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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The Einstein Rosen bridge and the Einstein Podolsky Rosen paradox, ER and EPR: Wormhole and entanglement

The Einstein-Rosen Bridge and the Einstein Podolsky Rosen paradox. I demonstrate that the two-body problem in general relativity was a heuristic guide in Einstein’s and collaborators’1935 work on the Einstein-Rosen bridge and EPR paradox.

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 call 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.

EPR

This image was published in a Nature article, Ron Cowen, “The quantum source of space-time”,  explaining the geometry–entanglement relationship and Maldacena’s and Susskind’s ER = EPR idea: Quantum entanglement is linked to a wormhole from general relativity. This representation is deterministic and embodies the many worlds interpretation: Collapse of the wave function never takes place. Instead, interactions cause subsystems to become entangled. Each measurement causes the branches of the tree to decohere; the quantum superposition being replaced by classical probabilities. The observer follows a trajectory through a tree. The entire tree, i.e., the entire wave function, must be retained and the universe is the complicated network of entanglements, branches of the tree: the wormhole bifurcating throats and mouths in the universe. See Susskind’s new paper from April 2016. Hence general relativity and quantum mechanics are linked by ER = EPR and Einstein’s soul can rest in peace because god will not play dice.

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.

I uploaded a paper to the ArXiv: “Two-body problem in general relativity: A heuristic guide for the Einstein-Rosen bridge and EPR paradox”

In this paper I discuss the possible historical link between the 1935 Einstein-Rosen bridge paper and the 1935 Einstein-Rosen-Podolsky paper. The paper is a first version and I intend to upload a second version.

Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and, with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was also occupied with quantum theory. He believed that quantum theory was an incomplete representation of real things. Together with Rosen and Boris Podolsky he invented the EPR paradox. In this paper I demonstrate that the two-body problem in general relativity was a heuristic guide in Einstein’s and collaborators’1935 work on the Einstein-Rosen bridge and EPR paradox.

In 1935 Einstein explained that one of the imperfections of the general theory of relativity was that as a field theory it was not complete in the following sense: it represented the motion of particles by the geodesic equation. A mass point moves on a geodesic line under the influence of a gravitational field. However, a complete field theory implements only fields and not the concepts of particle and motion. These must not exist independently of the field but must be treated as part of it. Einstein wanted to demonstrate that the field equations for empty space are sufficient to determine the motion of mass points. In 1935 Einstein attempted to present a satisfactory treatment that accomplishes a unification of gravitation and electromagnetism. For this unification Einstein and Rosen needed a description of a particle without singularity. In 1935, they joined two Schwarzschild solutions at the Schwarzschild limit and omitted part of the space-time beyond the Schwarzschild singularity. They showed that it was possible to do this in a natural way and they proposed the Einstein-Rosen bridge solution.

In the Einstein-Rosen bridges paper of 1935, Einstein negated the possibility that particles were represented as singularities of the gravitational field because of his polemic with Ludwig Silberstein. Silberstein thought he had demonstrated that general relativity was problematic. He constructed, for the vacuum field equations for the two-body problem, an exact static solution with two singularity points that lie on the line connecting these two points. The singularities were located at the positions of the mass centers of the two material bodies. Silberstein concluded that this solution was inadmissible physically and contradicted experience. According to his equations the two bodies in his solution were at rest and were not accelerated towards each other; these were nonallowed results and therefore Silberstein thought that Einstein’s field equations should be modified together with his general theory of relativity. Before submitting his results as a paper to the Physical Review, Silberstein communicated them to Einstein. This prompted Einstein’s remark, in his paper with Rosen in 1935, that matter particles could not be represented as singularities in the field.

Einstein and Rosen were trying to permanently dismiss the Schwarzschild singularity and adhere to the fundamental principle that singularities of the field are to be excluded. Einstein explained that one of the imperfections of the general theory of relativity was that as a field theory it was not complete because it represented the motion of particles by the geodesic equation. Einstein also searched for complete descriptions of physical conditions in quantum mechanics. It seems that the two-body problem in general relativity was a heuristic guide in the search of a solution to the problem that the psi function cannot be interpreted as a complete description of a physical condition of one system. He thus proposed the EPR paradox with Rosen and Podolsky.

Updated 2016