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A nonorientable spacetime can obstruct a global choice of temporal or spatial orientation while remaining locally smooth. We develop three spacecraft thought experiments: temporal (T), spatial (P), and combined (PT) orientation reversal. An explicit Lorentzian quotient shows how a proper-time clock can advance while the returned trajectory has decreasing time in the departure region. A spatial quotient reverses molecular handedness while preserving the ordinary temporal arrow; a combined quotient reverses both comparisons. These geometric statements do not establish an intact returning organism, antimatter conversion, advanced communication, or a computational resource. Those claims require a specified matter theory, radiation state and probability law.The analysis connects wormhole and active-camera sketches to the two-boundary programme, corrects several common identifications of T , P , CP T , entropy and photon recoil, and treats observed T violation explicitly. Mirror biology is discussed alongside the Stanford-hosted 2024 technical report, with attention to the difference between molecular chirality and a new mirror particle sector. A seam–lift table separates exact field consistency from approximate chemistry. A literature survey and a worked Ellis crossing quantify tides, support and instability. A stochastic bridge illustrates opposite entropy arrows; exact quantum and classical examples distinguish a future selection effect from an ordinary complete experiment. The Earth–rocket verifier and a weak-weight photon model make the proposed 2WQC resource and its unverified assumptions explicit. We close with Earth-return stories and a film premise in which the restrictions generate the drama.
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Jarek Duda (2026) studied this question.
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