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.
If a time traveler attempts to change the past, the laws of physics will ensure that events unfold in a way that avoids paradoxes.
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.
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] In 1991, David Deutsch proposed a method to explain how quantum systems interact with closed timelike curves (CTCs) using time evolution equations.
[13] Furthermore, Deutsch's method may not align with common probability calculations in quantum mechanics unless we consider multiple paths leading to the same outcome.
For instance, if everything except a single qubit travels through a time machine and flips its value according to a specific operator: Deutsch argues that maximizing von Neumann entropy is relevant in this context.
[17] For example, Tolksdorf and Verch demonstrated that quantum systems in spacetimes without CTCs can achieve results similar to Deutsch's criterion with any prescribed accuracy.
Consequently, they argue that their findings raise doubts about Deutsch's explanation of his time travel scenario using many-worlds interpretations of quantum physics.
Seth Lloyd proposed an alternative approach to time travel with closed timelike curves (CTCs), based on "post-selection" and path integrals.
[22] Unlike classical approaches, path integrals can accommodate histories involving CTCs, although their application requires careful consideration of quantum mechanics' principles.
This aligns with post-selection, where specific outcomes are considered based on predetermined criteria; however, it does not guarantee that all paradoxical scenarios are eliminated.
Michael Devin (2001) proposed a model that incorporates closed timelike curves (CTCs) into thermodynamics,[23] suggesting it as a potential way to address the grandfather paradox.
[24][25] This model introduces a "noise" factor to account for imperfections in time travel, proposing a framework that could help mitigate paradoxes.