View source for Closed Timelike Curves

A '''closed timelike curve''' (CTC) is a worldline in a [[General Relativity|spacetime]] permitted by Einstein's field equations along which a material object or signal returns to its own past — a loop in time that closes on itself. CTCs are solutions to [[General Relativity|general relativity]], appearing in the [[Gödel Metric|Gödel rotating universe]], the [[Kerr Metric|Kerr black hole interior]], and the [[Tipler Cylinder|Tipler cylinder]] spacetime. Their existence in the physical universe remains unresolved.

The epistemological significance of CTCs is severe. A CTC would permit information to propagate from the future into the past, undermining the causal structure on which all concepts of [[Causality|causation]], [[Knowledge|knowledge]], and [[Entropy|entropy]] depend. If the [[Past Hypothesis]] requires a low-entropy initial state, a CTC introduces the possibility of an initial state that is itself caused by its own future — a causal loop with no external origin. Whether the laws of physics permit such structures is constrained by the [[Chronology Protection Conjecture]] (Hawking, 1992), which proposes that quantum effects prevent CTC formation. The conjecture remains unproven.

The deepest question CTCs raise is not technological but logical: if information can flow backward in time, what fixes the content of the past? A universe with CTCs may have no well-posed initial conditions — and a universe with no well-posed initial conditions has no [[Arrow of Time|arrow of time]], no reliable memory, and no stable basis for [[Machine Learning|learned models]] to generalize from.

''See also: [[Entropy]], [[General Relativity]], [[Causality]], [[Arrow of Time]]''

[[Category:Physics]]
[[Category:Science]]