Professor Juan Maldacena, one of the most influential theoretical physicists of the past three decades, discusses the deep connections between quantum entanglement, space-time geometry, and black hole physics — ideas that have reshaped how physicists think about the fundamental nature of reality.
What Space-Time Is Made Of
In general relativity, space-time is a primary, fundamental object — not made of anything else. But in a more complete quantum theory of gravity, space-time may emerge from more fundamental quantum degrees of freedom, such as qubits living on a boundary far away.
This is the holographic picture: the interior of a space-time is described by quantum systems living on its boundary, and the geometry of the bulk emerges from those boundary degrees of freedom.
The fields of the Standard Model (electromagnetic, electron, Higgs, etc.) live in space-time and are well-tested experimentally. But the field that describes the metric — the geometry of space-time itself — is only understood classically. A full quantum description fails in key places: the Big Bang and the interior of black holes.
Why General Relativity and Quantum Mechanics Are Hard to Combine
The core conceptual difficulty is that quantum mechanics requires an ordering of measurements and an external observer, but in gravity everything — including the observer — is inside the system. There is no observer with zero mass or energy who can stand outside and measure.
Space-time in general relativity can have different geometries and topologies, and there is no fixed background to define the order of operations.
Technical issues (like infinities in four dimensions) are separate from these conceptual ones. Even in two dimensions, where technical problems are tamer, the conceptual puzzles — black holes, closed universes, the role of the observer — remain.
Black Hole Entropy and the Work of Witten, Pennington, and Others
A black hole’s entropy, in the leading approximation, is its horizon area in Planck units. Hawking radiation contributes a quantum correction that naively diverges as you approach the horizon.
Recent work by Witten, Pennington, and collaborators derived a finite expression for black hole entropy in semi-classical gravity by combining the area contribution and the radiation contribution without ever encountering infinities. This uses type 3 to type 2 von Neumann algebra techniques.
This is an improvement within semi-classical gravity — it does not resolve what happens at the singularity or at the Big Bang, but it gives a cleaner description of black hole entropy when the black hole interacts with small amounts of matter.
The Singularity: What We Don’t Understand
The deepest unsolved problem about black holes is the interior. Einstein’s equations predict that curvature becomes infinite at the singularity — but the singularity is not a place inside the black hole, it is a moment in the future that anything falling in must hit.
The singularity is “just a name for things we don’t understand.” A full theory of quantum gravity should describe what actually happens there.
From the outside, we have a fairly precise conceptual understanding of black holes (temperature, Hawking radiation, entropy). From the inside, we do not.
Extremal Black Holes and Quantum Corrections
A charged black hole that evaporates down to its minimum mass for a given charge is called extremal — its Hawking temperature goes to zero, and it develops a long, self-similar near-horizon region.
For very large black holes, quantum gravity corrections are generally tiny, but very close to extremality, a particular quantum correction becomes important. This gives a controllable setting where one aspect of geometry is quantized while the rest remains classical.
Iliesiu and Turiaci showed that for four-dimensional near-extremal black holes, quantum corrections drive the entropy to zero at extremality, making these black holes consistent with the third law of thermodynamics (zero temperature implies zero entropy), unlike the classical prediction.
The Island Formula and the Page Curve
Hawking’s information paradox: black holes seem to emit featureless thermal radiation regardless of what fell in, apparently violating unitarity. But the laws of physics should, in principle, allow information to be recovered — just as shredded documents can be reassembled.
The island formula, developed by Almheiri, Engelhardt, Marolf, Maxfield, and Pennington, computes the entropy of Hawking radiation using an area formula — the area of a surface inside the black hole (the “island”) that extremizes area.
This entropy follows the Page curve: it grows as the black hole evaporates, then decreases back to near zero when evaporation is complete, consistent with unitary evolution and information preservation.
The formula was originally derived using Euclidean path integral techniques (needed to prepare thermal states and get real-valued answers), but more recent work by Marolf, Pennington, and others has given it a more purely Lorentzian derivation.
The Ryu-Takayanagi Formula and Quantum Information
In 2006, Ryu and Takayanagi discovered a new entropy formula: the fine-grained (von Neumann) entropy of a region is given by the area of a minimal surface in the interior, not the horizon.
This connects space-time geometry directly to quantum information — specifically to the Shannon/von Neumann entropy that measures the information available to an observer with infinite resources.
The island formula is an extension of this idea, applied to the radiation outside the black hole.
ER = EPR
In the same year (1935), Einstein and Rosen wrote two papers: one on entanglement (EPR) and one on what is now called the Einstein-Rosen bridge (ER) — a wormhole connecting two black hole exteriors through a shared interior.
The conjecture ER = EPR proposes that entanglement between two quantum systems is equivalent to a geometric connection — a wormhole — between them. In the specific case of two black holes in the thermofield double entangled state, the resulting geometry is the Einstein-Rosen bridge, and the argument is fairly convincing.
The bolder claim — that any entanglement gives rise to a geometric connection — requires a generalized notion of geometry beyond Einstein’s equations. For two entangled spin-1/2 particles, there is no conventional connected geometry, so the claim must involve some new, broader concept of geometry.
Maldacena views ER = EPR as an aspiration or principle that a complete theory of quantum gravity should satisfy.
Wormholes: Leaky Pipes
Wormholes are a central puzzle in quantum gravity. They produce useful effects — they are essential for deriving the island formula and for understanding aspects of quantum chaos (as shown by Saad, Shenker, and Stanford) — but they also suggest that the constants of nature might not be fixed, which conflicts with how they appear in string theory.
The various ideas surrounding wormholes are not all mutually compatible. Resolving these tensions is an active area of research.
Traversable Wormholes
The wormholes arising from entanglement (ER = EPR) are not traversable — you cannot send signals through them, consistent with the fact that entanglement alone cannot transmit information.
However, if the two black holes are brought close together and allowed to interact, the geometry can change and form a traversable wormhole — one without a horizon, where you can enter one mouth and exit the other.
These traversable wormholes do not allow faster-than-light travel in the ambient space. They are more like tunnels through the Earth: a shortcut that, from the traveler’s perspective, takes very little time due to gravitational time dilation, even though an outside observer sees a long duration.
They are classically forbidden but can exist thanks to quantum corrections (negative energies). They are compatible with general principles of physics but would require conditions not present in our universe.
Quantum Computers and Wormhole Simulation
Recent experiments with small numbers of qubits (around seven per side) have simulated the simplest models that display features analogous to wormholes — correlated quantum systems with some wormhole-like properties.
Whether this counts as “simulating” or “creating” a wormhole is partly a philosophical question. As quantum computers become more powerful, the simulations will become more convincing, much like a sandpile becomes unambiguously a sandpile once you have enough grains.
Celestial Holography
Strominger and collaborators study gravity in flat space at long distances, uncovering symmetries (the BMS group, recognized in the 1960s) and connecting them to scattering amplitudes and the gravitational memory effect.
This program seeks an alternative description of flat-space gravity in terms of a quantum system on a celestial sphere, analogous to how AdS/CFT describes negatively curved spaces. It is viewed as a stepping stone toward understanding more realistic cosmologies.
dS/CFT and Dark Energy
AdS/CFT relates negatively curved (anti-de Sitter) spaces to quantum field theories on their boundaries. dS/CFT would do the same for de Sitter space — the expanding universe that describes our cosmos at late times.
The boundary of de Sitter space is a spatial three-surface in the far future, and the hope is that a statistical theory on this boundary describes the universe with emergent time.
The main difficulty is that de Sitter space lacks the extra symmetries (like supersymmetry) that made AdS/CFT tractable, and no concrete example of dS/CFT has been found. It may be that the relationship is only approximate.
If DESI’s results suggesting time-varying dark energy hold up, the far future of the universe would not be exactly de Sitter, but this does not obviously rule out dS/CFT — the dark energy might eventually settle down. More worrisome would be evidence that the equation of state parameter w goes below minus one, which would violate the null energy condition and causality.
Unitarity and Locality
Unitarity — the conservation of probability — is considered sacred because without it, probabilities could become negative or exceed one, making the theory uninterpretable.
Locality is more subtle in quantum gravity. When the geometry itself is fluctuating, the distance between two points is not fixed — there is always some probability of a geometry where they are close. So manifest locality (in a fixed background) may be given up, but a deeper notion of causality — that signals cannot travel faster than light in the asymptotic region — is expected to survive.
Quantum Error Correction and Holography
Almheiri, Dong, and Harlow proposed that the way bulk degrees of freedom are encoded in the boundary theory is analogous to quantum error correction. Tensor networks — mathematical structures similar to neural networks for quantum systems — have shed light on how the bulk is embedded in the boundary.
Harlow raised objections to some of the assumptions in entanglement wedge reconstruction, and the discussion of the precise relationship between quantum error correction and holography remains active.
Is the Boundary or the Bulk More Fundamental?
Many physicists now say the bulk emerges from the boundary, because the boundary theory is better understood. But Maldacena thinks it is possible that in the future, the bulk theory (e.g., string theory/M-theory) will be understood well enough that the duality will be seen as a true equivalence, with neither side privileged.
Erik Verlinde disagrees, arguing the boundary is more real. Maldacena notes that general relativity is an effective field theory with known limitations, and string theory — while not fully understood — could in principle provide a complete bulk description.
Is Space-Time Doomed?
The slogan “space-time is doomed” means that the fundamental concept of quantum gravity will not be space-time as we know it. Just as Minkowski unified space and time into space-time, a new theory will require a new basic concept — one that nobody has yet identified.
Candidate approaches include Verlinde’s entropic gravity (which works well near black hole horizons but is unclear beyond them) and Nima Arkani-Hamed’s program of deriving space-time from scattering amplitudes and positive geometries. The amplitude program has already produced powerful mathematical tools used in collider physics and cosmology.
Inflation and Gravitational Waves
Maldacena hopes that the field range during inflation is finite — a constraint from quantum gravity (related to wormhole effects) that is debated, notably by Eva Silverstein.
If true, this would predict that upcoming CMB experiments would not detect primordial gravitational waves. Maldacena is of two minds: he would welcome a falsifiable prediction from quantum gravity, but he would also be more excited to actually detect the waves, as it would confirm that inflation happened and that quantum gravity effects are real.
Observers and the Emergence of Time
In de Sitter space, quantum corrections to the thermal entropy produce imaginary contributions — the number of states is not positive. Including a real observer moving through the space makes the answer positive.
This suggests there is no “view from nowhere” in quantum gravity — an observer (or clock) is necessary to define time. Time is what a clock measures, and a clock is a physical system with energy and mass that must be included in the quantum description.
Similarly, length requires a ruler. In classical general relativity, observers can be treated as massless and non-disruptive, but in quantum gravity they must be accounted for as physical systems.
Maldacena’s Personal Reflections
His father, who fixed elevators and cars, inspired a hands-on, problem-solving approach. Maldacena sees theoretical physics as fixing conceptual architectures — making formulas and ideas fit together.
He is not able to turn off his mind and constantly jots down ideas, a trait his wife finds both characteristic and occasionally disruptive.
His office at the Institute for Advanced Study is nearly empty — he prefers to keep the focus on the blackboard.
He describes himself as a perpetual student, learning from students, postdocs, and collaborators. He had to learn the mathematical techniques behind Witten and Pennington’s entropy formula from scratch.
A great PhD student, in his view, comes up with ideas that initially seem wrong but turn out to be correct — as happened when Aron Wall proposed a generalization of the Ryu-Takayanagi formula that Maldacena initially dismissed.
His landmark 1997 AdS/CFT paper grew out of a “boring” project assigned by his advisor Curtis Callan on statistical models in hyperbolic space — the tools he developed became essential later.
He did not feel good enough as a graduate student. His advice: it is common to feel inadequate, but contributions come with time — first small ones, then larger ones. Understanding things deeply and in your own way, rather than repeating lore, is essential.
He uses AI as a learning tool, for checking formulas, and for doing integrals (sometimes more effectively than Mathematica), but encourages others to experiment and find their own uses rather than imitate his approach.
He admires Nima Arkani-Hamed for his unbounded energy and ability to move between deep mathematics and phenomenology, and Witten for his extraordinary depth and breadth — knowing things better than specialists in many fields, and expressing ideas with precision where every word matters.
