# Gravity's Rainbow Theory May Solve Black Hole Information Paradox

No, this isn't the story of Thomas Pynchon's novel solving the information paradox, but it's still pretty cool. According to a new extrapolation from Einstein's theory of gravity called "gravity's rainbow," the event horizons of black holes do not exist where space and time do not exist, and if this fact is taken into account, then there is nothing stopping information from leaving a black hole.

Gravity's rainbow is a theory that arose from attempts by physicists to generate a "theory of everything," or a theory of the universe that unites quantum mechanics and general relativity: "Even though no one has been able to discover such a theory, there are various candidates," study coauthor Ahmed Farag Ali told Phys.org. "These include ideas like taking space and time as fundamentally discrete, or using some mathematical loops as a fundamental quantity to construct space and time, or even replacing particles by tiny strings, and many other exotic ideas.

"What many of these models have in common is that it can be inferred from them that the energy of a particle cannot get as large as possible, but that there is a maximum energy that any particle can reach. This restriction can be easily combined with Einstein's special theory of relativity, and the resultant theory is called the doubly special theory of relativity, or DSR."

When scientists generalize the DSR to include gravity, gravity's rainbow is born, or the theory that gravity affects particles with different energies in different ways. "In gravity's rainbow, space does not exist below a certain minimum length, and time does not exist below a certain minimum time interval," said Ali. "So, all objects existing in space and occurring at a time do not exist below that length and time interval [which are associated with the Planck scale]. As the event horizon is a place in space which exists at a point in time, it also does not exist below that scale."

This theory could solve one of the biggest questions the scientific community has for black holes: the information paradox. According to the classical theory of black holes, physical information is destroyed within the event horizon as matter devolves into a particular physical state. But one of the fundamental tenets of quantum mechanics, called unitarity, postulates that physical information is encoded into a system's wave function, and therefore is conserved in the quantum sense. So if the information cannot truly be destroyed, then many observed effects of black holes, such as Hawking radiation, fail to make sense.

One of the most common theories postulated to solve this paradox involves asymptotic and ingoing observers seeing completely different things when observing a black hole. According to this theory, if a person is falling into a black hole, then he or she will theoretically observe the information (his or her body) fall into the event horizon, while someone who is observing the black hole from the outside will see the ingoing observer approaching the event horizon for an infinite amount of time, but never reaching it. There is technically no paradox inherent to this solution, but this solution is arguably just as counterintuitive as the paradox itself.

But according to their paper, making calculations based on gravity's rainbow leads to the conclusion that both observers see the ingoing observer fall into the event horizon in a finite amount of time, and therefore the information paradox is resolved. "If we restrict our description to scales at which space and time exist, then the apparent paradoxes associated with black holes seem to naturally resolve," Ali said. "For example, as the information paradox depends on the existence of the event horizon, and an event horizon like all objects does not exist below a certain length and time interval, then there is no absolute information paradox in gravity's rainbow. The absence of an effective horizon means that there is nothing absolutely stopping information from going out of the black hole."

"The most important lesson from this paper is that space and time exist only beyond a certain scale," said Ali. "There is no space and time below that scale. Hence, it is meaningless to define particles, matter, or any object, including black holes, that exist in space and time below that scale. Thus, as long as we keep ourselves confined to the scales at which both space and time exist, we get sensible physical answers. However, when we try to ask questions at length and time intervals that are below the scales at which space and time exist, we end up getting paradoxes and problems."