Special Relativity Length Expansion?

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Homework Statement


Like time dilation, length contraction cannot be seen directly by a single observer. To explain this claim, imagine a rod of proper length L_0 moving along the x axis of frame S and an observer standing away from the x axis and to the right of the whole rod. Carefully measurement of the rod's length at any one instant in the frame S would, of course, give the result L = L_0/gamma...

(b) Show that the observer would see (and a camera would record) a length more than L. [It helps to imagine that the x axis is marked with a graduated scale.]

(c) Show that if the observer is standing close beside the track, he will see a length that is actually more than L_0; that is, the length contraction is distorted into an expansion.


Homework Equations



L = L_0/gamma
gamma = 1/(1-v^2/c^2)^(1/2)


The Attempt at a Solution


Let's say that the rod is moving away from the observer. At one instant, light from the back of the rod will reach him at the same time as light from the front of the rod--which left earlier. Hence the observer sees a shorter rod. I don't understand why the length would be more than L, or why it would be more than L_0 if you were close to the rod.
 

Answers and Replies

  • #2
ideasrule
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Let's say that the rod is moving away from the observer. At one instant, light from the back of the rod will reach him at the same time as light from the front of the rod--which left earlier. Hence the observer sees a shorter rod.
Yes, that's true. However, if the rod is moving towards the observer, the observer sees a longer rod. The question is badly worded.

I don't understand why the length would be more than L, or why it would be more than L_0 if you were close to the rod.
You've basically already proven that the length would be more than L if the rod were moving towards the observer. To prove that it would be more than L_0, assume that the observer is directly in the path of the rod. Assume that light left the front at tf, and left the back at tb. Can you calculate the apparent length of the rod?
 

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