**Entangled universe: Could wormholes hold the cosmos together?**

Weird wormholes through space-time might stitch the cosmos together and make reality real

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