Einstein actually had two profound theories related to each other. The first was the special theory of relativity. And that's a theory that says that nothing can travel faster than light. It's a theory that talk about how signals or messages or information propagates between experimenters who are measuring things with a clock and measuring distances between them. Special relativity does apply in the terrestrial world and in the laboratory. But in the universe at large, the superior and more general theory, as its name implies, of general relativity is what matters. And in general relativity, there is actually no speed limit implied on cosmic phenomenon. For example, the universe itself can expand faster than light. That's perfectly permissible within general relativity. And general relativity is not about constant, uniform relative motion, but about accelerated relative motion. That's the real difference between the two theories. Let's see some animations that describe the basic features of these two theories. [MUSIC] >> Someone watching a car accelerate toward light speed would see something very strange. It would seem as though the car itself was getting shorter and that time for the person in the car was slowing down. However, you wouldn't see these effects until the car began to approach the speed of light. At 90% of the speed of light, the car would appear to shrink to 44% of its usual length. [MUSIC] This thought experiment answered Einstein's old question about what he would see if he traveled along with a beam of light. He simply couldn't make the trip. For at the speed of light, length would contract to zero and time would stop. [MUSIC] In one of Einstein's famous thought experiments, he realized that gravity and acceleration appear to be the same phenomenon. Think about what would happen if an elevator suddenly went into a free fall. [MUSIC] The person inside would effectively weigh nothing. [MUSIC] Next, imagine that same person in a motionless rocket ship, so far from Earth that the force of gravity is practically zero. Just like in the free-falling elevator, he would also weigh nothing. [MUSIC] Now put the rocket in motion. [MUSIC] As the rocket speeds up, the passenger's weight increases. To him, it feels just as if gravity had planted his feet firmly on the floor. [MUSIC] Einstein realized that the force of gravity is just the acceleration that you feel as you move through space time. [MUSIC] >> How did Einstein come up with this spectacular theory, which has now amply confirmed and is considered one of the most well-tested theories of nature we have? He was motivated by what was a coincidence at the time of Galileo. And it's called the equivalence principle. The idea that gravitational and inertial masses are identical. He was surprised by this coincidence. To see how he was surprised, let's look at the difference between these two ways of thinking about mass. Inertial mass is the resistance that an object gives to a change in its motion. Let's imagine a situation where a massive object like a stone or a boulder is on an icy surface where the frictional force can be reduced and we try to change its motion by pushing it. We know that the inertia of this large mass is its resistance to us trying to accelerate it. And we get a sense of this mass, if we did the experiment. The gravitational mass is quite different. So if we set up a situation where this same large object is falling freely through space, we'd let it go and drop it towards the Earth's surface. Gravity describes how this object accelerates, caused by the mass of the Earth and the gravity force. Galileo's realization and Einstein's subsequent puzzlement was the fact that these two masses are conceptually quite different. And yet, they're mathematically and observationally the same. Think about it. One form of mass is just the resistance of an object to a change in its motion. If it's a horizontal force, gravity is not implied at all. The other is the change in the motion of an object subject to the force of gravity. Why should these two masses be identical? To Einstein, it could not just be a simple coincidence. It had to be a profound realization about how the universe worked. And so he built the equivalence principle as a foundational tool in his theory. For the rest of his theory, he reached back into the toolkit of mathematics provided almost a 100 years before, the idea of curved space time. And he developed a geometric theory of gravity, where mass energy causes curvatures in space time. And that's what his equations codify. To make clear how profound his insight was, let's consider a couple of situations that Einstein speculated in thought experiments could not be distinguished. Imagine two situations. One, where you're in a spacecraft that's just floating in free space, far from any planet, maybe even far from the sun. You're not subject to any local gravity force, so you would float around within that spaceship as if you were weightless. Clearly you have mass, but there's no local gravity. And so there's no gravitational force acting on you. He then imagined a situation where you were in an elevator, maybe even the same kind of space as the spacecraft so you couldn't tell the difference between them. And unfortunately, the cable of the elevator had been severed, and you were in free fall towards the Earth and towards a certain death. And this situation will be identical to the free-floating spacecraft. You would be floating around within the elevator, both plummeting towards the Earth with an acceleration of 9.8 meters per second, per second. These are very different situations. One, obviously very ominous, the other not so much. In one situation, gravity is clearly operating and the other, it isn't. His theory of relativity removed the distinction between these situations. He removed the distinction between acceleration due to gravity and acceleration due to any other force. To see this, let's look at the second pair of situations. Imagine you are stationary on the Earth's surface, in that elevator. The door won't open. You're just stuck there. You have your normal weight. Everything seems normal to you. And that is because you're being accelerated towards the Earth's core at 9.8 meters per second, per second, giving you the sensation of your weight. The second situation is you're in that free-floating spacecraft, but now an evil alien is accelerating you towards their home planet to do unspeakable experiments on you at a 9.8 meters per second, per second. In that elevator, you will experience your normal weight. Because you're being accelerated by a spacecraft at that same acceleration as you would be falling towards the Earth's surface if the Earth's surface were not there. And in Einstein's view, there's no way you could distinguish these two situations, yet they are clearly quite different. In one the gravity force is operating, and in the other, a force caused by a spacecraft is accelerating you at the same rate. This is the basis of his theory. This is the equivalent principle. The fact that you cannot distinguish these situations. It's artificial and arbitrary that we just ascribe one to gravity and we ascribe one to the other force. Now let's think of another experiment. We can use the same elevator as the idea. Imagine you're in an elevator, stuck in the elevator, a windowless elevator and you don't really know your situation and you have a flashlight. If the elevator is not moving, you can shine the flashlight across the elevator and it will hit the opposite wall at the same level as you aim it. Imagine that the elevator is moving at a constant speed. You can see the light is travelling across the elevator and so will hit a place on the opposite wall slightly below the level where you aimed it. A simple vector addition of the speed of light with the speed of the elevator. If the elevator is accelerating, the same thing will happen. Only the light will take a curved trajectory because of the elevator's acceleration. And once again, the light beam will hit a point on the opposite wall slightly below, directly opposite from you. Well, that's the situation where the elevator is accelerating upward. The light beam is deflected, slightly. Einstein's point of relativity was that the same thing applies when the elevator is sitting stationary on the Earth and you are subject to the Earth's gravity acceleration, 9.8 meters per second, per second. And so he implies that the same phenomenon, that slight curvature of the beam of light, should also happen to the man or woman stationary in the elevator. That is the gravitational deflection of light. That is gravitational lensing. And it is, of course, observed. So we know that even the Earth, with its rather subtle gravity, is subtly bending space and time around it, leading to this gravitational deflection of radiation. And indeed, it can be measured. General relativity was a profound re-conception of time and space, from the hands of Einstein. Instead of the linear time and space of Newton that were independent of each other, we had coupled space time that could be curved according to the mass energy density in any region of space. This amazing conception of gravity has been validated by experiments over the 100 years since general relativity was first published.
