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1 Basics of Special Relativity

1.1 Conceptual Basics of Special Relativity

Perhaps the most exciting aspect of learning special relativity is having your physical intuition turned on its head and sent through a meat grinder. Please refer to this webpage1 to get a conceptual background for special relativity, then answer the questions below. You may skip the ps on World Lines and Light Cones.

1.1.1 Problem: The Barn Paradox

This is a classic problem in special relativity; it will be up to you, however, to determine whether or not it is truly deserving of the label paradox" In Fig. 1, a runner is carrying a pole that is slightly longer than the length of a barn. The barn in question has two doors; one in the front and one in the back. The runner is capable of running at speeds comparable to the speed of light, and wants to know if she can t the length of the pole inside the barn in a single instant; to test this, a farmer standing outside the barn will close both of the doors at the same time, and then open them again immediately after (you may assume the doors take only an innitesimal length of time to open and close, and remain closed for a negligible amount of time). Is there any way the pole will t inside the barn? Describe the events of the runner entering the barn, the doors closing, and the runner leaving the barn from the point of view of the runner and of the farmer. Is this really a paradox"? Why or why not?

Figure 1: The Pole in the Barn Paradox