[Quora] 把一粒沙子加速到多快就能够摧毁地球？

How fast would a grain of sand have to be going to destroy the earth?

把一粒沙子加速到多快就能够摧毁地球？

原文地址：https://www.quora.com/How-fast-would-a-grain-of-sand-have-to-be-going-to-destroy-the-earth

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C Stuart Hardwick:

99.9999% the speed of light, just like pretty much all of the particles fired in any large research accelerator today. Such particles reach this speed very quickly. After that point, it’s no longer meaningful to talk of speed. That’s why particle accelerators are rated not in speed, but in electron volts.
光速的 99.9999% ，正如现在所使用的大型粒子加速器所能达到的速度一样。这些粒子可以在极短的时间内达到这个速度，在这之后，讨论速度就变成了一件没有意义的事情。这也是为什么粒子加速器采用了电子伏特而不是速度来作为分级的标准。

At this speed, relativistic physics takes hold, and additional acceleration adds to the mass of the particle faster than it adds to it’s speed. If it take X amount of energy to accelerate a proton to 99.9999%c, then if you put that much more energy into it, it will still be traveling at 99.9999%c. And if you put 20x the energy in, it will STILL be traveling at 99.9999%c—it will just have more relativistic momentum.
在这个速度之下，便是相对论的天下了，一个额外的加速给粒子带来的重量比其带来的速度的增长要快得多。如果把一个质子加速到光速的 99.9999% 需要花费 X 单位的能量，那么即使你再增加 X 单位的能量给这个质子，它的速度依然是光速的 99.9999% 。然后如果你增加 20X 单位的能量，这个质子的速度还会是光速的 99.9999%，改变的仅仅是这个质子将会有更多的动量。

Never mind the grain of sand. If you keep accelerating that proton long enough, it will eventually have more relativistic mass than the Earth. If you then allow it to escape, no more earth. Of course, that is not even remotely possible, for a large number of practical reasons. BUT, if you kept accelerating the proton indefinitely, it would eventually have more relativistic mass than the entire universe—which is impossible for a number of additional reasons.
别去管那粒沙子了。如果你把一个质子加速了足够长的时间，那么它将会拥有比地球更大的质量。如果你让这个质子逃脱了，地球自然也就不存在了。当然，由于一大堆实际的原因，从长远看这也是不可能的。但是，如果你永无止境的给这个质子加速，它的重量将会超过整个宇宙，当然，基于一些原因这也是不可能的。