IT WAS a cryptic email that pinged across the US to fellow physicist 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?
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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 (Â鶹´«Ă˝, 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 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. and 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”
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