The conjecture was proposed by
Leonard Susskind and
Juan Maldacena in 2013. They proposed that a wormhole (Einstein–Rosen bridge or ER bridge) is equivalent to a pair of maximally
entangled black holes. EPR refers to
quantum entanglement (
EPR paradox). The symbol is derived from the first letters of the surnames of authors who wrote the first paper on wormholes (
Albert Einstein and
Nathan Rosen) and the first paper on entanglement (Einstein,
Boris Podolsky and Rosen). The two papers were published in 1935, but the authors did not claim any connection between the concepts. that a maximally extended
AdS-Schwarzschild black hole, which is a non-traversable wormhole, is dual to a pair of maximally entangled thermal
conformal field theories via the
AdS/CFT correspondence. They backed up their conjecture by showing that the pair production of charged black holes in a background
magnetic field leads to entangled black holes, but also, after
Wick rotation, to a wormhole. This conjecture sits uncomfortably with the
linearity of quantum mechanics. An entangled state is a linear
superposition of separable states. Presumably, separable states are not connected by any wormholes, but yet a superposition of such states is connected by a wormhole.
Generalizations to Unequal Mass and Charge The original and most-studied formulation of the ER=EPR correspondence concerns the eternal Schwarzschild black hole, which is dual to two identical, entangled quantum systems described by the thermofield double (TFD) state. This idealized scenario involves two uncharged, non-rotating black holes of equal mass, connected by a perfectly symmetric, non-traversable Einstein-Rosen bridge. From the quantum perspective, the two systems are no longer in the symmetric TFD state. Instead, they are described by a more general entangled state, sometimes called an asymmetric or "lopsided" thermofield double, which reflects the fact that the Hamiltonians governing the two black holes (H_1 and H_2) are different. The entanglement between the two black holes persists, but the perfect symmetry under interchange is broken. From the geometric perspective, this asymmetry in the quantum state has a direct dual in the wormhole's structure: • A difference in mass (\Delta M = M_1 - M_2) or charge (\Delta Q = Q_1 - Q_2) creates a non-zero stress-energy tensor T_{\mu\nu} inside the wormhole. This can be visualized as a domain wall or a shockwave propagating through the wormhole's interior. The conjecture leads to a grander conjecture that the geometry of space, time and gravity is determined by entanglement.
Length of the ER bridge A particularly powerful extension of the ER=EPR dictionary relates the internal geometry of the Einstein-Rosen bridge, specifically its spatial volume or "length," to the detailed phase information of the entangled quantum state. The standard, symmetric thermofield double (TFD) state, |TFD\rangle = \sum_n e^{-\beta E_n/2} |n\rangle_L \otimes |n\rangle_R, corresponds to the eternal black hole at the moment of time-reversal symmetry (t=0), which represents the shortest possible wormhole connecting the two exteriors. This implies that the internal geometry of the wormhole is not merely a static representation of entanglement's existence, but a dynamic structure that precisely encodes the relative quantum phases of the state, with the wormhole's "length" acting as a geometric measure of the temporal offset or "computational time" separating the two entangled systems. == References ==