《那些古怪又让人忧心的问题》第109期:地球扩张(2)
What about our roads and bridges? Eventually, they would have to break up, right?
Not as quickly as you might think. Here's a puzzle I once heard:
是的，但没有你想象中那么快。我曾经听说过这么一个谜题：Imagine you tied a rope tightly around the Earth, so it was hugging the surface all the way around.
想象一下，你在地球表面紧紧绕了一圈绳子。
Now imagine you wanted to raise the rope 1 meter off the ground.
假设你想把绳子抬离地面一米。How much extra length will you need to add to the rope?
那么你需要加多长的绳子？Though it may seem like you'd need miles of rope, the answer is 6.28 meters. Circumference is proportional to radius, so if you increase radius by 1 unit, you increase circumference by 2π units.
虽然看上去你需要加上几十千米长的绳子，但正确答案是6.28米。圆的周长正比于半径，因而直径增加一单位，周长就增加2π单位。Stretching a 40,000-kilometer line an extra 6.28 meters is pretty negligible. Even after a day, the extra 5.4 kilometers would be handled easily by virtually all structures. Concrete expands and contracts by More than that every day.
把一根4万千米长的绳子拉长6.28米没什么大不了的。即使是扩张一天后，额外增长的5.4千米对于几乎任何建筑物来说，都是可以轻松承受的。混凝土每天被拉长和压缩的量都比这长。After the initial jolt, one of the first effects you'd notice would be that your GPS would stop working. The satellites would stay in roughly the same orbits, but the delicate timing that the GPS system is based on would be completely ruined within hours. GPS timing is incredibly precise; of all the problems in engineering, it's one of the only ones in which engineers have been forced to include both special and general relativity in their calculations.
在最初感到一些震动后，你首先会注意到的一些效应就是你的GPS设备不再正常工作了。因为GPS卫星基本还是待在原来的轨道上，但GPS系统所依赖的精密的授时系统在几个小时内就彻底被打乱了。在所有工程学问题中，GPS计时是极其精确的，这也是唯一一个迫使工程师同时考虑狭义和广义相对论效应的地方。Most other clocks would keep working fine. However, if you have a very precise pendulum clock, you might notice something odd-by the end of the day, it would be three seconds ahead of where it should be.
其他绝大部分的钟都会继续好好地运行下去。只是如果你家有个十分准确的单摆钟，那么你会发现一些端倪——在快到第二天的时候，你会发现这个钟快了3秒。
