lecture13

lecture13 - Lecture 13 Notes: 07 / 20 Invariance of the...

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Lecture 13 Notes: 07 / 20 Invariance of the speed of light The Michelson-Morley experiment, among other experiments, showed that the speed of light in vacuum is a universal constant, as predicted by Maxwell's equations. It is the same for all observers, and for light coming from any direction. This is at odds with our everyday experience with speeds, where the speed of any object relative to an observer depends on the motion of the observer. Albert Einstein started with the assumption that Maxwell's equations, along with all other fundamental laws of physics, in fact hold for all observers, and so the speed of light really is independent from the observer. The assumption that the laws of physics are the same for all observers, together with a finite and observer-independent speed of light, is known as the principle of relativity. The principle of relativity requires us to abandon the notion of absolute time. In particular, with the principle of relativity, two events that are simultaneous according to one observer are not simultaneous according to another. To see this, consider the following example: A train of length L is moving to the right with speed v . An observer, let's call him Bob, stands on top of the train, right in the middle, and sends a light pulse to both ends. Since the distance to both ends of the trains is the same, the pulses arrive at the same time. If we call the signal arriving at the back of the train event A, and the signal arriving at the front of the train event B, then A and B are simultaneous according to Bob. However, now consider that Alice is standing near the tracks, in the same spot as Bob when he sends the light pulses. By the principle of relativity, she also sees both light pulses moving at speed c . But now the back of the train moves towards the light pulse, while the front of the train moves away from it, so the light reaches the back of the train first. Thus A happens before B, according to Alice.
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Consider the following thought experiment. Bob is on the train. He constructs a clock by bouncing a pulse of light off a mirror, and measuring the amount of time it takes the light to get back. If the mirror is a distance d from the light source, then the light moves a distance 2 d at speed c , and Bob will see the light come back a time t 0 = 2d / c later. Now Alice watches this experiment from the ground near the train tracks. According to her, the apparatus is moving to the right, so the light takes a path shown below: The light has to travel a greater distance, but by the principle of relativity, it still moves at speed c . Therefore, the time it takes the pulse to go to the mirror and back is longer according to Alice than according to Bob. Since Bob could use this clock to time any kind of a physical process on the train (such as how fast a regular clock runs, or his heartbeat, or the rate at which radioactive particles decay), all processes on the train seem to run slower to Alice. This is known as
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lecture13 - Lecture 13 Notes: 07 / 20 Invariance of the...

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