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), which are 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 historical paradoxes. If a time traveler attempts to change the past, the laws of physics will ensure that events unfold in a way that avoids paradoxes. This means that while a time traveler can influence past events, those influences must ultimately lead to a consistent historical narrative.

However, Novikov's self-consistency principle has been debated in relation to certain interpretations of quantum mechanics. Specifically, it raises questions about how it interacts with fundamental principles such as 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 principle. 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. Both approaches can lead to insights into how time travel might be reconciled with quantum mechanics, although they may introduce concepts that challenge conventional understandings of these theories.^[8][9]