The information paradox is an interesting problem in cosmology and astrophysics regarding black holes (Figure 1). Bekenstein and Hawking went at it over this matter, but that’s another story that has made its way into many nonfiction books. Basically, the paradox, as stated in wiki:
The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state. This is a contentious subject since it violates a commonly assumed tenet of science—that in principle complete information about a physical system at one point in time should determine its state at any other time. A postulate of quantum mechanics is that complete information about a system is encoded in its wave function, an abstract concept not present in classical physics.
For the unindoctrinated in scientific terminology and concepts, this is a lot to take in. Thus, it is useful to shed light on several aspects of this matter. Quantum mechanics (QM) and general relativity (GR) are the two major mathematical models of the physical realm. Quite simply, QM models things small and GR models things big. There’s more to it than that, honestly; go to the links or do a web search if interested.
What’s important to know is this:
there is no single theory that has been able to unify these two physical models - the goal being a theory of quantum gravity. More on this below.