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In mid 1905, Albert Einstein derived what is now the most famous equation in the world:
1905年中期，阿尔伯特·爱因斯坦推导出了现在世界上最著名的方程：
E equals M C squared. But he didn't just write this down out of the blue,
能量E等于m乘以c的平方。但他不是突然而然就写出来的，
it followed directly from his paper on special relativity that we talked about in last week's video…
这直接引申自他的论文狭义相对论，我们在上周的视频中提到了……
and here's how he did it:
以下就是他如何做到的：
Suppose you're watching a cat float freely in empty space,
假设你正看着一只猫自由地漂浮在空中，
when suddenly it emits a flash of light in all directions.
突然它向各个方向发出一道闪光。
The light carries away some energy, we'll call it "E",
光携带一定的能量，我们将其命名为“E”，
so by conservation of energy the cat must have lost energy E…
因为根据能量守恒，猫一定损失了能量E……
but since the light was emitted symmetrically in all directions,
但是由于光线是对称地向各个方向发射的，
it won't have changed the cat's velocity.
所以不会改变猫的速度。
So where did the energy for the light come from? Never mind that now…
那么光的能量是从哪里来的呢？别管那些了……
let's imagine you get bored and zoom off in a spaceship in the middle of the experiment.
现在设想你很无聊，乘坐太空船穿过太空中。
But from your new perspective, you're sitting still in your spaceship
但从你的新视角来看，你正坐在你的飞船里，
and the cat is the one moving past outside the window!
而猫才在往后飞过去！
Therefore you'll calculate that the cat has some kinetic energy, that is, energy of motion…
因此，你会计算出猫有一些动能，即运动的能量。
and when you see the cat emit the flash of light,
当你看到猫发出一道光，
you'll again measure that its energy decreases by the energy of the light. Except now that you're moving,
你会再次测量到它的能量因为发出光而降低。除了现在你正在移动，
special relativity tells us that time passes at different rates for you and the cat,
狭义相对论告诉我们，时间对于你和猫以不同的速率流动，
so you'll measure a different value for the frequency, and thus energy of the flash of light.
所以你会测量到因闪光导致的频率差异。
This is the relativistic doppler effect, and for our purposes,
这就是相对论多普勒效应，而对我们来说，
it amounts to multiplying the energy of the light by one
它相当于将光的能量乘以一
plus your velocity squared divided by twice the speed of light squared.
加你的速度的平方除以光速平方的兩倍。
So to recap, if you take off at velocity v,
因此回顾一下，如果你以速度v起飞，
you'll see the cat gain some kinetic energy KE1,
你会看到猫获得了动能KE1，
then at the flash you'll see the cat's energy decrease by E
闪光之后，你将看到猫的能量降低了E
times one plus v squared over two c squared.
乘以1加上v的平方除以2个c平方。
On the other hand, if you wait, you'll see the cat's energy decrease by E,
另一方面，如果你静止等待，你会看到猫的能量减少了E，
and now when you take off you'll see it gain kinetic energy KE2.
而当你离去时又会看到它获得动能KE2。
But this is silly! You never touch or otherwise influence the cat in either case,
但这很荒唐！无论在哪种情况下，你都未以触摸或以其他方式影响猫，
so you should get the same total energy at the end… Rearranging,
所以你应该在最后得到相同的总能量。重新排列后，
we see that the kinetic energy before and after the flash must be different!
我们看到闪光之前和闪光之后的动能一定是不同的！
And the kinetic energy of an object is one-half of its mass times velocity squared,
物体的动能是二分之一的质量乘以速度的平方，
but we know that the velocity was the same in both cases…
但是我们知道在这两种情况下速度是相同的，
so in order to account for the difference,
所以为了解释这个差异，
the cat's mass must change when it emits the flash of light!
猫的质量必须在发光前后改变！
Now if we cancel things out,
现在如果我们消去各项，
you can see that the change in mass of the cat must be equal to the energy divided by c squared,
你可以看到猫的质量变化一定等于能量E除以c的平方，
or, as you've heard before, E equals M C squared!
或者就像你以前听说的，能量E等于m乘以c的平方！
