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Imagine learning for the first eighteen years of your life that the earth is flat.
想象一下， 在你十八岁之前，你都以为地球是平的。
All through elementary school and high school you grow up hearing about the flat earth we live on
整个小学和高中，你听到的都是，我们生活的地球是平的
and doing boring flat-earth physics homework and then (if you're lucky enough) you get to college and PSYCH!
然后做着无聊的扁平地球物理作业，（如果你足够幸运的话）你会上大学，随着一声霹雳！
for the first time they show you a globe and say'sorry for lying, the earth is actually round'.
有人第一次给你看了地球仪，并告诉你，不好意思，我们撒谎了，地球其实是圆的。
Well, this is, unfortunately, exactly what we do with.
不幸的是，这正是我们所做的。
1) Gravity. You probably learned that objects attract each other based on their mass
1. 地心引力。你可能学过物体根据各自的质量而互相吸引
so you probably grew up thinking that light can't possibly be affected by gravity because light is massless.
所以你可能从小就认为光不可能受到引力的影响，因为光是没有质量的。
I know I did. Well guess what? The source of gravity is not mass - it's energy and momentum,
我以前就是这么以为的。猜猜怎么着？引力的来源不是质量，而是能量和动量，
which light certainly has (of course, regular matter does too).
光也有能量和动量（当然，普通物质也有）。
So not only does light get bent passing by a star or planet or black hole, but light attracts the planet or star or black hole in return
所以光在经过恒星或行星或黑洞时不仅会发生弯曲，光还会反过来吸引行星或恒星或黑洞
(to be sure, it's only a very very small amount. But a small amount is not zero).
（当然，这只是一个非常非常小的量。但少量并不等于没有）。
Anyway, the point is that Newton's law of gravitation is just an approximation -
不管怎样，重点是牛顿的万有引力定律知识一个近似值—
good enough to get us to the moon, but not perfect. General relativity is better.
虽然足以让我们登上月球，但还不够完美。广义相对论更好。
2) Special Relativity. Speaking of the moon, you probably also learned that if a sheep is moving 2 mph relative to a train
2. 狭义相对论。说到月亮，你可能还学过，如果一只羊相对一列火车以每小时2英里的速度移动
and that train is moving 2 mph in the same direction relative to the ground,
同时火车也在以相对地面每小时2英里的速度朝相同方向前进，
then the sheep is moving four mph relative to the ground. 2mph+2mph=4mph, right? FALSE.
那么这只羊相对于地面的速度就是每小时4英里。2英里加2英里等于4英里，对吧？不对。
Experiments in special relativity have confirmed that velocities don't simply add together
狭义相对论试验已经证实速度不能简单相加
and so the sheep will in fact be moving very very ever-so-slightly slower than 4 mph relative to the ground.
所以这只羊实际上相对地面的速度会以比4英里/时略小一点。
And the formula that correctly predicts this deviation from just adding the velocities is (v1+v2)/(1+v1xv2/c 2).
能正确描述这种区别的公式是(v1+v2)/(1+v1xv2/c 2)，而不是简单相加。
It's not a very big effect, but then again, the earth looks pretty flat, doesn't it?
好像影响也不太大，但是地面看起来也是很平的，不是吗？
But the earth isn't flat: if I walk 10,000km away from my cat, and you continue on walking 10,000km more,
但地面不是平的：如果我离开我的猫10000千米，并且你又继续走了10000千米
you're NOT 20,000km away from my cat. You're just 12,750km away,
你和我的猫的距离并不是20000米。而是只有12750千米，
in fact, the farthest on earth you can get from ANYTHING on earth is 12,750km.
实际在地球上，你最多只能距离一个物体12750千米远。
It's the earthly distance-limit, though we normally call it the diameter of the earth.
这是地球上距离的极限了，我们通常称之为地球的直径。
And similarly, when you try to add two velocities together, there's a cosmic speed limit of 300,000,000m/s - that is, the speed of light.
同样，当你将两个速度相加时，也存在一个宇宙中速度的极限—3亿米/秒，也就是光速。
So, just because to our eyes the earth looks flat, velocities look like they simply add together,
所以仅仅是因为看起来地面是平的；速度好像能够简单的相加；
and light looks like it doesn't attract gravitationally, is that an excuse to mislead ourselves and our children about the true nature of things?
光看起来不吸引别的物体，这就能成为我们误导自己，不向后代展示世界真相的借口了吗？
