评论
打印
In our universe, when you change from a non-moving perspective to a moving one, or vice versa,
在我们宇宙中，当你从一个静止的视角转换到一个运动的视角，或者反之亦然，
that change of perspective is represented by a what's called Lorentz transformation,
视角的变化是由一个所谓的洛仑兹变换表示的，
which is a kind of squeeze-stretch rotation of spacetime
那是一种时空的挤压拉伸旋转，
that I've mechanically implemented with this spacetime globe.
我用这个时空球体机械地实现了它。
Lorentz transformations keep the speed of light the same for all perspectives,
洛伦兹变换使所有角度的光速都保持不变，
since that's the way our universe works.
因为这就是我们的宇宙的运作方式。
For example, let's say I'm not moving, that is, I'm at the same position at all times,
例如，假设我没有移动，也就是说，我一直处于相同的位置，
and you're moving a third the speed of light to my right, and you turn on a flashlight.
你以1/3光速向我的右边移动，然后你打开闪光灯。
Then that light will move at the speed of light c, or about 300 million m/s,
光将以光速c或大约3亿米/秒的速度移动，
which is drawn as a 45° line on this spacetime diagram.
在这张时空图上绘制成45度角的直线。
And viewed from your perspective, you're not moving
从你的角度来看，你没有移动
aka you're at the same position at all times.
也就是你一直处于相同的位置。
but the light ray still travels at the speed of light.
但是光线仍然以光速传播。
In fact, viewed from any moving perspective,
事实上，从任何移动的角度来看，
the light ray always moves along a 45° line on a spacetime diagram
光线总是沿着时空图上的45度角的方向移动
(at least one with the axes scaled like this).
（至少其中一个轴的比例是这样的）。
So light speed plus your speed equals light speed.
光速加上你的速度等于光速。
It's almost more like what happens when you add something to infinity
与将两个有限数加在一起相比，
than adding together two finite numbers.
这几乎更像是无限大加上一个数字.
But what about speeds slower than light speed?
但是比光速还慢的速度呢？
What if you're traveling at 60% the speed of light to the right, and you shoot a death-pellet,
如果以光速的60%向右发射一个子弹，
that is itself going 60% the speed of light to the right relative to you,
相对于本身也向右以60%的光速运动，
how fast is it going from my perspective?
从我的角度来看，它的速度有多快？
The intuitive answer to this question is that
对这个问题的直觉回答是，
if the death-pellet is going 180 million meters per second to the right relative to you,
如果子弹以每秒1.8亿米的速度相对于你向右边移动，
and you're going 180 million meters per second to the right relative to me,
你又以每秒1.8亿米的速度相对于我向右边移动，
then the death-pellet must be going 360 million meters per second to the right relative to me,
然后子弹必须以每秒3.6亿米的速度相对于我向右边移动，
which is fasterthan light. And which is wrong.
这比光速还快。但这是错误的。
In our universe, velocities don't simply add up when you change perspective.
在我们的宇宙中，当你改变视角时，速度不会简单地加起来。
They almost do for things moving much slower than light(which I'll explain in a bit).
它们几乎适用于比光移动慢得多的物体（我将在稍后解释）。
But in general that's not how our universe behaves.
但总的来说，我们的宇宙不是这样的。
Here's a spacetime diagram from your perspective of you,
这是一个时空图，从你的视角看，
shooting a death-pellet to the right at 50% the speed of light –
你以50%的光速速度向右射出一个子弹，
that is, taking 4 seconds to go as far as light would in 2 seconds.
也就是说，需要4秒的时间，就像光速在2秒内所能达到的那样。
And here's what happens when we shift to my perspective,
当转换到我的视角时，会发生什么，
from which you are moving to the right at 50% the speed of light.
从这里以光速的50%向右移动。
The death-pellet is still moving to the right relative to you,
相对你而言，子弹仍向右移动，
still moving really darn fast, but it's not moving faster than light.
仍然移动得非常快，但它的移动速度并不比光速快。
Its world line is not quite a 45 degree line.
它的世界线不是夹角45度的直线。
And it can't be, which you can kind of get a feeling for
基于洛伦兹变换，
from how Lorentz transformations work.
你不可能感觉到夹角是45度。
They're essentially stretching and squeezing spacetime.
洛伦兹变换实际上是在拉伸和挤压时空。
And stretching out a line on a rubber sheet,
在橡胶布上拉伸一条线，
makes the line's angle approach the direction of stretching,
使线的角度接近拉伸的方向，
never 'flipped over' to be pointing the other way.
决不能"翻转"指向相反的方向。
And while stuff going 60% the speed of light
当物体以60%的光速行进时，
is kind of reaching the limits of what the spacetime globe can reasonably display,
就会达到时空球体所能合理显示的极限，
if you shoot a death-pellet at 60% the speed of light,
如果你以光速60%的速度射出一颗子弹，
and then we shift to my perspective from which you're going 60% the speed of light,
然后从我的角度来看，你以60%光速移动，
the death-pellet still isn't going faster than light.
子弹的速度仍然不会比光速快。
So even if we shot a death-pellet going 60% the speed of light,
所以即使我们射出的是光速为60%的子弹，
from a death-pellet going 60% the speed of light,
在这基础之上，再射出另一个光速为60%的子弹，
from a death-pellet going 60% the speed of light and so on,
再射出另一个这样的子弹，以此类推，
the final speed would be close to but not quite the speed of light,
最终速度将接近光速，但达不到光速，
because of how relative velocities combine in our universe.
这是基于宇宙相对速度结合法则的。
This is one of the consequences forced upon us by the constancy of the speed of light:
这是恒定的光速得出的必然结果：
in a universe (like ours) where changes ofvelocity don't change the speed of light,
在一个像我们这样的宇宙中，速度的变化不会改变光速，
then changes of moving perspective can never make other velocities
那么，移动视角的变化永远不会使其他速度
change from a relative speed less than the speed of light,
从小于光速的相对速度
to a relative speed equal to or greater than light.
变化到等于或大于光速。
If we have an object moving at a speed v relative to your perspective,
如果在你的视角物体以速度v移动，
and you're moving relative to me with speed u,
而你以速度u相对于我移动，
then the equation that describes precisely
那么相对于我的视角，精确地描述
what speed the object is moving relative to my perspective
物体移动的速度的方程是，
is v from my perspective equals v from the moving perspective
我的视角的v 等于运动视角的v
plus u all over 1 plus v from the moving perspective times u over c squared,
加上u的总和除以1加上运动视角的v乘以u除以c的平方，
where c is the speed of light.
其中c是光速。
You'll notice that if you put the speed of light in as one of the velocities,
你会注意到，如果你把光速作为速度之一，
the equation always gives the speed of light back,
方程总是给出光速，
no matter what the other velocity is,
不管另一个速度是多少，
which of course jives with the whole "constant speed of light" thing.
当然这与“光速不变原理”是一致的。
And you'll notice that if both velocities are less than the speed of light,
你会注意到，如果两个速度都小于光速，
then the equation always gives back an answer less than the speed of light,
方程给出的答案总是小于光速，
which is what we were describing earlier about relative speeds never adding up to a speed faster than light.
这就是我们先前所描述的相对速度加起来永远不会超过光速。
And you'll notice that if both velocities are a lot lot smaller than the speed of light,
你会注意到，如果两个速度都比光速小很多，
then the v times u divided by c squared term in the bottom is essentially zero,
那么在底部，v乘u除以c的平方等于零，
and so the whole thing is essentially v+u.
所以整个方程即v+u。
This is the sense in which, for slow speeds, velocities DO simply add together.
在这种意义上，对于低速，速度只是简单地加在一起。
But not for speeds close to light speed; our universe is more subtle than that.
但对于接近光速的速度就不能这样，我们的宇宙是极其微妙的。
For a deeper look into how to compare relativistic velocities,
为了更深入地研究如何比较相对速度，
I highly recommend heading over to Brilliant.org's course on special relativity.
我强烈建议去Billiant.org这里找关于狭义相对论这方面的课程学习一下。
There, you can explore custom scenarios that build off the topics in this video
在那里，你可以探索在这个视频中建立主题的自定义场景，
to get an intuitive understanding of the mathematics of relativistic velocity addition.
以获得对相对论速度合成数学基础的直观理解。
like how to warn earth of an incoming relativisticalien invasion.
就像如何警告地球外星人即将入侵。
The special relativity questions on Brilliant.org are specifically designed to help you take
在Brilliant.org上专门设计的狭义相对论问题是为了帮助你
the next step on the topics I'm including in this series,
在深入了解本系列中所包括的主题后进行下一步的学习计划，
and you can get 20% off of a Brilliant subscription by going to Brilliant.org/minutephysics.
你可以通过访问Brilliant.org/minutephysics获得Brilliant订阅的20%的折扣。
Again, that's Brilliant.org/minutephysics
再次说明是这些网站，Brilliant.org/minutephysics，
which gets you 20% off premium access to all of Brilliant's courses and puzzles,
它能让你享受所有Brilliant课程和问题的高级访问权限，
and lets Brilliant know you came from here.
让Brilliant网站知道你来自本视频。
