LOG#075. Batmobile “paradox”.

The Batmobile “fake paradox” helps us to understand Special Relativity a little bit. This problem consists in the next experiment:

batparadox

There are two observers. Alfred, the external observer, and Batman moving with his Batmobile.

Now, we will suppose that the Batmobile is moving at a very fast constant speed with respect to the garage. Let us suppose that v=0.866c=\dfrac{\sqrt{3}}{2}c. Then, we have the following situation from the external observer:

batparadox1

However, with respect to the Batmobile reference frame, we have:

batparadox2

The question is. Who is right? Alfred or Batman? The surprinsig answer from Special Relativity is that Both are correct. Alfred and Batman are right! Let’s see why it is true. For Alfred, there is a time during which the Batmobile is completely inside the garage with both doors closed:

batparadox3

By the other hand, for Batman, the front and rear doors are not closed simultaneously! So there is never a time during which the Batmobile is completely inside the garage with both doors closed.

batparadox4

So, there is no paradox at all, if you are aware about the notion of simultaneity and its relativity!

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