[MUSIC] Let's imagine that twins named Leia and Luke are preparing for an interstellar voyage. Leia will stay behind on the Earth to monitor the journey, while Luke the adventurous one takes off in his spaceship capable of reaching nearly the speed of light. Since Leia stays on the earth as Luke speeds away, Luke's clock appears to slow down the faster he zooms off in his ship. But to Luke, Leia appears to be speeding away. So to Luke, Leia's clocks have slowed down. Both observers see the other clock as being slow, while all clocks are at regular speed, how can that be? Surely both observers can't be right. Welcome to the Twin Paradox, proposed by Einstein, not as a paradox, but as a peculiarity of special relativity. In Einstein's 1905 paper, he reasoned that if two clocks were synchronized, and one of them were to go on a lengthy journey, the traveling clock would return to the original location, with its time lagging behind the stationary clock. However, since relativity says that either clocks could view the other as being the one in motion, that is the traveling clock could consider itself at rest and the stationary clock would therefore be the one moving away. Shouldn't the stationary clock be the one lagging behind when the other returns again? Let's watch as Luke flies to a nearby star system six light years away, while Leia stays behind on the earth. Looking travel at a significant fraction of the speed of light, say 0.6 c. When we say that something is traveling at one c, it is the same as saying that it goes one light year per year. So if Luke travels and 0.6 c, he will travel 0.6 of light year for each year of travel. As such, Leia will say that Luke's journey takes 10 years. However, let's carefully assess what Luke observes on his particular journey. Luke sets a spaceship to travel at 0.6 c. In doing so, the distance to his destination changes at 0.6 c, the length between the Earth and the destination has shortened by 20%. So instead of six light years, the star appears to be only 4.8 light years away from Luke's perspective. At 0.6 c, Luke's time of arrival is only eight years after his departure from the earth. Meanwhile, Luke has turned his ship around and begins his journey back to the earth again at 0.6 c. So the same length contraction applies, instead of flying across six light years of space, Luke only flies the length contracted 4.8 light years and he is back from his distant star system after another eight year journey. For Leia, Luke has been gone for 20 years, but from Luke's perspective, he has only been gone 16 years. Luke is now four years younger than Leia. Hopefully you can now see why Einstein said this was a peculiarity and not a paradox. Luke is the moving observer, sees space itself foreshortened. But in Leah's reference frame, the distances haven't changed, merely the shape of Luke's ship. We should know that Einstein developed special relativity to describe Physics for observers who are not experiencing a strong gravitational force. But what happens near an object with a strong gravitational field such as a black hole? Einstein realized that he had to modify his theory of special relativity to make it more general and to allow for gravity. Einstein called this relativistic theory of gravity General Relativity. In order to understand the theory of General Relativity, we'll begin with Einstein's first ponderings on the subject, something called the equivalence principle.