The Famous Train Example of Relativity

The famous example of relativity by Einstein was the moving train problem.

When one man stand before a fast moving train, and two lightening strikes, he’ll see the two lightening strikes appear at the same time.

However, if the man stands on the train as the train is moving from left to right, he’ll see the the two lightening strikes appear at different time, as the right lightening strike appears first and the left lightening strike appears later.

Why is it?

I couldn’t grasp this example when I first encountered it, but when I applied some maths onto it, I cracked the relativity code.
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So this is you when you see the two lightening strikes, they appear to you at the same time because you view the ground and the train as the reference frame.

But when you are inside the train, especially when the train is moving between the two lightening strikes, the distance, respectively, between you and the two lightening strikes differs.


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As you are fast moving indefinitely towards lightening on the right, the distance b, is indefinitely shorter than the one between you and the lightening on the left, a.

Speed of light is definite, c=3×108m/s. So when b<a, and b=c×t1 and a=c×t2So t1<t2.

If you have a hard time understanding, try imagine you are on a train, and the two lightening strikes are really really far, and speed of light travels at 100m/s, the distance between two lightening strikes is 1km, whilst you, are on a train that is 50m/s moving from left to right. Then you’ll see why the right lightening strike comes to you first than the left one.

But the example is merely a vague, or simple one to explain the general relativity. If you change the speed of light to speed of sound, that would make more sense to our human senses.

At first I couldn’t grasp this concept was also because my senses were not trusting it because it seemed to be the lightening strikes would appear the same no matter what, because light is fast, and our visual perception could not catch the subtle difference even, we were on a fast moving train.

But the connotation on relativity is simple. It’s basically reference frame–when you are on a car, whilst there is another car that is moving at the same speed as you, you won’t find that car moving at all. Suppose you set yourself as the reference frame.

We see things moving, because we have a relative reference frame that is still. Cars are moving before us, because we are still and the traffic lights are still and all the people waiting for traffic are still. If we are all moving, as the car moving, and with same speed, we won’t notice difference as the car is either leaving us or reaching us.

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