Traversable ER = EPR wormholes are possible

In 2013 Juan Maldacena and Leonard Susskind demonstrated that the Einstein Rosen bridge between two black holes is created by EPR-like correlations between the microstates of the two black holes. They called this the ER = EPR relation, a geometry–entanglement relationship: entangled particles are connected by a Schwarzschild wormhole. In other words, the ER bridge is a special kind of EPR correlation. Maldacena and Susskind’s conjecture was that these two concepts, ER and EPR, are related by more than a common publication date 1935. If any two particles are connected by entanglement, the physicists suggested, then they are effectively joined by a wormhole. And vice versa: the connection that physicists call a wormhole is equivalent to entanglement. They are different ways of describing the same underlying reality.
Maldacena and Susskind explain that one cannot use EPR correlations to send information faster than the speed of light. Similarly, Einstein Rosen bridges do not allow us to send a signal from one asymptotic region to the other, at least when suitable positive energy conditions are obeyed. This is sometimes stated as saying that (Schwarzschild) Lorentzian wormholes are not traversable.
In 2017, however, Ping Gao, Daniel Louis Jafferis, and Aron C. Wall showed that the ER = EPR allows the Einstein-Rosen bridge to be traversable. This finding comes with implications for the black hole information paradox (of Stephen Hawking) and black hole interiors because hypothetically, an observer can enter a Schwarzschild black hole and then escape to tell about what they have seen. This suggests that black hole interiors really exist and that what goes in must come out and we can learn about the information that falls inside black holes.
Consider a light signal, traveling through the throat of the wormhole. In 1962, Robert Fuller and John Archibald Wheeler were troubled by the apparent possibility that a test particle, or a photon, could pass from one point in space to another point in space, distanced perhaps extremely far away, in a negligible interval of time. Such rapid communication of a particle or a photon, passing through an Einstein-Rosen bridge violates elementary principles of relativity and causality, according to which a light signal cannot exceed the speed of light.
Wheeler and Fuller, however, showed that relativity and causality, despite first expectations, are not violated. It is perfectly possible to write down a mathematical expression for the metric of a space-time which has simple Schwarzschild wormhole geometry. However, when we deal with the passage of light by the “long way” from one wormhole mouth to the other, both on the same space, the throat becomes dynamically unstable and the Einstein-Rosen bridge is non-traversable (see figure, middle).

Wormhole
What would cause an Einstein-Rosen bridge to be traversable? Recall that according to the ER = EPR, an Einstein Rosen bridge between two black holes is created by EPR-like correlations between the microstates of the two black holes. In 2017 scholars found that if one extends the ER = EPR conjecture by equating, not a Schwarzschild wormhole between two black holes and a pair of entangled particles, but a Schwarzschild wormhole and a situation which is somewhat analogous to what occurs in quantum teleportation (between the two sides of the wormhole), then the Einstein-Rosen bridge becomes traversable.
Entanglement alone cannot be used to transmit information and we need quantum teleportation because the qubit is actually transmitted through the wormhole say Gao, Jafferis and Wall: “Suppose Alice and Bob share a maximally entangled pair of qubits, A and B. Alice can then transmit [teleport] the qubit Q to Bob by sending only the classical output of a measurement on the Q-A system. Depending on which of the 4 possible results are obtained, Bob will perform a given unitary operation on the qubit B, which is guaranteed to turn it into the state Q”. But: “Of course in the limit that Alice’s measurement is essentially instantaneous and classical, the traversable window will be very small … — just enough to let the single qubit Q pass through. Therefore, we propose that the gravitational dual description of quantum teleportation understood as a dynamical process is that the qubit passes through the ER=EPR wormhole of the entangled pair, A and B, which has been rendered traversable by the required interaction”.
Next, say Alice throws qubit Q into black hole A. She then measures a particle of its Hawking radiation, a, and transmits the result of the measurement through the external universe to Bob, who can use this knowledge to operate on b, a Hawking particle coming out of black hole B. Bob’s operation reconstructs Q, which appears to pop out of B, a perfect match for the particle that fell into A. The new traversable ER = EPR wormhole allows information to be recovered from black holes. Thus, Gao, Jafferis and Wall write regarding the black hole information paradox:
“Another possible interpretation of our result is to relate it to the recovery of information … [from evaporating black holes]. Assuming that black hole evaporation is unitary, it is in principle possible to eventually recover a qubit which falls into a black hole, from a quantum computation acting on the Hawking radiation. Assuming that you have access to an auxiliary system maximally entangled with the black hole, and that the black hole is an efficient scrambler of information, it turns out that you only need a small (order unity) additional quantity of Hawking radiation to reconstruct the qubit. In our system, the qubit may be identified with the system that falls into the black hole from the left and gets scrambled, the auxiliary entangled system is … on the right, and the boundary interaction somehow triggers the appropriate quantum computation to make the qubit reappear again, after a time of order the scrambling time”. …
Thus, the Gao, Jafferis, Wall ER = EPR wormhole idea seems to extend to the so-called real world as long as two black holes are causally connected and coupled in the right way. If you allow the Hawking radiation from one of the black holes to fall into the other, the two black holes become entangled, and the quantum information that falls into one can exit the other. Thus, Gao, Jafferis and Wall conclude:
“Our example thus provides a way to operationally verify a salient feature of ER=EPR that observers from opposite sides of an entangled pair of systems may meet in the connected interior. … What we found is that if, after the observers jump into their respective black holes, a … coupling is activated, then the Einstein-Rosen [bridge] can be rendered traversable, and the meeting inside may be seen from the boundary. This seems to suggest that the ER=EPR wormhole connection was physically ‘real'”.
Finally the ER = EPR wormhole does not require energy-matter that violates the average null energy condition; the negative energy matter in the ER = EPR configuration is similar to the Casimir effect, and any infinite null geodesic which makes it through the ER = EPR wormhole must be chronal, i.e. the ER = EPR wormhole does not violate Hawking’s chronology protection conjecture. In addition, the ER = EPR wormhole does not violate the generalized second law of thermodynamics.
Therefore, the ER = EPR wormhole is not a configuration with closed time-like curves and it, therefore, does not permit one to travel faster than light over long distances through space; in other words, it cannot serve as a time machine and thus does not violate causality.

 

For further details:

Ping Gao, Daniel Louis Jafferis, Aron C. Wall (2017). Traversable Wormholes via a Double Trace Deformation.

Natalie Wolchover, Newfound Wormhole Allows Information to Escape Black Holes

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Time Travel into the Past: How can a wormhole be transformed into a time machine?

In 1988, Kip Thorn and his students published a technical article about traversable wormholes (see here). In their article, they conjectured that if the laws of physics were to permit traversable wormholes they would probably also permit such a wormhole to be transformed into a time machine, which violates causality. This would allow for travel into the past. More than 25 years later, Thorn was involved with the movie Interstellar from its inception and he helped the producer Christopher Nolan and others weave science into the film’s fabric. However, according to Thorn, today almost thirty years have gone by and, the preponderance of evidence still suggests that traversable wormholes are an impossibility.

Wormhole creation would be governed by the laws of quantum gravity. A seemingly plausible scenario entails quantum foam (“foamy” topologies of space-time on length-scales of the order of the Planck length 1.3 x 10-33). One can imagine an advanced civilization pulling a wormhole out of the quantum foam, enlarging it to classical size, and threading it with exotic matter to hold it open. Of course, says Thorn, we do not understand the quantum gravity laws that control the foam, the pull, and the stages of enlargement. Moreover, we do not understand exotic matter very well either.

Thorn suggests the following thought experiment. I am paraphrasing here. Suppose both California desert and Dublin are connected by a wormhole. The two mouths of the wormhole are synchronized. Since the California desert and Dublin are not moving with respect to each other, I in the California desert can synchronize my clock with that of my friend in Dublin. Hence clocks remain synchronized inside the throat and between the two mouths regardless of the outside time. While a wormhole is a single unit connected by a throat, its two mouths open onto places that are totally different from each other. The wormhole throat itself is a single reference system. According to special relativity, we can, therefore, synchronize clocks in this reference system.

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Mouth in California Desert                             Mouth in Dublin

The images seen through a wormhole’s mouths. Photos by Catherine MacBride and Mark Interrante.

Both mouths look like crystal balls. When I look into my California desert mouth, I see a distorted image of a street in Dublin. That image is brought to me by light that travels through the wormhole from Dublin to California, rather like light traveling through an optical fiber. When you look into your Dublin mouth, you see a distorted image of the trees in the California desert.

In Thorn, Kip, The Science of Interstellar, W. W. Norton & Company, p. 133.

Imagine a situation where the wormhole has been created by an advanced civilization in some future year, say 3000. On January 1, 3000 the wormhole’s two mouths, A and B, are at rest with respect to each other. Subsequently, mouth A remains at rest in Dublin, while mouth B, in California desert, accelerates to near-light speed, then reverses its motion and returns to its original location. Suppose the advanced beings produce this motion by pulling on mouth B gravitationally. I, therefore, take mouth B for a round trip and travel outside the wormhole with mouth B moving at relativistic velocities. Mouth A will not have moved since nothing has been pulling on it. The two mouths A and B of the wormhole are moving with respect to each other, and the wormhole throat now has mouth A at one end and a hole B at the other end. Hence the geometry of the wormhole throat does not change during the whole trip of mouth B so that the length of the wormhole’s throat remains fixed.

Since the two mouths move with respect to each other, time dilation creates a time difference between the clocks next to each mouth. The motion of the mouth is like that of the twins in the standard special-relativistic twin paradox. Outside the wormhole, mouth B ages less than mouth A, but inside the wormhole, the clocks are still synchronized; mouth A and hole B are at rest relative to each other and therefore, both entrances of the wormhole will age equally. If I have traveled with mouth B at close to the speed of light, I might find myself ensconced for many years in the future after returning to my original location in California desert.

I finally return to California desert with mouth B and find I have aged only one day (namely, on the date January 2, 3000, as measured by my own time – my proper time). Suppose that I find myself, on returning to California desert, to have arrived on, say, January 1, 3010 (according to the standard special-relativistic twin paradox). This is the date that appears on the calendar on the wall of an abandoned creepy cabin in the desert. Stepping through mouth B in California desert on January 1, 3010 and emerging out of A in Dublin will take me back in time. I will emerge from A and find that it is January 2, 3000. This is so because it is as seen from Dublin and my clock remains synchronized with the clock in mouth A. Recall that I have aged only one day during the trip (on my subsequent return to California desert, the date was January 2, 3000, as measured by my own time).

Consequently, by traversing the wormhole from mouth B to mouth A, one can travel backward in time, namely one can traverse a closed timelike curve. The same relative aging that occurs in the twin paradox produces, here, closed timelike curves that loop through the wormhole. However, that traveler could never go further back into the past than the year 3000. No traveler can ever go further back in time than the original date of creation of the wormhole.

Fur further reading see my book: General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists.

How do science fiction writers explain traversable wormholes? In The Strange Days at Blake Holsey High science fiction television program, a group of science students (science club) at a private boarding school have discovered that their science teacher’s office floor has a traversable wormhole that connects major time periods and therefore deposits a traveler back in time to October 4, 1987, April 11, 1977, and October 4, 1879 (when Blake Holsey High and the wormhole were founded). One of the students is getting sucked into the wormhole:

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