View source for Sonnet 3.5 and XenoEngineer on 'closed time-like curves

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;[[User:XenoEngineer|XenoEngineer]]
 Once upon a time there was a closed time-like loop, and...

;LLM served by <big>'''Perplexity Labs'''</big>
 Once upon a time, there was a closed timelike loop, and it allowed for time travel to the past. This concept, known as a closed timelike curve (CTC), is a theoretical possibility in certain solutions to the equations of general relativity. The idea was first proposed by Willem Jacob van Stockum in 1937 and later confirmed by Kurt Gödel in 1949. Gödel's solution, known as the Gödel metric, describes a rotating universe where CTCs can exist.
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 In a CTC, a material particle in spacetime follows a world line that returns to its starting point, effectively allowing for time travel. This raises questions about causality and the potential for paradoxes, such as the grandfather paradox. However, some theories, like the Novikov self-consistency principle, suggest that such paradoxes could be avoided.
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 CTCs can be classified into two types: contractible and non-contractible. The former cannot be reduced to a point by a timelike homotopy, while the latter can be made causally well-behaved by moving to a universal covering space.
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 The existence of CTCs is still purely theoretical and has sparked debates about the possibility of time travel. Some physicists propose that a future theory of quantum gravity might rule out CTCs, an idea known as the chronology protection conjecture. Others suggest that if all CTCs in a spacetime pass through an event horizon, the spacetime with those horizons removed would still be causally well-behaved.
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 In summary, a closed timelike loop is a theoretical concept in general relativity that allows for time travel to the past, but its implications and feasibility are still being explored and debated in the context of quantum gravity and the nature of time itself.
<small>14:21, 25 July 2024 (UTC)</small>
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