Quantum mechanics of time travel

The theoretical study of time travel generally follows the laws of general relativity. Quantum mechanics requires physicists to solve equations describing how probabilities behave along closed timelike curves (CTCs), theoretical loops in spacetime that might make it possible to travel through time.^[1][2][3][4]

In the 1980s, Igor Novikov proposed the self-consistency principle.^[5] According to this principle, any changes made by a time traveler in the past must not create paradoxes. If a time traveler tries to change the past, the laws of physics will ensure that history remains consistent. This means that the outcomes of events will always align with the traveler’s actions in a way that prevents any contradictions.

However, Novikov's self-consistency principle may be incompatible when considered alongside certain interpretations of quantum mechanics, particularly two fundamental principles of quantum mechanics, unitarity and linearity. Unitarity ensures that the total probability of all possible outcomes in a quantum system always sums to 1, preserving the predictability of quantum events. Linearity ensures that quantum evolution preserves superpositions, allowing quantum systems to exist in multiple states simultaneously.^[6]

There are two main approaches to explaining quantum time travel while incorporating Novikov's self-consistency. The first approach uses density matrices to describe the probabilities of different outcomes in quantum systems, providing a statistical framework that can accommodate the constraints of CTCs. The second approach involves state vectors,^[7] which describe the quantum state of a system. This approach sometimes leads to concepts that deviate from the conventional understanding of quantum mechanics.