Contemplating ripples in water can help us understand Einstein’s theory of special relativity. Suppose an observer were someone on a moving boat. The wave front would appear to move ahead of the boat more slowly than those behind the boat. This is because of the motion of the boat and of the observer relative to the water. Now suppose that light is like a wave moving through a medium which pervades all of space. We would expect to ind the speed of light relative to us observers travelling along with the earth to differ depending on the direction. However, the speed of light has been found to be the same speed in all directions. This means that the speed of light is completely independent of whether either the source or the observer is considered to be moving.
Thus, the principle of relativity states that the laws of nature are the same for all inertial frames of reference. One of these laws allows us to work out the value of the speed of light in a vacuum. This value is the same regardless of one’s inertial frames and regardless of the velocity of the source or observer. These are the two central postulates of the theory of special relativity.
Physicists had known this information or a while. So what made Einstein so special? Einstein noted that, while the two principles made sense apart from one either, they seemed to contradict one another. Only one could be right. It would be quite bizarre if both were correct. “The fact that the speed of light is the same for all inertial observers regardless of the motion of the source or observer means that our usual way of adding and subtracting velocities is wrong,” in the words of Russell Stannard. Keep in mind that velocity is simply distance divided by time.
If there is something wrong with our understanding of velocity, therefore, this means that there is something radically wrong with our understanding of space, time or both. Keep in mind, furthermore, that it is not as though there is something special about light apart from its speed. Anything whatsoever that troubles at the speed of light is the same regardless of one’s inertial frame of reference. Light simply happens to travel at the relevant speed.
Imagine an astronaut in a rocket ship. Both he and a mission controller on the ground have identical clocks. The astronaut fixes a lamp on the floor which emits a light pulse. This pulse travels directly upwards at right angles to the direction of the craft’s motion. The pulse hits a bulls-eye target on the ceiling. Suppose the height of the ship is 4 meters. With the light traveling at its speed, he determines that the time taken or the trip is 4/c. Let time be represented by t’.
What does this look like from the perspective of the mission controller? He likewise observers the trip performed by this light pulse. From his perspective, from the time it takes for the pulse to hit its target, the latter will have moved forward from where it had been when the light pulse was produced. The pulse slopes, rather than being vertical, in other words. This slope’s length will be obviously longer than it was from the point of the view of the astronaut. Suppose the ship moves forward three meters in the time it took for the light pulse to travel from its original point to the target. We can use the Pythagorean theorem, where 3^2 + 4^2 = 5% to see that the distance traveled by the pulse to get to its target is 5 meters, from the perspective of the controller. He takes five meters, which is the distance traveled, divided by the speed at which he observes the light travelling. Therefore, for the controller, the time taken, t, is observed on his clock as t = 5/c.
This is quite different from what the astronaut measured. He observed it as 4/c. Thus, there is a notable discrepancy between how long it took for the pulse to perform the trip. The controller thinks that the reading on the astronaut’s clock is is too low. It is going slower than his. In fact, all of the activity in the rocket ship is slowed down according to the same ratio. This is why the astronaut does not see his clock going more slowly. If other components of her inertial frame were not slowed down by the same ratio, he would be able to see what the controller sees, namely, that his clock was going unusually slow. But this is not the case. Everything seems to be functioning normally for the astronaut within his own frame of reference. Indeed, thanks to the principle of relativity, all uniform motion is relative. The astronaut experiences life the same way that the mission controller experiences his. This is known as time dilation.