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Anyone can travel through time. Regardless of your intentions, you perform it at a constant rate of one second per second. There may not seem to be any comparison between moving at, say, one foot per second in one of the three spatial dimensions. However, according to Einstein's theory of relativity, time and space are interchangeable inside the four-dimensional continuum that is space-time. According to Einstein, time moves more slowly the quicker you go across space, which means you age more slowly. Nothing can move faster than the speed of light, which is roughly 186,000 miles per second, according to one of the fundamental principles of relativity.
That much is evident, but now comes the bizarre part. The trip would take the astronauts on board that spacecraft just seven weeks. The astronauts had essentially jumped around 10 months into the future as a result of time dilation, a consequence of relativity.
Time Dilation and Wormholes
It's not necessary to be moving quickly to experience time dilation. Even the relatively weak field here on Earth's surface, according to Einstein, produces a comparable effect. Because we spend our entire lives here, we aren't aware of the fact that time moves more quickly—by roughly 45 microseconds each day—and gravity is measurable weaker at a height of greater than 12,400 miles (20,000 kilometres). That's more important than you might realise since that's the height at which GPS satellites circle the Earth, and in order for the system to function correctly, their clocks must be exactly synchronised with those on the ground.
However, for more dramatic results, we must examine gravitational fields that are considerably stronger, such as those that surround black holes, which have the power to warp space-time to the point where it collapses in on itself. The outcome is a "wormhole," a term popularised by science fiction films but whose roots are in Einstein's theory of relativity. A wormhole essentially serves as a shortcut between two points in space-time. You go into one black hole and come out of another in a different location. "Closed time-like curves" is the technical term for space-time trajectories that travel back in time. There are many references to them in reputable scholarly journals, many more than there are references to "time travel." But in reality, time travel is what closed time-like curves are all about.
Although, why not?
Despite how improbable these occurrences seem on the surface; we are not yet aware of any basic scientific reason why they cannot happen. That's a challenging scenario because, in the words of physicist Michio Kaku (a quote from T.H. White's book "The Once and Future King"), "Everything not forbidden is compulsory." While Kaku is not saying that time travel must occur everywhere all the time, he is arguing that given the size of the universe, it should at least periodically occur someplace. Perhaps a highly developed culture from another galaxy has figured out how to construct a working time machine, or perhaps closed time-like curves can even exist naturally under rare circumstances.
Hawking and his Party
This creates issues of a different kind, pertaining to fundamental logic rather than science or engineering. A wide variety of paradoxical scenarios might be imagined if the principles of physics permit time travel. Some of these seem so absurd that it's hard to think they could ever happen. These kinds of ideas led Stephen Hawking, who was never a believer in the possibility of going back in time, to formulate his "chronology protection conjecture" — the hypothesis that some as-yet-unknown physical law prevents closed time-like curves from occurring. But until there is concrete evidence to back up that hypothesis, it can only be inferred that time travel is conceivable.
He came up with a funny technique to test this hypothesis in 2009. Hawking had a champagne party, but he didn't publicise it until after it had taken place (it was included in his Discovery Channel programme). He reasoned that someone in the future might read about the party and travel back in time to join it if time machines ever become a reality. But none did, so Hawking sat by himself the entire evening. This doesn't rule out the possibility of time travel, but it does imply that it won't ever be a widespread occurrence on Earth.