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The following thought experiment followed a conversation I had with a co-worker, who was expressing doubt that a mexican wave could keep up with an F1 car as it went round the track. In a way, of course, she is correct, since it would not be a "true" mexican wave, as it is prompted by an external source (the F1 car) rather than being self-propagating. This caveat aside, in trying to explore how fast I could get a mexican wave to move, I reasoned as follows:
Stand in the middle of a large arena — packed with a cooperative crowd — wielding a spotlight. The spotlight is the signal for the crowd to stand up and wave. Swing the spotlight around, and watch the mexican wave that results.
Now scale the whole thing up. Say it takes five seconds to swing the spotlight around. Scale up the arena so that it is five light seconds in diameter. (Approximately 1.5 million km — thanks, Google.) You might need to up the wattage of the spotlight as well. Now swing it around. The spot made by the spotlight will move at ( 5 × c × π ) / 5 = π × c, or ~3.14 times the speed of light.
Congratulations, you've created a mexican wave moving at faster than the speed of light. 8^)
Stand in the middle of a large arena — packed with a cooperative crowd — wielding a spotlight. The spotlight is the signal for the crowd to stand up and wave. Swing the spotlight around, and watch the mexican wave that results.
Now scale the whole thing up. Say it takes five seconds to swing the spotlight around. Scale up the arena so that it is five light seconds in diameter. (Approximately 1.5 million km — thanks, Google.) You might need to up the wattage of the spotlight as well. Now swing it around. The spot made by the spotlight will move at ( 5 × c × π ) / 5 = π × c, or ~3.14 times the speed of light.
Congratulations, you've created a mexican wave moving at faster than the speed of light. 8^)
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