《那些古怪又讓人憂心的問題》第109期:地球擴張(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，但沒有你想象中那麼快。我曾經聽說過這麼一個謎題：Imagine you tied a rope tightly around the Earth, so it was hugging the surface all the way around.
想象一下，你在地球表面緊緊繞了一圈繩子。
Now imagine you wanted to raise the rope 1 meter off the ground.
假設你想把繩子擡離地面一米。How much extra length will you need to add to the rope?
那麼你需要加多長的繩子？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.
雖然看上去你需要加上幾十千米長的繩子，但正確答案是6.28米。圓的周長正比於半徑，因而直徑增加一單位，周長就增加2π單位。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4萬千米長的繩子拉長6.28米沒什麼大不了的。即使是擴張一天後，額外增長的5.4千米對於幾乎任何建築物來說，都是可以輕鬆承受的。混凝土每天被拉長和壓縮的量都比這長。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.
在最初感到一些震動後，你首先會注意到的一些效應就是你的GPS設備不再正常工作了。因爲GPS衛星基本還是待在原來的軌道上，但GPS系統所依賴的精密的授時系統在幾個小時內就徹底被打亂了。在所有工程學問題中，GPS計時是極其精確的，這也是唯一一個迫使工程師同時考慮狹義和廣義相對論效應的地方。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.
其他絕大部分的鐘都會繼續好好地運行下去。只是如果你家有個十分準確的單擺鍾，那麼你會發現一些端倪——在快到第二天的時候，你會發現這個鐘快了3秒。
