ADM-201 dump PMP dumps pdf SSCP exam materials CBAP exam sample questions

爱因斯坦的质能方程 – 译学馆
未登录,请登录后再发表信息
最新评论 (0)
播放视频

爱因斯坦的质能方程

Einstein's Proof of E=mc²

1905年中期 阿尔伯特·爱因斯坦提出现在是世界上最著名的方程:
In mid 1905, Albert Einstein derived what is now the most famous equation in the world:
E=mc²
E equals M C squared.
但是他没有写下来
But he didn’t just write this down out of the blue.
这直接来源于他的狭义相对论论文 我们在上周的视频中有所谈及
It followed directly from his paper on special relativity that we talked about in last week’s video.
这是他计算的过程
And here’s how he did it.
假设你正在看一只猫在空间中自由浮动
Suppose you’re watching a cat float freely in empty space,
突然它向各个方向发出闪光
when suddenly it emits a flash of light in all directions.
这种光带有某种能量 我们称之“E”
The light carries away some energy, we’ll call it “E”.
根据能量守恒 猫一定失去了能量E
So by conservation of energy the cat must have lost energy E.
但由于光是对称地向四面八方发出的
But since the light was emitted symmetrically in all directions,
它不会改变猫的速度
it won’t have changed the cat’s velocity.
那么光的能量是哪来的?
So where did the energy for the light come from?
现在先不急
Never mind that now.
想象你登上飞船 在实验中飞船极速运动
Let’s imagine you get board and zoom off in a spaceship in the middle of the experiment.
但从你的角度看 你仍坐在飞船里
But from your new perspective, you’re sitting still in your spaceship
猫在窗外移动
and the cat is the one moving past outside the window.
因此 你计算出猫有一些运动的能量
Therefore you’ll calculate that the cat has some kinetic energy.
这就是动能
That is energy of motion.
而当你看到猫发出的闪光
And when you see the cat emit the flash of light,
你再次测量光减少后的能量
you’ll again measure that its energy decreases by the energy of the light.
尽管现在你在移动
Except now that you’re moving,
狭义相对论告诉我们 你和猫有不同的运动速度
special relativity tells us that time passes at different rates for you and the cat,
所以测量出的频率差异值即为闪光的能量
so you’ll measure a different value for the frequency, and thus energy of the flash of light.
这是相对论多普勒效应
This is the relativistic doppler effect.
对我们来说 它相当于光的能量乘以
And for our purposes, it amounts to multiplying the energy of the light
1加上速度的平方 除以2倍光的速度的平方
by one plus your velocity squared divided by twice the speed of light squared.
回顾一下 如果你以速度v飞行
So to recap, if you take off at velocity v,
你会看到猫获得一些动能KE1
you’ll see the cat gain some kinetic energy KE1
然后你会看到猫的能量以闪光形式减少E*(1+v²/2c²)
then at the flash you’ll see the cat’s energy decrease by E times one plus v squared over two c squared.
另外 如果你继续等 你会看到猫的能量减少E
On the other hand, if you wait, you’ll see the cat’s energy decrease by E.
此时起飞 你可以看到它获得了动能KE2
and now when you take off you’ll see it gain kinetic energy KE2.
但这是愚蠢的!在这两种情况下猫都没有被影响
But this is silly! You never touch or otherwise influence the cat in either case,
所以 最后你会得到的相同的总能量
so you should get the same total energy at the end.
重新设计的话我们前后看到的光的动能一定是不同的
Rearranging, we see that the kinetic energy before and after the flash must be different!
一个物体的动能是质量的一半乘以速度的平方,
And the kinetic energy of an object is one-half of its mass times velocity squared,
但我们知道 两种情况速度相同
but we know that the velocity wasthe same in both cases.
为了解释不同
so in order to account for the difference,
在闪光时 猫的质量必须发生变化
the cat’s mass must changewhen it emits the flash of light!
如果我们约掉等式两边相同成分你会发现猫的质量变化
Now if we cancel things out, you can see that the change in mass of the cat
一定等于 能量作被除数 除以C的平方
must be equal to the energy as the dividenddivided by C squared,
或者 就是前面说的 E=mc²
or, as you’ve heard before, E equals M C squared.

发表评论

译制信息
视频概述

通过解说让你快速了解爱因斯坦的质能方程E=mc²

听录译者

收集自网络

翻译译者

川上川

审核员

W

视频来源

https://www.youtube.com/watch?v=hW7DW9NIO9M

相关推荐