In classical general relativity, black holes represent those points at which the fabric of space-time becomes so steeply warped that nothing can escape from them. One of the key goals of a quantum theory of gravity is precisely to resolve such "pathological" situations and to describe black holes as complex but self-consistent quantum systems. The problem is that as physicists have attempted to do just that, they have encountered the so-called "information paradox." Quantum mechanics tells us that information about quantum states of a system falling into a black hole cannot be irretrievably lost. At the same time, black holes can evaporate through the emission of Bekenstein-Hawking radiation. What happens to the information, then? Put differently, can two observers, one outside the black hole's boundary of no return (the "event horizon") and one falling through it, compare or share information?

Opinions on these questions varied, with some physicists arguing that the information is lost, and other contending that it is not. In the language of *quantum entanglement*, when the Bekenstein-Hawking radiation is emitted, the particle that escapes and the one that is swallowed by the black hole are mutually entangled. However, research suggested that the escaping particle is also entangled with all the previously emitted Bekenstein-Hawking radiation, contrary to a principle of "monogamy" stating that no particle can be entangled with two systems at the same time. To resolve this paradox, it has recently been suggested that there exists at the event horizon a "firewall," high-energy quanta emitted as the entanglement between the infalling and outgoing particles is broken. However, this in itself violates an important general relativistic concept: that if the black hole is massive enough, nothing dramatic should happen at the event horizon, since any system there is at free fall.

Faced with the possibility of having to relinquish either a principle of quantum mechanics (loss of information, or "unitarity") or one of general relativity (no drama at the event horizon, or the "equivalence principle"), physicists are now considering the potential loss of another assumption: *locality*. Locality basically asserts that particle interactions occur when the particles find themselves at adjacent points in space-time. Until now, this is what allowed particle physicists to calculate probabilities of interactions using small diagrammatic representations known as Feynman diagrams (*e.g.*, *Fig. 1*).

*Figure 1. A Feynman diagram representing an electron-positron pair annihilating into a photon, which in turn produces a quark-antiquark pair, with the antiquark radiating a gluon. (Credit: Joel Holdsworth/Wikimedia Commons.)*

Now Princeton physicist Nima Arkani-Hamed and colleagues have introduced a new method for calculating such probabilities, by determining the volume of a geometrical figure known as the *amplituhedron* (see an image here). The calculations are currently done for gluons, and they don't assume locality at all. Since graviton interactions may perhaps be computed through copies of gluon interactions (see "Toward a Quantum Theory of Gravity? (Part 1)"), the amplituhedron may provide insights into a non-local description of quantum gravity.

One thing is clear: While the road ahead still seems to be long and winding, with the possibility that physicists will have to give up some cherished concepts, there is no shortage of new ideas and fascinating research.