglement is a big piece of the story, but it’s
not the whole story,” says Susskind.
He thinks physicists may have to embrace another concept from quantum information theory: computational complexity,
the number of logical steps, or operations, needed to construct the
quantum state of a system. A system with low complexity is analogous to a
quantum computer with almost all the qubits on zero: it is easy to
define and to build. One with high complexity is analogous to a set of
qubits encoding a number that would take aeons to compute.
Susskind’s
road to computational complexity began about a decade ago, when he
noticed that a solution to Einstein’s equations of general relativity
allowed a wormhole in AdS space to get longer and longer as time went
on. What did that correspond to on the boundary, he wondered? What was
changing there? Susskind knew that it couldn’t be entanglement, because
the correlations that produce entanglement between different particles
on the boundary reach their maximum in less than a second. In an article last year,
however, he and Douglas Stanford, now at the Institute for Advanced
Study, showed that as time progressed, the quantum state on the boundary
would vary in exactly the way expected from computational complexity.
Quantum quest: Reinventing quantum theory
“It appears more and more that the growth
of the interior of a black hole is exactly the growth of computational
complexity,” says Susskind. If quantum entanglement knits together
pieces of space, he says, then computational complexity may drive the
growth of space — and thus bring in the elusive element of time. One
potential consequence, which he is just beginning to explore, could be a
link between the growth of computational complexity and the expansion
of the Universe. Another is that, because the insides of black holes are
the very regions where quantum gravity is thought to dominate,
computational complexity may have a key role in a complete theory of
quantum gravity.
Despite the remaining
challenges, there is a sense among the practitioners of this field that
they have begun to glimpse something real and very important. “I didn’t
know what space was made of before,” says Swingle. “It wasn’t clear that
question even had meaning.” But now, he says, it is becoming
increasingly apparent that the question does make sense. “And the answer
is something that we understand,” says Swingle. “It’s made of
entanglement.
