Quantum mechanics of time travel

In general relativity, theories about time travel have traditionally been explored based on its laws. However, incorporating quantum mechanics into the picture requires physicists to solve equations describing how probabilities (represented by density matrices) behave along closed timelike curves (CTCs). CTCs are loops in spacetime that could theoretically enable time travel.

In the 1980s, Igor Novikov proposed the self-consistency principle. This principle suggests that regardless of a time traveler's attempts to alter the past, calculations would always lead to a consistent history. However, Novikov's self-consistency principle challenges determinism, which holds that every event has a cause, some standard interpretations of quantum mechanics (particularly unitarity), which maintains a total probability of 1, and linearity, which calculates combined probabilities.^[1]

There are two primary approaches to applying Novikov's self-consistency concept to quantum time travel. The first approach, the Deutsch prescription, utilizes a specific mathematical tool called a density matrix. The second approach employs a different concept, the state vector, and leads to theories deviating from standard interpretations of quantum mechanics.