[MUSIC] If humans decide to explore other solar systems, we'll need to get there using generation ships. Ships like these can carry a self-sustaining human colony which can survive for many generations. This is the premise of a television series called Ascension. The characters in the show walk around as if they're in Earth gravity, which is generated by the acceleration of their ship. But without windows to see outside, can the characters tell the difference between uniform acceleration of their spaceship or simply being stationary on Earth's surface? Suppose you awaken in just such a situation. You're trapped in a small room unable to remember how you got there and with no way of seeing what's outside. Could you tell the difference between the room being here on Earth or in an accelerating rocket ship. Einstein realized that these two scenarios are indistinguishable so long as the room is small enough. In an experiment that you could try in your small room is to drop a ball. There are two possible outcomes depending on where the room is. If it's here on earth, the ball will appear to accelerate downwards, falling to the ground due to gravity. In the second scenario, we're in an accelerating rocket ship far away from any sources of gravity, the ball still appears to fall, only this time, it's because the rocket is accelerating upward. If the acceleration of the rocket is precisely 9.81 meters per second squared, the motion of the ball will be indistinguishable from the effects of gravity on Earth. Nice try, but dropping the ball won't tell you which of the two scenarios you're in. You might say that you dropped the ball by dropping the ball. Not knowing whether it's the rocket ship accelerating or the ball accelerating due to gravity is called the equivalence principle. In fact the formal definition of equivalence principle given by Einstein himself states, we assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. What Einstein discovered is that gravity is not a force as it was believed to be by Newton and classical physicists. In small regions of space, gravity is indistinguishable from acceleration. Now we should note that Einstein's statement of the equivalence principle requires that your choice of a reference frame is small. Earth's gravity for example doesn't change much between your toes and your head. However, if you chose a tall reference frame, or an extremely wide reference frame, it would become pretty obvious that you were on Earth. Just by measuring changes in gravity as you moved around. Gravity would become weaker the higher you were from Earth's surface. The force of the gravity on the surface always points to the center of the Earth. So if you have a large horizontal frame, the direction of the balls will fall becomes different. The converse of our ball analogy is also true. When an astronaut is orbiting the Earth, they appear weightless because they are in free fall. In free fall the force due to gravity is exactly matched by the centripetal acceleration towards the earth. This is similar to riding your favorite drop of doom style amusement park ride where you feel temporarily weightless. Astronauts are in a perpetual drop of doom. This would be indistinguishable from an astronaut who has run out of fuel far from any sources of gravity. Many science fiction shows, including Star Trek, portray artificial gravity. But failed to explain the technology necessary in order to produce these fields. However, some science fiction gets it right. In the movies 2001, A Space Odyssey and Interstellar, gravity is produced by rotating the spacecraft to introduce centripetal acceleration, which mimics gravity, an example of the equivalence principle at work. If a ball thrown on Earth travels on a curved path due to gravity, we'd expect the same curvature to occur on an accelerating rocket ship. Einstein's explanation of gravity introduces the idea of the thrown ball's trajectory being the shortest possible path through a curved space time. Gravity itself, Einstein believed, was the result of space time being curved by mass and energy.