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The Loop (TV)
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Let's say you got in a spaceship and flew at the speed of light to a star 10 light years from Earth, then immediately flew back here at the same speed. Would it be 20 years from your perspective, or 20 years from ours?
- Short answer: It would be 20 years from the person on Earth's perspective and it would be less time from the traveler's perspective.
- Long answer: The scenario is impossible as mass increases exponentially as a body approaches the speed of light. This would result in an object of infinite mass that would violate the laws of physics which, depending on your sci-fi of choice, would result in anything from a black hole to the destruction of all reality. A more practical scenario would be two guys with stopwatches start them at exactly the same time on Earth. The one staying on the ground tells the one going into space to return to the same spot in exactly 24 hours. The astronaut blasts off, circles the earth a few times and returns, according to his watch, right on time. His buddy on Earth would tell him he was late (albeit, by a fraction of a second). This very phenomenon must be taken into account for anything in orbit for long stretches of time that needs to communicate real-time with Earth.
- To make it even more complicated, there are multiple factors affecting how fast each person's watch is running. The person on the ground is deeper in a gravity well (thus theoretically making his watch run slower than the astronaut's), but the astronaut is in motion, at a pretty fair clip, having had to accelerate to climb out of the gravity well and achieve orbital velocity (acceleration slows down the astronaut's watch). How the factors balance out, and who hits the 24-hours-passed mark first, probably takes higher-order math than this troper is competent to handle.
- Full answer: Special relativity allows for converting between any pair of inertial reference frames.^{[1]} It also states that none of these frames is 'preferred'; that is, that it makes just as much sense to say that Earth is moving away from the spaceship as that the sapaceship is moving away from Earth. This means that if we ignore gravity and assume the ship travels at a constant speed of 0.87c,^{[2]} when it arrives at a star 10 light-years away the crew will think they've been travelling for eleven and a half years, but that clocks on Earth had slowed down and only measured six and three-quarter years. People on Earth, however, would observe exactly the opposite: eleven and a half years have passed on Earth but only six and three-quarter on the spacecraft. This apparant paradox is a classic example for students of relativity; the key is that for the spaceship to return to Earth (and the two groups to actually check their clocks against the other) it has to turn around.^{[3]} Coming to a stop from 0.87c and then reaching the same speed in the opposite direction will take a lot of acceleration, and at this point the spacecraft no longer represents an inertial reference frame. When the spacecraft returns to Earth again, because of the effects of that turn-around, both groups will agree that more time has passed on Earth than on the spacecraft.^{[4]} In summary: the one who turns around will think the trip took less time than the other.
- To make it even more complicated, there are multiple factors affecting how fast each person's watch is running. The person on the ground is deeper in a gravity well (thus theoretically making his watch run slower than the astronaut's), but the astronaut is in motion, at a pretty fair clip, having had to accelerate to climb out of the gravity well and achieve orbital velocity (acceleration slows down the astronaut's watch). How the factors balance out, and who hits the 24-hours-passed mark first, probably takes higher-order math than this troper is competent to handle.
- Short answer revisited: the closer the traveler can get to light-speed for the round-trip journey, the less time will pass on his wristwatch.
Notes
- ↑ An inertial reference frame is one in which Newton's Laws of Motion are true, I.E. one which is either not moving or travelling in a straight line at a constant speed.
- ↑ This will give a time dilation factor of 1/2. The Other Wiki has the maths.
- ↑ we can definitively say that the spacecraft is the one which turned around rather than the earth because the astronauts will experience feel themselves thrown forwards, much like a passenger in a car when the driver brakes.
- ↑ General Relativity allows you to transfrom to and from non-inertial reference frames, and so could calculate what is happening while the spaceship turns around as well, but at the expense of making the mathematics much more complicated.
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