EINSTEIN’S PRINCIPLE OF RELATIVITY

In 1905 Albert Einstein provided a new perspective on the problems we have been discussing. He was apparently unaware of the Michaelson-Morley experiments. Instead, Einstein was familiar with Maxwell’s equations for electricity and magnetism, and noted that these equations had a far simpler form if you took the point of view that you are at rest. He suggested that these equations took this simple form, not just for some privileged observer, but for everybody. If the principle of relativity were correct after all, then everyone, no matter how they were moving, could take the point of view that they were at rest and use the simple form of Maxwell’s equations.
How did Einstein deal with measurements of the speed of light? We have seen that if someone, like Bill in our thought experiment, detects a pulse of light coming at them at a speed faster than c = 1 foot/nanosecond, then that person could conclude that they themselves were moving in the direction from which the light was coming. They would have thereby violated the principle of relativity.
Einstein’s solution to that problem was simple. He noted that any measurement of the speed of a pulse of light that gave an answer different from c = 1 foot/ nanosecond could be used to violate the principle of relativity. Thus if the principle of relativity were correct, all measurements of the speed of light must give the answer c.
Let us put this in terms of our thought experiment. Suppose the instructor observed that the light pulse passed the 3.24 foot long meter stick in precisely 3.24 nanoseconds. And suppose that Bill, moving at nearly the speed of light toward the laser, also observed that the light took 3.24 nanoseconds to pass by his meter stick. And suppose that Joan, moving away from the laser at half the speed of light, also observed that the pulse of light took 3.24 nanoseconds to pass by her meter stick. If the instructor, Bill and Joan all got precisely the same answer for the speed of light, then none of their results could be used to prove that one was at rest and the others moving. Since their answer of 3.24 feet in 3.24 nanoseconds or 1 foot/nanosecond is in agreement with the predicted value  from Maxwell’s theory, they could all safely assume that they were at rest. At the very least, their measurements of the speed of the light pulse could not be used to detect their own motion. As we said, the idea is simple. You always get the answer c whenever you measure the speed of a light pulse moving past you. But the idea is horrendous. Einstein went against more than 200 years of physics and centuries of observation with this suggestion.
Suppose, for example, we heard about a freeway where all cars traveled at precisely 55 miles per hour – no exceptions. Hearing about this freeway, our three people in the thought experiment decide to test the rule. The instructor sets up measuring equipment in the median strip and observes that the rule is correct. Cars in the north bound lane travel north at 55 miles per hour, and cars in the south bound lane go south at 55 miles per hour.
For his part of the experiment, Bill gets into one of the north bound cars. Since Bill knows about the principle of relativity he takes the point of view that he is at rest. If the 55 miles per hour speed is truly a fundamental law, then he, who is at rest, should see the south bound cars pass at 55 miles per hour.
Likewise, Joan, who is in a south bound car, can take the point of view that she is at rest. She knows that if the 55 miles per hour speed limit is a fundamental law, then north bound cars must pass her at precisely 55 miles per hour. If the instructor, Bill and Joan all observe that every car on the freeway always passes them at the same speed of 55 miles per hour, then none of them can use this observation to detect their own motion.
Freeways do not work that way. Bill will see south bound cars passing him at 110 miles per hour. And Joan will see north bound cars passing at 110 miles per hour. From these observations Bill and Joan will conclude that in fact they are moving – at least relative to the freeway. Measurements of the speed of a pulse of light differ, however, in two significant ways from measurements of the speed of a car on a freeway. First of all, light moves through empty space, not relative to anything.

Secondly, light moves at enormous speeds, speeds that lie completely outside the realm of common experience. Perhaps, just perhaps, the rules we have learned so well from common experience, do not apply to this realm. The great discoveries in physics often came when we look in some new realm on the very large scale, or the very small scale, or in this case on the scale of very large, unfamiliar speeds.