A simple equation indicates wormholes may be the key to quantum gravity

SEP 19, 2021


Could this equation finally unite two of the biggest theories in physics?

Theoretical physicists have spent nearly a century trying to reconcile a unified physical theory of our universe out of quantum mechanics and general relativity.

The problem they face is that both prevailing theories work incredibly well at describing our world, and have both held up under repeated experimentation.

But the two might as well be describing two entirely different realities that never actually intersect.

General relativity can mathematically describe a leaf falling from a tree, the orbits of moons and planets, even the formation of galaxies, but is not much use when trying to predict the motion of an electron.

Quantum mechanics, meanwhile appears to violate nearly everything we know about the universe — that matter can only be in one place at any given time, that something can only be in one state at a time, or that observing something is not the same thing as interacting with it — but which nonetheless gives us the mathematical tools we need to create lasers, quantum computers, and many other modern technologies.

Recently, though, an interesting proposal about a thorny paradox involving black holes, ER = EPR, has been causing quite a stir among physicists, and it's easy to see why. This simple equation might be the wormhole we've been looking for that bridges the two seemingly irreconcilable theories.

The Great Black Hole Firewall Controversy

A Simple Equation Indicates Wormholes May Be the Key to Quantum Gravity
Source: Jeremy Schnittman/Wikimedia Commons

The equation ER = EPR was proposed in 2013 by the theoretical physicists Leonard Susskind and Juan Maldacena as a possible solution to one of the most contentious issues in modern physics: the black hole firewall.

The problem began in 1974, when British cosmologist Stephen Hawking proposed that black holes would actually leak particles and radiation, and eventually explode. This combined general relativity with quantum theory, but there was a big problem. Dr. Hawking concluded that the radiation coming from a black hole would be completely random, and would convey no information about what had fallen into it. When the black hole finally exploded, that information would be erased from the universe forever.

For particle physicists, this violated a basic tenet of quantum theory, that information is always preserved. Following a 30-year controversy, Dr. Hawking announced in 2004 that his theory was incorrect. However, Dr. Hawking might have been too hasty. At the time, nobody had figured out how information could get out of a black hole. But a group of researchers based in Santa Barabara may have found an answer.

First put forward in a 2012 paper published in the Journal of High Energy Physics, the black hole firewall theory states that immediately behind every event horizon of a black hole there must exist a veil of energy so intense that it completely incinerates anything that falls into it.

The authors demonstrated that information flowing out of a black hole is incompatible with having an area of Einsteinian space-time, the event horizon, at its boundary. Instead of the event horizon, a black hole would have a region of energetic particles — a “firewall” — located just inside.

The reason for this, according to the paper's authors, Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully — known collectively as AMPS — is that three key assumptions about black holes can't all be true: that information which falls into a black hole is not lost forever (unitarity); that physics outside the event horizon still functions as normal even if it breaks down beyond the event horizon (quantum field theory); and that an object passing the beyond the event horizon would not experience an immediate change (equivalence).

It is this last assumption that AMPS says gives rise to the firewall. AMPS argues that the entanglement of a pair of virtual particles responsible for Hawking radiation is broken at the event horizon, releasing an incredible amount of energy just behind and all along the entire visible boundary of a black hole.

This violation of a key principle of Einstein's General Relativity, however, would essentially lead to the unraveling of the core model of modern physics. If physicists don't like that idea, AMPS argues, then one of the other two pillars of physics as we know it must fall instead.

This has produced fierce debate ever since, with no satisfactory solution. Raphael Bousso, a string theorist at the University of California, Berkeley, says the problem posed by the firewall theory, "shakes the foundations of what most of us believed about black holes...It essentially pits quantum mechanics against general relativity, without giving us any clues as to which direction to go next."

Susskind and Maldacena, however, proposed a novel solution to this problem: wormholes, and this has far-reaching implications beyond just the firewall paradox.

Einstein, Black Holes, and Wormholes

A Simple Equation Indicates Wormholes May Be the Key to Quantum Gravity
Source: Rost-9D / iStock

When Albert Einstein published his theory of general relativity in 1916, he revolutionized our understanding of gravity by describing it as the curvature in the fabric of space and time created by the masses of objects in space.

Curvature in space-time can vary with mass, and in theory, in extreme cases, space-time can even curve so much that it touches some other point in the fabric, linking the two points together even if they are separated by vast distances, represent different points in time, or exist in different universes entirely.

Formally known as an Einstein-Rosen (ER) bridge, named for Einstein and his co-author of the 1935 paper describing the bridge, Nathan Rosen, this theoretical bridge in space time is more popularly called a wormhole.

Among the cases where wormholes are hypothesized to be most likely to form are black holes, and if two black holes form an ER bridge with each other, then the point where one black hole begins and the other one ends would essentially disappear.

An ER bridge isn't restricted to singularities though, and if the entwining of two distinct objects into a connected pair sounds familiar, then you're on your way to understanding ER = EPR.

Einstein and the Quantum Entanglement Paradox

Quantum entanglement, which Einstein famously derided as "spooky action at a distance", is the quantum phenomenon where two interacting particles becoming inextricably linked, so that knowledge of one of the pair immediately gives you knowledge of the other.

More critically, however, because a particle can be in more than one quantum state at once and will only assume a definite state when it is observed or interacted with in some manner, a particle's collapse from superposition into a defined state forces its entangled partner to collapse into the complementary quantum state instantaneously, regardless of the distance between the two.

For example, if one entangled particle's superposition, also described as its waveform or wave function, collapses into an "up" state when it is observed, its entangled partner simultaneously collapses into a "down" state, even if it is on the other side of the universe and it is not being observed at all. How does the other particle know to do this?

This question is what so rattled Einstein and others. This phenomenon clearly implies the communication of information from one particle to the other in violation of General Relativity, since this information exchange appears to travel faster than the speed of light, which is supposed to be the official speed limit of everything in the universe, information included.

Einstein, along with co-authors Rosen and Boris Podolsky, wrote in a 1935 paper that this violation of Relativity meant, "either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality."

Essentially, quantum mechanics as described must be leaving out some key principle that conforms it to general relativity, or the two particles could not instantaneously communicate.

Yet, entangled particles appear to be capable of doing exactly what Einstein, Podolsky, and Rosen say they cannot possibly do, giving rise to the Einstein-Podolsky-Rosen (EPR) paradox, a more formal way of describing quantum entanglement.

In fact, quantum entanglement plays a crucial role in quantum computing and, apparently, in explaining how information encoded in the Hawking radiation could get out of a black hole.

With the second half of the equation laid out, we can finally start to reckon with the implications of ER = EPR and how it could be key to unlocking the "Theory of Everything."

What is ER = EPR?

When Susskind and Maldacena first approached the black hole paradox in 2012, they weren't the first to see the possible connection between quantum entanglement and the structure of space-time.

Mark Van Raamsdonk, a theoretical physicist at the University of British Columbia, Vancouver, described an important thought experiment that suggests that an inscrutably complex network of quantum entanglements could actually be the threads that form the fabric of space-time itself.

What Susskind and Maldacena did was take this assumption and make the logical step that wormholes (ER) could be a form of quantum entanglement (EPR), and so entangled particles falling into black holes could still be connected to their partners outside the black hole via quantum-sized wormholes, or ER = EPR.

This form of entanglement would maintain the link between the particles on the interior of a black hole with the older exterior Hawking radiation without having to cross the event horizon and without having to violate the principle that a particle cannot be strongly entangled with two separate partners at once, thus avoiding the creation of the dreaded firewall.

This theory isn't without its critics though, especially since this kind of entanglement would require a re-evaluation of quantum mechanics itself (as AMPS rightly predicted it would). But what would it mean if Susskind and Maldacena are right and ER = EPR? It could mean everything, at least for the long-elusive unified theory of physics.

Could ER = EPR Bridge the Gap between Relativity and Quantum Mechanics?

A Simple Equation Indicates Wormholes May Be the Key to Quantum Gravity

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What makes ER = EPR more interesting, beyond AMPS' Firewall problem, is what it would mean if we had a describable principle that was the same in both quantum mechanics and relativistic physics.

If quantum entanglement and wormholes are fundamentally linked, then we would have our first real overlap between Relativity and quantum mechanics. Much like the wormholes or entangled particles they describe, these two seemingly disparate fields that have been separated for nearly a century would finally have a thread connecting them.

There is other evidence that this may be the case beyond ER = EPR. There is a lot of excitement around something known as tensor networks, a way of linking entangled particles with other entangled particles, so that A is linked to B and C is linked to D, but also that A and B are collectively linked as a pair to the pair C and D.

These linked pairs could be linked to other linked pairs and start to build complex quantum geometry that implies a strong connection to a curved, hyperbolic geometry of space-time. Our observations of the microwave background radiation strongly suggest a flat, Euclidean plane as a model for our universe, however, at least for the parts that are observable.

In both spherical and hyperbolic geometric models of the universe, though, the universe could still appear flat locally, with the curvature of space-time only becoming apparent once we take the part of space-time beyond the 13.8 billion light-years limit of the observable universe into account.

It's would be similar to the way the Earth looks flat from where you're standing (or sitting) right now, but that's only because you aren't high enough off the ground to perceive its true shape. Get high enough into the air and the spherical shape of the Earth becomes indisputable.

Using ER = EPR to connect quantum mechanics to relativistic physics could, in a way, provide us the theoretical elevation we've been missing to see the true shape of things and finally start to understand how the two theories are actually one and the same.

That's the idea, anyway. Whether that turns out to be the case remains to be seen, and ER = EPR could turn out to be a dud in the end. It wouldn't be the first time, but even those who express warranted skepticism, like AMPS' own Polchinski, find the idea worth looking into: "I don’t know where it’s going, but it’s a fun time right now."