Please help,i\'m stuck. Special relativity says that observers perceive objects
ID: 1998867 • Letter: P
Question
Please help,i'm stuck.
Special relativity says that observers perceive objects in motion relative to them to be shortened along the direction of travel. This is known as length contraction. How do we know that length contraction only occurs along the direction of travel leaving dimensions perpendicular to the direction of travel unchanged? Because contraction of the perpendicular dimensions would lead to contradictions as the following thought experiment shows. Start with a long straight pipe. Paint one end with a checkerboard pattern and the other end with a stripe pattern, then cut the pipe in half. Now shoot the two ends toward each other. Suppose that lengths perpendicular to the direction of motion did contract. This would mean that an observer who sees the pipe moving would measure the pipe to have a smaller diameter. Imagine an observer watching the pipes from the side. Would this observer see the checkered pipe pass inside the striped pipe, the striped pipe pass inside the checkered pipe, or both pipes collide with neither passing inside the other? Explain. (Each of your explanations should involve explaining which pipe(s) the observer perceives to be moving and hence would perceive to have a smaller diameter.) Imagine an observer riding atop the checkered pipe. What would this observer see happen (same choices as in part a). Explain. Imagine an observer riding atop the striped pipe. What would this observer see happen (same choices as in part a). Explain. The fact that you have different answers for parts a, b, and c represents a contradiction. Different observers should all agree about the experimental result. They can disagree about the reason but they need to agree about the result. The fact that we have a contradiction here means that lengths perpendicular to the motion must not contract, only lengths parallel to the motion contract. (We also have experimental evidence for this, not just thought experiments.)Explanation / Answer
a) Accordog to this observer, both collide as diameter of both pipes are decreased.
b) striped pipe should pass inside the checkered pipe as stripped pipe is moving relative to the observer.
c) checkered pipe should pass inside the stripped pipe as checkered pipe is moving relative to the observer.