Imagine you are standing on a platform, waiting for your train to arrive (the same train that George happens to be on). In the distance, you notice a beautiful mountain with the silhouette of an isosceles triangle (after all, you’re traveling in Switzerland, where Einstein developed special relativity). George also sees this exquisitely symmetrical Alp from his train window. Do you and George agree on the slope of the sides of the mountain (i.e., the angle of inclination relative to the horizontal axis)? Why?
The mountain is moving from Georges perspective and so the horizontal distance between the top and bottom of the mountain is less in his frame of reference than in mine. Since the vertical distance is not in the same direction as George’s motion, he and I will agree on the vertical distance between the top and bottom. Therefore, as he measures the same height but a different length, he must also measure a different slope.
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