March 18, 2006

Special Relativity

Albert Einstein, On the Electrodynamics of Moving Bodies, 1905

In 1887 Michelson and Morely experimentally determined that light in a vacuum appears to travel at exactly the same speed, no matter what direction it moves and no matter what speed or direction the detectors are moving. This is effectively saying that if you are running towards or away from light makes no difference to how fast it appears to be going.

Many scientists couldn't accept this, including Michelson, who kept repeating the experiments until being awarded the Nobel Prize in 1907. Einstein was the first to start with the assumption that the observations were correct and work out the consequences in detail.

Actually, he starts with two assumptions. Along with assuming light always appears to travel at the same speed, he assumes that all the known laws of motion and time work normally for objects at rest relative to each other. A key insight here is that relative to the speed of light nothing around us is moving. Any distortions to the normal laws of motion and time caused by the fixed speed of light are so tiny that we can't detect them in our daily lives.

Imagine, if you will, a bullet train with a lightbulb at each end and a light detector exactly between them. The detector is rigged to go off only if light from both bulbs arrives at the same time. The people on the train, the light bulbs, and the detector are all at rest relative to each other, so normal physics applies: if both light bulbs are turned on at the same time, the light will reach the detector at same time. To people watching the train whip by, however, the light travelling from the front of the train towards the back must cover a smaller distance than the light travelling from back to front. However, since the two light beams must arrive at the detector at the same time (otherwise the detector won't go off), and must travel at the same speed, the lightbulbs cannot have been switched on at the same time.

This is counter to our day-to-day experience only because bullet trains, at a mere 300km/h, are barely moving relative to the speed of light. If you were to perform this experiment in real life, the lightbulb at the front of the train would appear to be switched on less than a trillionth of a second before the lightbulb in the back.

Through similar constructions, Einstein worked out exactly how time, distance, and simultaneity change as relative velocity increases. The math is high-school level geometry, but Einstein takes his analysis all the way, working out every detail. In later years, thousands of concrete predictions were made based on his work, all of which have been confirmed by experiment. The results are staggering: time and space are not constant; light is. This is a paradigm shift comparable to the notion that the Earth orbits the Sun rather than the other way around. Light is, in some way, fundamental to the universe.


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