Entanglement = Wormholes

One of the most enjoyable and inspiring physics papers I have read in recent years is this one by Mark Van Raamsdonk. Building on earlier observations by Maldacena and by Ryu and Takayanagi. Van Raamsdonk proposed that quantum entanglement is the fundamental ingredient underlying spacetime geometry.* Since my first encounter with this provocative paper, I have often mused that it might be a Good Thing for someone to take Van Raamsdonk’s idea really seriously.

Now someone has.

I love wormholes. (Who doesn’t?) Picture two balls, one here on earth, the other in the Andromeda galaxy. It’s a long trip from one ball to the other on the background space, but there’s a shortcut:You can walk into the ball on earth and moments later walk out of the ball in Andromeda. That’s a wormhole.

I’ve mentioned before that John Wheeler was one of my heros during my formative years. Back in the 1950s, Wheeler held a passionate belief that “everything is geometry,” and one particularly intriguing idea he called “charge without charge.” There are no pointlike electric charges, Wheeler proclaimed; rather, electric field lines can thread the mouth of a wormhole. What looks to you like an electron is actually a tiny wormhole mouth. If you were small enough, you could dive inside the electron and emerge from a positron far away. In my undergraduate daydreams, I wished this idea could be true.

But later I found out more about wormholes, and learned about “topological censorship.” It turns out that if energy is nonnegative, Einstein’s gravitational field equations prevent you from traversing a wormhole — the throat always pinches off (or becomes infinitely long) before you get to the other side. It has sometimes been suggested that quantum effects might help to hold the throat open (which sounds like a good idea for a movie), but today we’ll assume that wormholes are never traversable no matter what you do.

Alice and Bob are in different galaxies, but each lives near a black hole, and their black holes are connected by a wormhole.

Love in a wormhole throat: Alice and Bob are in different galaxies, but each lives near a black hole, and their black holes are connected by a wormhole. If both jump into their black holes, they can enjoy each other’s company for a while before meeting a tragic end.

Are wormholes any fun if we can never traverse them? The answer might be yes if two black holes are connected by a wormhole. Then Alice on earth and Bob in Andromeda can get together quickly if each jumps into a nearby black hole. For solar mass black holes Alice and Bob will have only 10 microseconds to get acquainted before meeting their doom at the singularity. But if the black holes are big enough, Alice and Bob might have a fulfilling relationship before their tragic end.

This observation is exploited in a recent paper by Juan Maldacena and Lenny Susskind (MS) in which they reconsider the AMPS puzzle (named for Almheiri, Marolf, Polchinski, and Sully). I wrote about this puzzle before, so I won’t go through the whole story again. Here’s the short version: while classical correlations can easily be shared by many parties, quantum correlations are harder to share. If Bob is highly entangled with Alice, that limits his ability to entangle with Carrie, and if he entangles with Carrie instead he can’t entangle with Alice. Hence we say that entanglement is “monogamous.” Now, if, as most of us are inclined to believe, information is “scrambled” but not destroyed by an evaporating black hole, then the radiation emitted by an old black hole today should be highly entangled with radiation emitted a long time ago. And if, as most of us are inclined to believe, nothing unusual happens (at least not right away) to an observer who crosses the event horizon of a black hole, then the radiation emitted today should be highly entangled with stuff that is still inside the black hole. But we can’t have it both ways without violating the monogamy of entanglement!

The AMPS puzzle invites audacious reponses, and AMPS were suitably audacious. They proposed that an old black hole has no interior — a freely falling observer meets her doom right at the horizon rather than at a singularity deep inside.

MS are also audacious, but in a different way. They helpfully summarize their key point succinctly in a simple equation:


Here, EPR means Einstein-Podolsky-Rosen, whose famous paper highlighted the weirdness of quantum correlations, while ER means Einstein-Rosen (sorry, Podolsky), who discovered wormhole solutions to the Einstein equations. (Both papers were published in 1935.) MS (taking Van Raamsdonk very seriously) propose that whenever any two quantum subsystems are entangled they are connected by a wormhole. In many cases, these wormholes are highly quantum mechanical, but in some cases (where the quantum system under consideration has a weakly coupled “gravitational dual”), the wormhole can have a smooth geometry like the one ER described. That wormholes are not traversable is important for the consistency of ER = EPR: just as Alice cannot use their shared entanglement to send a message to Bob instantaneously, so she is unable to send Bob a message through their shared wormhole.

AMPS imagined that Alice could distill qubit C from the black hole’s early radiation and carry it back to the black hole, successfully verifying its entanglement with another qubit B distilled from the recent radiation. Monogamy then ensures that qubit B cannot be entangled with qubit A behind the horizon. Hence when Alice falls through the horizon she will not observe the quiescent vacuum state in which A and B are entangled; instead she encounters a high-energy particle. MS agree with this conclusion.

AMPS go on to say that Alice’s actions before entering the black hole could not have created that energetic particle; it must have been there all along, one of many such particles constituting a seething firewall.

Here MS disagree. They argue that the excitation encountered by Alice as she crosses the horizon was actually created by Alice herself when she interacted with qubit C. How could Alice’s actions, executed far, far away from the black hole, dramatically affect the state of the black hole’s interior? Because C and A are connected by a wormhole!

The ER = EPR conjecture seems to allow us to view the early radiation with which the black hole is entangled as a complementary description of the black hole interior. It’s not clear yet whether this picture works in detail, and even if it does there could still be firewalls; maybe in some sense the early radiation is connected to the black hole via a wormhole, yet this wormhole is wildly fluctuating rather than a smooth geometry. Still, MS provide a promising new perspective on a deep problem.

As physicists we often rely on our sense of smell in judging scientific ideas, and earlier proposed resolutions of the AMPS puzzle (like firewalls) did not smell right. At first whiff, ER = EPR may smell fresh and sweet, but it will have to ripen on the shelf for a while. If this idea is on the right track, there should be much more to say about it. For now, wormhole lovers can relish the possibilities.

Eventually, Wheeler discarded “everything is geometry” in favor of an ostensibly deeper idea: “everything is information.” It would be a fitting vindication of Wheeler’s vision if everything in the universe, including wormholes, is made of quantum correlations.

*Update: Commenter JM reminded me to mention Brian Swingle’s beautiful 2009 paper, which preceded Van Raamsdonk’s and proposed a far-reaching connection between quantum entanglement and spacetime geometry.

65 thoughts on “Entanglement = Wormholes

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