I thought about time travel and some fictional experiments.
1st Experiment: a gold ingot, from the future is sent to the past to be both fused. What would happen?
2nd one: A robot travels from the future to the past with these orders; going to a special room with a wall. If this wall is blue it has to be red-colored painted, if it's red color then to be blue-colored paint, if it's a different color then randomly to paint red or blue. After the time travel: what color is the wall?
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To avoid headaches about time travels in fantasy fiction, with ghost and deities I though something. The alteration of the past by the time travelers are possible, at least partially. The past isn't really erased and rewritten but more like using adding a layer or correction fluid. Then it would be something like "Schöringer's cat", yes and no at the same time. In my games, theses uchronies or alternate timelines, with changed little details are practically pocket universes. But if the alteration of the past is too radical, for example killing an important Historical character, then the things are different. Let's say these demiplanes need special "anchors" in the space-time continuum. When different time-traveler factions fights each other to change or keep the past, the key are these anchors. Without these the alternate timeline doesn't disappear, but suffer "planar holes" allowing cosmic gates to be opened by potential alien invaders, for example the Far Realm (D&D). These uchronies become
dream, or nightmare, realms. This could cause planar conflicts, for example nazis from the 4th Reich sending spies to an alternate timeline where Arthur, prince of England survived the sweating sickness and became king. Later Spain and England formed one empire (Anglican schism never happened because Henry VIII was not king but his older brother Arthur) and technologic advance arrived sooner.