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The amazing paradox of Einstein's relativity [Science]
posted March 6 2013 19:56.13 by Giorgos Lazaridis

Einstein's relativity is all around us, but it is not quite obvious due to the low speeds that we perceive. Scientists for example would not be able to explain why muons manage to go all the way from the atmosphere to the surface of the Earth, since muons do not have enough lifespan to do the trip even traveling nearly the speed of light. The trick which explains this is the Lorenz contraction, which is part of the theory of relativity. When an object travels nearly the speed of light, the distance to the direction of its motion is contracted. Muons therefore do not have to travel the distance that we perceive as atmosphere, but only a few meters. That is why we are able to detect them on the surface of the Earth.

One very famous paradox is the train in the tunnel. Imagine that you're watching a train going through a tunnel. When the train is not moving, it has precisely the same length as the tunnel. Now imagine that it speeds up to 99% the speed of light. The train will appear shorter to your eyes! So the train will eventually disappear into the tunnel for a short time.

And now imagine that a friend of yours is inside the speeding train. From his perspective, the tunnel will be shorter! So when the front of the train exits the tunnel, there will still be one part of it on the entrance of the tunnel that has not yet gone in, since the train is now longer than the tunnel.

And here comes the funny part. Suppose that someone has installed two guillotines , one at the entrance and one at the exit of the tunnel. And suppose that at the right time, he pulls the rope and the guillotines fall instantaneously. From your perspective nothing will happen because when the guillotines fall, the train will be completely inside the tunnel. But from your friend's perspective, the front, the back or both sides of the train will be cut from the guillotines.

So, what has really happened? Who is right and who is wrong? I mean, the train cannot be both cut and un-cut. How can relativity explain this? The answer is simple: Things appear to happen simultaneously, only because we move at very low speeds. But since the train speeds up to nearly the speed of light, the guillotine at the exit of the tunnel will fall faster than the guillotine at the entrance, so the train will still have time to enter completely into the tunnel before the guillotine cut its tail. Simultaneity is dependent on the point from which you observe the facts!!!

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