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Q & A: rigid rulers and the speed of light

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Most recent answer: 02/14/2016
Q:
I understand understand that it's impossible to send a message faster than the speed of light, but the following thought experiment occurs to me. Imagine I'm sitting next to someone in a library, so I can't talk to him. I want to attract his attention and I notice that there's a metre ruler lying between his elbow and me. I take a second to nudge it a centimetre and it touches his elbow. I've just sent a message at 1 metre per second whilst only moving the ruler at 1 centimetre per second. If I push the ruler at, say, 2% of the speed of light, haven't I communicated information faster than the speed of light without any part of the system moving anywhere near light speed?I'm sure there's something I'm missing here, and I'd love to know what it is !ThanksSimon
- Simon Tweddle (age 52)
Brisbane,Australia
A:

Yes, that would be a problem if the ruler were rigid. So you've proven that, unless all of relativity breaks down, those rulers can't be rigid. Nothing can. One way to see that is that the parts of the ruler exert forces on each other via electromagnetism, which only propagates at the speed of light. So when you push on one end it takes a while before the other end notices. See some old discussion: https://van.physics.illinois.edu/qa/listing.php?id=1398.

Mike W.


(published on 02/14/2016)

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