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Time travel to the future is possible and has been experimentally verified millions of times. If an astronaut were to travel near the speed of light, it might take him, say, one minute to reach the nearest stars. Four years would have elapsed on Earth, but for him only one minute would have passed, because time would have slowed down inside the rocket ship. Hence he would have travelled four years into the future, as experienced here on Earth. (Our astronauts actually take a short trip into the future every time they go into outer space. As they travel at 18,000 miles per hour above the Earth, their clocks beat a tiny bit slower than clocks on Earth. The world record for travelling into the future is held by the Russian cosmonaut Sergei Avdeyev, who orbited for 748 days and was hence hurled .02 seconds into the future.)
But perhaps the thorniest problems are the logical paradoxes raised by time travel. For example, what happens if we kill our parents before we are born? This is a logical impossibility. It is sometimes called the 'grandfather paradox'...Third, the universe splits into two. On one timeline the people whom you killed look just like your parents, but they are different, because you are now in a parallel universe. This latter possibility seems to be the one consistent with the quantum theory.