Of speeding bullets and Einstein
Julian Kinnaird, of Arrowtown, asked:
James' rifle shoots a bullet out of the barrel with a speed of 1000m/sec. One day James catches a train whose travel speed is also 1000m per second. James fires his rifle out the back of the train directly backwards. Does the bullet stay in the same physical location, move back down the track? If so, how fast?
Florian Beyer, a mathematician at the University of Otago, responded:
Questions such as this have puzzled many great scientists, more recently Albert Einstein in the early 20th century. How do different observers describe the same event? In this case what would James see on the train and what would his friend, Rosalie, see, standing beside the tracks?
Eventually in 1905, Einstein's famous relativity theory provided satisfying, yet often surprising, answers. It was his insight that, while the laws of nature are the same from all observers' points of view, their description of an event may differ dramatically: ‘‘Everything is relative.’’
From James' point of view, the bullet does what it is supposed to do: it travels with a speed of 1000m/sec in the opposite direction of the train, irrespective of the speed of the train. From Rosalie's point of view, however, the speed of the bullet depends on the speed of the train. If the train has exactly the same speed as the bullet, the bullet does not appear to move at all (gravity makes the bullet drop like a stone though). If you want to see with your own eyes, check this out: youtu.be/ZH7GpYJoptU
In general, the speed of the bullet measured by Rosalie is the ‘‘bullet speed with respect to the train minus train speed’’ (this is correct only for ‘‘small’’ speeds though). The faster the train goes, the slower the bullet appears. If trains could move faster than bullets, then Rosalie would see the bullet flying in the same direction as the train goes.
Strange already? Well, Einstein found that things really start getting strange, when they move with (or close to) the speed of light (about
300,000,000m/sec). Imagine that the ‘‘riffle’’ is actually a laser pointer and the ‘‘bullet’’ is laser light. In this case, Rosalie sees this ‘‘bullet’’ moving with the very same speed of light, irrespective of how fast the train moves. Even if the train itself moved with almost the speed of light, this ‘‘laser bullet’’ would never appear to be slowed down. Light always moves with the same speed irrespective of the observers and the speed of the light source.
Such weird ‘‘relativistic effects’’ are real! Your smartphone, for example, needs to take these effects into account whenever you use GPS.
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