Entangled universe: Could wormholes hold the cosmos together?
Weird wormholes through space-time might stitch the cosmos together and make reality real
us a promising new route to a theory of everything
IT WAS a cryptic email that Juan Maldacena pinged across the US to
fellow physicist Leonard Susskind back in 2013. At its heart lay a
single equation: “ER = EPR”. The message clicked with its recipient.
“I instantly knew what he was getting at,” says Susskind. “We both
got quite excited.”
Excited, because that one equation promises to forge a connection
between two very different bits of physics first investigated by
Albert Einstein almost 80 years ago. Excited, because it could help
resolve paradoxes swirling around those most befuddling of cosmic
objects, black holes, and perhaps provide a route to a unified
theory of physics. Excited, because it might even answer one of the
most fundamental questions of all: what is reality made of?
The origins of the story lie precisely a century ago. In November
1915, Einstein presented the final form of his revolutionary theory
of gravity to the Prussian Academy of Sciences in Berlin. The
general theory of relativity overturned notions of gravity that
stretched back as far as Isaac Newton’s day. It said that everything
that happens in the cosmos at large — be it an apple falling from a
tree on Earth or the distant whirling of a cluster of galaxies —
happens because stuff follows invisible contortions in space and
time that are caused by the presence of other stuff. Gravity follows
from the geometry of a warped space-time.
In the past century, general relativity has never failed an
experimental test. Yet the suspicion has grown that it is missing
something (New Scientist, 10 October, p 29). The theory describes
space-time as a malleable yet smooth and featureless backdrop to
reality. Problems start when a great agglomeration of matter folds
this cosmic fabric so tightly that a black hole singularity arises —
an object with a gravitational pull so great that nothing can
escape.
Black holes are a prediction from the earliest days of general
relativity. But in the 1970s, physicists Jacob Bekenstein and
Stephen Hawking derived a strange result about them: black holes
have a temperature, and hence a property called entropy. This takes
us into the realms of quantum theory where everything, be it forces
or matter, comes in discrete chunks. Entropy measures how many ways
you can organise a system’s various constituents — the arrangement
of atoms in a gas, for example. The greater the number of possible
configurations, the higher the entropy.
Hole in the theory
But if a black hole is just an extreme scrunching of smooth
space-time, it should have no substructure, and thus no entropy. For
Susskind, of Stanford University in California, this contradiction
points to a hole in Einstein’s theory. “We know that general
relativity is incomplete,” he says. “Its inability to account for
the entropy of black holes is probably the most obvious
incompleteness of the theory.”
That’s a turn up for the books. In his lifetime, Einstein levelled a
similar charge at quantum theory. In May 1935, the New York Times
ran a story with the headline “Einstein Attacks Quantum Theory”,
reporting on a paper Einstein had written with Boris Podolsky and
Nathan Rosen. It brought to light a weird property of the quantum
world in which two particles could instantly influence each other,
even if they were at opposite ends of the universe. In Einstein’s
view, this “spooky action at a distance” — quantum entanglement, as
it became known — was preposterous. It was a clear sign there was
something missing from the quantum description of reality.
But quantum theory has breezed through even more precise
experimental tests than those devised for general relativity. And it
is the very property that Einstein discovered — entanglement — that
continues to expose the contradictions between the two theories.
Allowing quantum entanglement and general relativity to cohabit in
the contorted space-time around black holes yields unpleasant and
unsustainable consequences. For example, information seems to be
destroyed — an impossibility according to quantum physics — or the
black hole becomes surrounded by a blazing “firewall” of energetic
particles (see “Paradox regained”).
So we need some way to square the two schools of thought — to
quantise space-time and form a quantum theory of gravity. Susskind
and Maldacena, who works at the Institute of Advanced Studies in
Princeton, have long been leading lights in perhaps the most
promising field with this aim: string theory. It replaces the
point-like particles of current quantum theories with wiggling
strings of infinitesimal size, and suggests space-time has a grainy
substructure — you can’t keep chopping it indefinitely into smaller
and smaller pieces.
But if string theory does hold the answer, it’s well hidden. The
theory has more than 10⁵⁰⁰ solutions, each describing a different
sort of universe — making it nigh-on impossible to find the one
solution that corresponds to the geometrically flat, expanding
space-time filled with the exact complement of fundamental particles
we observe around us.
A startling insight from Maldacena in 1997 gave new hope. He
conjectured that string theory equations describing gravity in some
volume of space-time were just the same as a set of quantum
equations describing the surface of that volume. If you could solve
the surface equations, you could get a viable theory describing
gravity inside.
This “Maldacena duality” was a bold leap — but physicists found that
it held. “The funny thing was that it was not proven, and it was
difficult to even understand why this was happening,” says theorist
Mark Van Raamsdonk of the University of British Columbia in
Vancouver, Canada. “It was very mysterious.”
In 2001, Maldacena himself provided an intriguing example, going
back to a paper written by — you guessed it — Einstein, again with
Rosen, and again in 1935. This one exposed another peculiarity of
black holes. It showed how something that looked like two separate
black holes from the outside might be connected on the inside. This
interior connection formed a shortcut through space-time, and came
to be known as an Einstein-Rosen bridge — or in common parlance, a
wormhole.
Quantum chewing gum
The really odd thing, though, was that Maldacena’s duality showed
that such a wormhole would only form if the outsides of the black
holes were quantum-entangled.
By 2009, the underlying mathematics was sufficiently well developed
for Van Raamsdonk to explore further. Entanglement is not an on/off
thing — it can exist in varying degrees. So what would happen if you
were to slowly reduce the amount of entanglement between the black
holes’ surfaces to nothing? The answer was rather like pulling at
two ends of a piece of chewing gum. “The two sides get further
apart, and what’s connecting them is this really thin piece of gum,
and eventually it snaps,” he says. The wormhole becomes thinner
until it breaks, and you have two unconnected bits of space-time
(see diagram). Reverse the process — increase the entanglement — and
the wormhole starts to form again.
It took a few more years for the penny to finally drop in
Maldacena’s mind, and for him to make the suggestion laid out in
that excited email. ER = EPR. ER — the paper Einstein wrote with
Rosen in 1935 introducing the concept of wormholes. EPR — the paper
he wrote with Podolsky and Rosen the same year introducing the
concept of entanglement. What if, asked Maldacena, wormholes and
entanglement are in fact two sides of the same coin: the same
physics in two different guises?
The immediate attraction was that the principle seemed to get rid of
those pesky paradoxes involving firewalls around black holes (see
“Paradox lost”). But it also provided some form of explanation for
the phenomenon Van Raamsdonk’s work had exposed, in which space-time
in the form of wormholes could be created and destroyed simply by
tweaking the amount of entanglement.
“It’s pointing to a statement that is really quite dramatic,” says
Van Raamsdonk. “Space-time is really just some geometrical
manifestation of entanglement.” Maldacena comes to the same
conclusion. “There is a very close connection between quantum
mechanics and space-time,” he says. “The continuity of space-time,
which seems to be something very solid, could come from the ghostly
properties of entanglement.” Susskind speculates further. Quantum
entanglement is a form of information, and so “space-time is a
manifestation of quantum information”, he says.
Heady stuff. But does that really mean that when quantum
entanglement exists between two particles — as can easily be made to
happen, say between photons in a lab experiment — they are connected
by a microscopic wormhole? Or that we live on a backdrop that is
nothing more than the 1s and 0s of entangled information?
The short answer is we don’t know. One very big caveat is that all
of the work linking entanglement with space-time so far has been
done with a space-time that isn’t expanding. Van Raamsdonk and
others are working to extend the results to the sort of expanding,
accelerating space-time that makes our cosmos.
But for those involved, this is the most positive lead yet towards a
theory of quantum gravity that can unify the forces of nature. The
ER = EPR principle is something “that a theory of quantum gravity
should obey”, says Maldacena. Susskind thinks so too. “We are sure
that these things are going to be part of the final story,” he says.
“But I don’t think we have a clear picture of what that final story
is yet.”
Others are less convinced. Joe Polchinski and Don Marolf are
physicists at the University of California, Santa Barbara, and part
of the team that exposed the black hole firewall paradox. Polchinski
is concerned that the ER = EPR idea will end up modifying a central
principle of quantum theory, known as superposition. Exemplified by
Schrödinger’s cat, this principle explains that a quantum system can
exist in two different states at the same time. When quantum objects
become entangled, they also enter a superposition.
At first glance, the ER = EPR hypothesis would mean quantum systems
that become entangled, and therefore enter a superposition, suddenly
gain a wormhole — a conjuring trick the superposition principle
doesn’t obviously allow. That’s problematic, says Polchinski.
“Quantum mechanics is weird, but it works,” he says. “When you give
up superposition, it’s just weird.”
Still, he remains open to the eventuality. “In the history of
science, things that seemed absolute in many important cases have
turned out to be not absolute,” he says — Newton’s law of
gravitation, for example. “Maybe superposition is one of them.”
Maldacena says that it’s too early to say if their work is
threatening the superposition principle, because the mathematics
hasn’t been worked out in detail.
Marolf for his part isn’t convinced the ER = EPR equality works in
all circumstances: Susskind and Maldacena have shown how to avoid
the firewall only for a particular entangled state of black holes.
“You might think that it shows how to get out of the [firewall]
paradox for any highly entangled state, but that’s not true,” says
Marolf.
Given that Einstein developed the ideas of both wormholes and
entanglement, one can only wonder what he would have made of it all.
“My guess is that the old Einstein would have said poppycock,” says
Susskind — after all, Einstein spent much of his later years arguing
for a hidden reality that wasn’t subject to the vagaries of quantum
mechanics. “But the young Einstein apparently had a much more
flexible mind. My guess [is] that the young Einstein would have
embraced these ideas, loved them.”
Paradox regained: The black hole problem
In the 1970s, Stephen Hawking showed that black holes emit
radiation. The mechanism has to do with quantum mechanics, which
allows pairs of quantum-entangled particles to spontaneously pop
into existence. When this happens near a black hole’s event horizon,
one particle may travel outwards, while the other goes towards the
black hole. The result is a steady stream of outgoing particles,
called Hawking radiation.
If no new matter falls into the black hole, this emission means the
black hole will eventually evaporate. But matter is information, and
in quantum theory information is sacrosanct: it can never be
destroyed. So if a black hole evaporates, what happens to the
matter, and therefore information, that fell into it?
One possible solution to this “black hole information loss paradox”
is the idea that information escapes with the Hawking radiation. But
in 2012, Joseph Polchinski and Don Marolf of the University of
California, Santa Barbara, and colleagues showed this option creates
other problems. General relativity demands that the space-time
around a black hole’s horizon should be smooth and featureless. It
turns out that for this to be the case and for information not to be
lost, a Hawking particle on its way in would have to be entangled
with all other Hawking particles that left the black hole at all
earlier times, rather than just its partner outside the horizon.
This offends a fundamental quantum rule known as “monogamy of
entanglement” — that a quantum particle can only ever be fully
entangled with one particle at a time. But if you break the
polyamorous entanglement of Hawking particles, an energetic
“firewall” of radiation forms at the event horizon. That,
unfortunately, goes against the tenets of general relativity.
Paradox preserved.
Paradox lost: the black hole solution
The main problem with the black hole paradox is the idea of quantum
monogamy — a particle can only be entangled with one other particle
at a time (see “Paradox regained”). This means that three quantum
systems — say a particle inside a black hole’s event horizon, a
particle outside it, and a third far, far away — can’t all be
entangled at the same time.
But physicists Juan Maldacena and Leonard Susskind argue that this
can be resolved if the particles just inside the horizon and the
particles far away are connected via a wormhole. When a wormhole
connects two objects, one must lie to the future of the other.
So, although these two particles might be entangled, their
entanglement doesn’t necessarily conflict with the entanglement of
the particle inside the horizon and its immediate partner outside
the horizon — because they aren’t all happening at the same time.
Uncomfortable apparitions such as blazing firewalls at the event
horizon disappear. Paradox removed.
This article appeared in print under the headline “Entangled
universe”
By Anil Ananthaswamy
Anil Ananthaswamy is a consultant for New Scientist
