- Education and Science»
Understanding Special Relativity: Twin Paradox Explained
The Twin Paradox is a scenario that, at first glance, seems to make nonsense out of Einstein's theory of special relativity. The situation is that a man sets off in a rocket travelling at high speed away from Earth, whilst his twin brother stays on Earth.
Einstein's theory of special relativity says that moving clocks run slower than those that are stationary. This effect is known as time dilation. So, by applying the theory of special relativity to the situation with the two separated twins, we should reach the conclusion that the twin in the moving rocket should experience time passing more slowly than the twin who is stationary on Earth. The twin in the rocket therefore ages much more slowly than his brother.
But wait a minute... doesn't Einstein's theory of special relativity also say that all inertial frames are equivalent? That is, we can only say that a particular frame (such as the planet or the rocket) is moving relative to something else. We could define the Earth as stationary and the rocket as moving, but it is equally valid to say that the rocket is stationary and it is actually the Earth that is moving. But that would mean we reach the opposite conclusion to what we did before: now instead of the twin on Earth growing old whilst the twin in the rocket beats the ageing process through time dilation, we conclude that it is the twin on Earth for whom time is running slowly.
But surely that's a paradox? We can't conclude that the twin in the rocket is both older and younger than his brother! Well, actually, no: there is no paradox. What happens is that the twin on Earth, viewing himself as stationary and his brother as moving at high speed, sees his brother experiencing time dilation and thus ageing more slowly. At the same time, the twin in the spaceship considers himself to be the stationary twin, and therefore as he looks back towards Earth he sees his brother ageing more slowly than himself. Each sees the other as moving, and therefore as experiencing time dilation.
But which brother is "correct" in the way he perceives the situation? Both are. Each sees the other as being younger than himself. How they were perceived by any onlooker would depend on which frame of reference the onlooker was in. It doesn't make sense to ask which brother is "really" older, because the answer depends on where you stand to ask the question!
But what about when the brother in the spaceship returns to Earth? Surely the contradiction will be apparent then? Ah, but in order to return to Earth, the spaceship must slow down, stop moving, turn around and go back the other way. During those periods of deceleration and deceleration, it is not an inertial frame and therefore the normal rules of special relativity don't apply. When the twin in the spaceship turns around to make his journey home, the shift in his frame of reference causes his perception of his brother's age to change rapidly: he sees his brother getting suddenly older. This means that when the twins are finally reunited, the stay-at-home twin is the older of the two.
But wait one more time.... why can't we interpret it as the spaceship being stationary and the Earth decelerating and accelerating to change direction? Well, the answer is that you can. However, regardless of interpretation, the twin in the spaceship will experience forces (the forces which are required to stop and turn around the spaceship in the frame where this occurs). He will be thrown forwards in his seat as the spaceship brakes, and thrown back when it accelerates to begin its return journey. He can either interpret these forces as being associated with his acceleration, or if he insists that he is in fact stationary he has no choice but to interpret it as a gravitational force. And as Einstein's theory of General Relativity tells us, a gravitational force is a distortion in space and time. The upshot is that in both interpretations, the twin in the space-ship experiences time dilation effects which the other twin does not. This is why he is younger than his brother upon their reunion.
A note on time travel
It is sometimes said that relativity theory predicts the possibility of travelling backwards in time. An object that moves faster than the speed of light would be seen to be moving backwards in time by some observers. However, that means that some observers would see events happening before their causes, which is a violation of causality. Special relativity says that the laws of physics must be the same in all inertial frames, but a frame in which effects occur before causes would definitely not fit our current understanding of the laws of physics.
For this reason, the speed of light is commonly regarded to be a universal speed limit which nothing can travel faster than: which means nothing can travel backwards in time. This is supported by the fact that special relativity predicts that it would take an infinite amount of energy to accelerate an object up to the speed of light.
This hub was inspired by rohitworld90's hub which questions the possibility of time travel and asks how the twin paradox can be resolved.