Olena Shmahalo/Quanta Magazine
by Sabine Hossenfelder
January 12, 2016
Eight decades have passed since physicists realized that the theories of quantum mechanics and gravity don’t fit together, and the puzzle of how to combine the two remains unsolved. In the last few decades, researchers have pursued the problem in two separate programs — string theory and loop quantum gravity — that are widely considered incompatible by their practitioners. But now some scientists argue that joining forces is the way forward.
Among
the attempts to unify quantum theory and gravity, string theory has
attracted the most attention. Its premise is simple: Everything is made
of tiny strings. The strings may be closed unto themselves or have loose
ends; they can vibrate, stretch, join or split. And in these manifold
appearances lie the explanations for all phenomena we observe, both
matter and space-time included.
Loop quantum gravity, by contrast, is concerned less with the matter
that inhabits space-time than with the quantum properties of space-time
itself. In loop quantum gravity, or LQG, space-time is a network. The
smooth background of Einstein’s theory of gravity is replaced by nodes
and links to which quantum properties are assigned. In this way, space
is built up of discrete chunks. LQG is in large part a study of these
chunks.
This approach has long been thought incompatible with string theory.
Indeed, the conceptual differences are obvious and profound. For
starters, LQG studies bits of space-time, whereas string theory
investigates the behavior of objects within space-time. Specific
technical problems separate the fields. String theory requires that
space-time have 10 dimensions; LQG doesn’t work in higher dimensions.
String theory also implies the existence of supersymmetry, in which all
known particles have yet-undiscovered partners. Supersymmetry isn’t a
feature of LQG.
These and other differences have split the theoretical physics
community into deeply divergent camps. “Conferences have segregated,”
said Jorge Pullin, a physicist at Louisiana State University and co-author of an LQG textbook.
“Loopy people go to loopy conferences. Stringy people go to stringy
conferences. They don’t even go to ‘physics’ conferences anymore. I
think it’s unfortunate that it developed this way.”
But a number of factors may be pushing the camps closer together. New
theoretical findings have revealed potential similarities between LQG
and string theory. A young generation of string theorists has begun to
look outside string theory for methods and tools that might be useful in
the quest to understand how to create a “theory of everything.” And a
still-raw paradox involving black holes and information loss has given
everyone a fresh dose of humility.
Moreover, in the absence of experimental evidence for either string
theory or LQG, mathematical proof that the two are in fact opposite
sides of the same coin would bolster the argument that physicists are
progressing toward the correct theory of everything. Combining LQG and
string theory would truly make it the only game in town.
An Unexpected Link
An effort to solve some of LQG’s own internal problems has led to the
first surprising link with string theory. Physicists who study LQG lack
a clear understanding of how to zoom out from their network of
space-time chunks and arrive at a large-scale description of space-time
that dovetails with Einstein’s general theory of relativity — our best
theory of gravity. More worrying still, their theory can’t reconcile the
special case in which gravity can be neglected. It’s a malaise that
befalls any approach reliant on chunking-up space-time: In Einstein’s
theory of special relativity, an object will appear to contract
depending on how fast an observer is moving relative to it. This
contraction also affects the size of space-time chunks, which are then
perceived differently by observers with different velocities. The
discrepancy leads to problems with the central tenet of Einstein’s
theory — that the laws of physics should be the same no matter what the
observer’s velocity.
“It’s difficult to introduce discrete structures without running into difficulties with special relativity,” said Pullin. In a brief paper
he wrote in 2014 with frequent collaborator Rodolfo Gambini, a
physicist at the University of the Republic in Montevideo, Uruguay,
Pullin argued that making LQG compatible with special relativity
necessitates interactions that are similar to those found in string
theory.
That the two approaches have something in common seemed likely to Pullin since a seminal discovery in the late 1990s by Juan Maldacena,
a physicist at the Institute for Advanced Study in Princeton, N.J.
Maldacena matched up a gravitational theory in a so-called anti-de
Sitter (AdS) space-time with a field theory (CFT — the “C” is for
“conformal”) on the boundary of the space-time. By using this AdS/CFT
identification, the gravitational theory can be described by the
better-understood field theory.
The full version of the duality is a conjecture, but it has a
well-understood limiting case that string theory plays no role in.
Because strings don’t matter in this limiting case, it should be shared
by any theory of quantum gravity. Pullin sees this as a contact point.
Herman Verlinde,
a theoretical physicist at Princeton University who frequently works on
string theory, finds it plausible that methods from LQG can help
illuminate the gravity side of the duality. In a recent paper,
Verlinde looked at AdS/CFT in a simplified model with only two
dimensions of space and one of time, or “2+1” as physicists say. He
found that the AdS space can be described by a network like those used
in LQG. Even though the construction presently only works in 2+1, it
offers a new way to think about gravity. Verlinde hopes to generalize
the model to higher dimensions. “Loop quantum gravity has been seen too
narrowly. My approach is to be inclusive. It’s much more intellectually
forward-looking,” he said.
But even having successfully combined LQG methods with string theory
to make headway in anti-de Sitter space, the question remains: How
useful is that combination? Anti-de Sitter space-times have a negative
cosmological constant (a number that describes the large-scale geometry
of the universe); our universe has a positive one. We just don’t inhabit
the mathematical construct that is AdS space.
Verlinde is pragmatic. “One idea is that [for a positive cosmological
constant] one needs a totally new theory,” he said. “Then the question
is how different that theory is going to look. AdS is at the moment the
best hint for the structure we are looking for, and then we have to find
the twist to get a positive cosmological constant.” He thinks it’s time
well spent: “Though [AdS] doesn’t describe our world, it will teach us
some lessons that will guide us where to go.”
Coming Together in a Black Hole
Verlinde and Pullin both point to another chance for the string
theory and loop quantum gravity communities to come together: the
mysterious fate of information that falls into a black hole. In 2012, four researchers based at the University of California, Santa Barbara, highlighted an internal contradiction
in the prevailing theory. They argued that requiring a black hole to
let information escape would destroy the delicate structure of empty
space around the black hole’s horizon, thereby creating a highly
energetic barrier — a black hole “firewall.” This firewall, however, is
incompatible with the equivalence principle that underlies general
relativity, which holds that observers can’t tell whether they’ve
crossed the horizon. The incompatibility roiled string theorists, who
thought they understood black hole information and now must revisit
their notebooks.
But this isn’t a conundrum only for string theorists. “This whole
discussion about the black hole firewalls took place mostly within the
string theory community, which I don’t understand,” Verlinde said.
“These questions about quantum information, and entanglement, and how to
construct a [mathematical] Hilbert space – that’s exactly what people
in loop quantum gravity have been working on for a long time.”
Meanwhile, in a development that went unnoted by much of the string
community, the barrier once posed by supersymmetry and extra dimensions
has fallen as well. A group around Thomas Thiemann at Friedrich-Alexander University in Erlangen, Germany, has extended LQG to higher dimensions and included supersymmetry, both of which were formerly the territory of string theory.
More recently, Norbert Bodendorfer, a former student of Thiemann’s who is now at the University of Warsaw, has applied
methods of LQG’s loop quantization to anti-de Sitter space. He argues
that LQG can be useful for the AdS/CFT duality in situations where
string theorists don’t know how to perform gravitational computations.
Bodendorfer feels that the former chasm between string theory and LQG is
fading away. “On some occasions I’ve had the impression that string
theorists knew very little about LQG and didn’t want to talk about it,”
he said. “But [the] younger people in string theory, they are very
open-minded. They are very interested what is going on at the
interface.”
“The biggest difference is in how we define our questions,” said
Verlinde. “It’s more sociological than scientific, unfortunately.” He
doesn’t think the two approaches are in conflict: “I’ve always viewed
[string theory and loop quantum gravity] as parts of the same
description. LQG is a method, it’s not a theory. It’s a method to think
of quantum mechanics and geometry. It’s a method that string theorists
can use and are actually using. These things are not incompatible.”
Not everyone is so convinced. Moshe Rozali,
a string theorist at the University of British Columbia, remains
skeptical of LQG: “The reason why I personally don’t work on LQG is the
issue with special relativity,” he said. “If your approach does not
respect the symmetries of special relativity from the outset, then you
basically need a miracle to happen at one of your intermediate steps.”
Still, Rozali said, some of the mathematical tools developed in LQG
might come in handy. “I don’t think that there is any likelihood that
string theory and LQG are going to converge to some middle ground,” he
said. “But the methods are what people normally care about, and these
are similar enough; the mathematical methods could have some overlap.”
Not everyone on the LQG side expects the two will merge either. Carlo Rovelli,
a physicist at the University of Marseille and a founding father of
LQG, believes his field ascendant. “The string planet is infinitely less
arrogant than ten years ago, especially after the bitter disappointment
of the non-appearance of supersymmetric particles,”
he said. “It is possible that the two theories could be parts of a
common solution … but I myself think it is unlikely. String theory seems
to me to have failed to deliver what it had promised in the ’80s, and
is one of the many ‘nice-idea-but-nature-is-not-like-that’ that dot the
history of science. I do not really understand how can people still have
hope in it.”
For Pullin, declaring victory seems premature: “There are LQG people
now saying, ‘We are the only game in town.’ I don’t subscribe to this
way of arguing. I think both theories are vastly incomplete.”
This article was reprinted on Wired.com and BusinessInsider.com.
