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黑洞中的时间是如何转换的

How Time Becomes Space Inside a Black Hole | Space Time

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This episode is sponsored by crunchyroll.
在今天的Space Time栏目中 我们将讨论时空
Today on Space Time, we’re going to talk about time-space,
或者说时间与空间的奇妙角色转换
or the strange switching in the roles of space and time
当我们降低到黑洞的视界上时 它们之间的角色转换
that occurs in the mathematics when we drop below the event
将会以数学的形式发生
horizon of a black hole.
[音乐播放中]
[MUSIC PLAYING]
“空间与时间之间互相转换”这种奇异的说法
What does this bizarre statement, space and time
实际上意味着什么呢?
switch roles, even mean?
关于时空的难以解释部分难道纯粹是数学上的巧合吗?
Is this space-time dyslexia purely a mathematical quirk?
又或者是时空错乱的偶然产物?
Or does it correspond to real timey-wimey weirdness?
我们已经讨论到了这个层面
We’ve been working up to this one.
因此 如果你认为你需要更多背景知识
So you might want to hit pause and check out these episodes
你可能会想要暂停并且去回顾之前的视频内容
if you think you need some more background.
让我们开始吧
Let’s get started.
首先我们将思考在没有黑洞或
First we’ll think about what the flow of time
甚至是没有时空曲率的情况下 时间的流动是怎样的
looks like without black holes or even spacetime curvature.
当我们谈起几何的因果关系时
When we talked about the geometry of causality,
我们所看到的这个被称为时空间隔的量
we saw that this quantity that we call the spacetime interval
控制着因和果的流动
governs the flow of cause and effect,
这也是在相对宇宙中事件的唯一可靠顺序
the only reliable ordering of events in a relative universe.
我会再一次向你展示它的数学原理
I’m going to show you the math one more time.
然后我们会重新用图表形式来展示一遍
And then we’ll get back to doing all of this graphically.
时空间隔被定义为这样
The spacetime interval is defined like this,
适用于无聊又陈旧的平面或闵科夫斯基空间
for boring old flat or Minkowski space.
不同的观察者可能会认为两个事件的时空间隔
Different observers may report that two events are separated
受不同的距离Δx和不同的时间增量
by different distances delta x and by different amounts
所影响
of time delta t.
然而 每一个观察者都记录到了相同的时空间隔
However all observers record the same spacetime interval.
如果一个结果导致了另一个附加的结果
If one event causes a second event,
那么其时空间隔必为0或负值
the spacetime interval must be 0 or negative.
这仅意味着相当于光速的因果联系
That just means that a lightspeed causal link
可能已经在两者之间穿越了
may have traveled between them.
你可以说一个给定时空瞬间内的物体
You could say that an object at a given spacetime instant
是通过自我倒置
is caused by way of a version of itself
存在于早期的
existed an instant earlier.
因此 物体世界线的时空间隔是负增长的
So world lines of objects have decreasing spacetime intervals.
事实上 早期的时间演化
In fact forward temporal evolution
需要负的时空间隔来支持
requires a negative spacetime interval.
在平面时空中 在Δt前面的
In flat space time, that negative sign
这个负号控制了先前的演变
in front of the delta t drives that forward evolution.
这使得t相当于是类时坐标
This makes t, the time-like coordinate,
以此类推 x为类空坐标
while x is the space-like coordinates.
由于因果关系要被维持 类时坐标
For causality to be maintained, the time-like coordinate
只能一直增长
must always increase.
颠倒因果关系即翻转
Reversing causality means flipping the sign
时间间隔的迹象
of the spacetime interval.
在我们超光速时空旅行的一集里
In our episode on superluminal time travel,
我们在平坦空间里看到了时间翻转
we saw that in flat space, this means
即意味着我们比光速还要快 当然
traveling faster than light, which is, of course,
这是不可能的
impossible.
但是 如果我们引入一个黑洞
But if we introduce a black hole,
我们将有第二个方式来翻转
we now have a second way to flip the side
时空间隔
of the spacetime interval.
我们将会看到这是如何以非常古怪的方式
We’re going to see how this changes the behavior of time
来改变时间行为的
in very strange ways.
增加一个不旋转且不带电的黑洞
Add a non-rotating, uncharged black hole,
然后时空间隔会变成这样
and the spacetime interval becomes this.
这个结论来自卡尔·史瓦西针对爱因斯坦
This comes from Karl Schwarzschild’s solution
场方程的一个解决方案 同时也是第一个精确
to the Einstein field equations, the very first accurate
描述了黑洞的结论
description of a black hole.
我已经忽略了一些术语
I’ve left out a few terms.
该公式假定没有轨道运动 只有
This equation assumes no orbital motion, only motion
朝向或远离于黑洞中心的运动
towards or away from the center of the black hole, which
运动距离为r
is a distance r away.
这rs是史瓦西半径
That rs is the Schwarzschild radius, the radius
即视界半径
of the event horizon.
从很远的视界 史瓦西间隔
Very far from the event horizon, the Schwarzschild interval
将适用于古老的闵可夫斯基间隔
becomes the good old Minkowski interval.
并且时间和空间漂亮地分离了
And time and space nicely separated.
但是 如果一个对象处于接近视界的状态
But if an object gets close to the event horizon,
并且r只是比rs大一点点
so r just a little bit bigger than rs,
这两个圆括号里的东西能最大限度描述
that stuff in the two brackets describes extreme warping
时空的弯曲
of spacetime.
但只要你在视界之外
But as long as you are outside the event horizon,
时间就会主要表现为它本身
time behaves itself mostly.
负时空间隔仍然意味着因果运动
A negative spacetime interval still means causal movement.
并且打破因果关系的唯一方式
And the only way to break causality
仍然是穿越得比光速更快
is still with faster than light travel.
在r变得比rs更小的情况下
Things change radically below the event horizon
事物在视界之下发生了本质变化
when r gets smaller than rs.
然后两个圆括号里东西都变成了负值
Then both of these brackets become negative.
现在整个的Δr都是负的
The entire delta r stuff is now negative.
并且Δt是正的
And the delta t stuff is positive.
在视界之下 只有一种方法
Below the event horizon, there is only one way
来维持一个预期有规律的时态实体的
to maintain the respectable causal progression expected
相当数量的因果进展
of a well-mannered temporal entity.
那将会塌陷 会产生一个非零变量Δr
That’s to fall inwards, to have a non-zero delta r.
碰巧 你没有选择
As it happens, you don’t have a choice.
空间本身塌陷的速度
Space itself is falling inwards faster
比光朝中心奇点的速度还要快
than the speed of light towards the central singularity.
它会带着你 驱动你的
It carries you with it and drives your personal clock
钟表向前走
forward as it does so.
对于数学坐标r
In the mathematics the coordinate r,
即曾经表示距离的坐标r
which once represented distance, now grants
现在gant需要保持你的因果关系
the negative sign needed to maintain your causal flow.
这变得类似于时间了
It becomes time-like.
它是单向的
It’s uni-directional.
同时 这个以前被称为时间 t的坐标
Meanwhile the coordinate previously known as time, t,
失去了它的负号 变得类似空间
lost its negative sign and become space-like.
因此 它可以横贯任何方向
So it can be traversed in any direction
或不穿过任何东西
or not traversed at all.
但这一切的时空转换
But what does all of this time-space switching
其实是什么样子的呢?
actually look like?
让我们再次落入黑洞 现在 用图表描绘
Let’s fall into the black hole one more time, now graphically
代替数学推导吧
instead of mathematically.
返回到常规宇宙
Back out here in the regular universe,
无论过去还是未来的所在之处都非常明显
it’s pretty obvious where the past and the future are.
在我们日益流行的时空图表中
On our ever popular spacetime diagram,
我们能看到两者之间壁垒分明
we see a sharp division between the two.
我们过去的光锥涵盖了所有时空
Our past light cone encompasses all of spacetime
即这可能已经影响了我们 而未来的
that could have influenced us, while that future light
光锥向我们展示了宇宙的一部分
cone shows us the part of the universe
即那些我们可能从不希望能遇见或影响的部分
that we might never hope to encounter or influence.
哪一个方向是未来?
Which direction is the future?
沿我们的时间轴以及直角
Ahead along our time axis and at right angles
到我们所有的空间轴
to all of our space axes.
我们的未来光锥固定向前盯着
Our future light cone stares fixedly
均匀地包括所有的空间方向
forwards, encompassing all spatial directions equally.
如果我们引入重力 这不再成立
This is no longer true if we introduce gravity.
靠近一个巨大的物体 你的未来
Close to a massive object, your future
不再是正确的空间角度
is no longer at right angles to space.
它变得稍微向质量的方向倾斜
It becomes slightly tilted in the direction of that mass.
发出一阵典型的未来光线
Send out a burst of future defining light rays,
它们将不会均匀地分布 因为它们
and they won’t spread out evenly because they
向重力场弯曲
bend towards the gravitational field.
当你接近黑洞的视界时
As you approach the event horizon of a black hole,
越来越多的光线被
more and more light rays are turned
导向视界
towards the event horizon.
你的未来光锥与你的时间轴
Your future light cone and your time axis
开始和黑洞内径向轴线
begin to blur together with the inward radial axis
一起模糊
of the black hole.
此时此刻 我们应该转换图表了
At this point, it’s time we switch diagrams.
靠近或在黑洞的内部时
Close to and within the black hole,
潘洛斯图表将更为有用
the Penrose diagram is much more useful.
它通过紧凑限定的恒定空间或时间线
It deals with the extreme stretching of space and time
接近它的边界来解决极端的时间伸展和
by compact defined lines of constant space or time
空间伸展
close to its boundaries.
我们之前讨论过关于这些图表
We talked about these diagrams previously.
但重要的是要记住
But an important thing to remember
是恒定的空间与时间的线
is that the lines of constant space and time
是弯曲的 所以使得光锥保持直立
are curved so that light cones remain upright.
并且光总是以45度角行进
And light always travels at a 45 degree angle,
甚至在黑洞里也是如此
even inside the black hole.
这整个对角线代表视界
This entire diagonal line represents the event horizon.
看看我们接近视野内宇宙发生了什么
Watch what happens to our view of the universe as we approach it.
我们整个未来光锥包含越来越多的事件视界
Our entire future light cone encompasses more and more of the event horizon.
这边的一小片是最后的狭窄窗口
That last tiny sliver is a narrowing window
你可以以光速来逃脱
directly above that you could escape to at close to the speed of light.
同时 我们的过去光锥现在还包括
Meanwhile our past light cone now encompasses
自以前就试图
light that has been struggling to escape
从视界上方逃脱的光
from just above the event horizon since the distant past.
我们在水平线下仍然看不到东西
But we still see nothing from below the horizon.
然而 只要我们经过了水平线 一切都改变了
Yet as soon as we passed the horizon, everything changes.
外部宇宙退出了我们的未来光锥
The outside universe exits our future light cone, which now
现在只包含着奇点
just contains the singularity.
我们也开始遇见一系列新的来自过去的光子
We also begin to encounter a new set of photons from the past.
在交叉的时刻 来自视界的光线
At the moment of crossing, light rays from the event horizon
突然变得可见
itself are suddenly visible.
事实上 我们下降穿过了光海
In fact, we plummet through a sea of light
即那些永远地向外攀升却到达不了任何地方的光
that is eternally climbing outwards but getting nowhere.
在那之后 我们可以访问黑洞的
After that, we have access to the history of the interior
内部历史
of the black hole.
当我们以比时空光流的下落速度更快时
As we fall with the faster than light flow of space time,
我们会赶上指向外部的光
we overtake light that is outward pointing.
那束光无法真正地向外突进
That light isn’t actually making headway outwards.
它试着逆流而上却
It’s trying to swim upstream and failing
无法对抗时空的光级联
against the faster than light cascade of spacetime.
一些光可能是来自崩溃的恒星表面
Some of this light might be from the collapsing surface
即那些首次形成黑洞的恒星
of the star that first formed the black hole, emitted
发射后过了很久 我们才进入了视界
long before we entered the event horizon.
它似乎来自地底下
It appears to come from below us because it’s
因为它在努力向上爬升
trying to climb upwards.
事实上 虽然它被比我们在任何地方遇到的无线电都要大的
In fact though, it was emitted at larger radio
巨大无线电所喷射
than wherever we encounter it.
同样 我们过去的光锥是光线
Also in our past light cone are light rays
即那些被指出向内的光线
that are pointed inwards, some of them coming
它们中的一些来自外部宇宙
from the outside universe.
当我们下落时 这光线会超过我们
This light overtakes us as we fall.
这是在我们之后进入事件视界的光
This is light that entered the event horizon
似乎从上方到达了我们这里
after we did and appears to reach us from above.
我们可以尝试向任一光源移动
We can try to move towards either source of light,
可以下朝黑洞过去的光移动
down towards light from the black hole’s past
或向上朝黑洞未来的光移动
or up towards light from the black hole’s future.
这些方向 这种空间的自由选择
Those directions, those spatial freedoms,
都由现在的时间坐标来描述
are now described by what was once the time coordinate.
但它不再是类时性质的
But it’s no longer time-like.
你可以在任一方向贯穿 来使它呈现类空性质
You can traverse in either direction making it space-like.
这样做实际上并没有在时间里穿越
Doing so isn’t actually traveling in time,
尽管有一种过去事件(恒星塌缩)
even though there’s a sense of past events in one direction– the collapsing star–
和未来事件的感觉 (我们之后掉进黑洞视界的一切)
and future events in the other, everything that fell into the
black hole after us.
但请记住 未来的光锥实际上只指向
But remember that future light cone actually just points
奇点
towards the singularity.
当我们尝试在任一方向加速时 向上或向下
If we try to accelerate in either direction, up or down,
我们只是加快了灭亡
we just quicken our demise.
最好只是下降
Best just to fall.
这是由黑洞给予的最后的怜悯
It’s the last mercy granted by the black hole.
它用最慢的路径把我们送入死亡尽头
It transports us to our doom by the slowest path
除非我们反抗
unless we resist.
在视界之下 仍有一种空间处于
Below the event horizon, there’s still a sense
向上或向下的状态的感觉
of spatial upness and downness.
然而 旧的径向尺寸不是类空的
However the old radial dimension isn’t space-like,
它是类时的
it’s time-like.
到达我们的每一个光子都被释放 它们释放的半径
Every photon that reaches us was emitted at some larger radius
比我们在任一地方遇到的都要大
than wherever we encounter.
即使旧光向外挣扎
Even if it’s old light struggling outwards,
过去仍然是径向向外的
the past is radially outwards.
并且所有可能的未来发展方向
And all possible future directions
导致径向向内
lead radially inwards.
所有的世界线以相同的方式
In the same way that all world lines move
朝外部宇宙的未来移动
towards the future in the outside universe,
时间被径向放置
time is laid radially.
并且r是类时的 单向的
And r is time-like, uni-directional.
奇点成为未来的时间 它没有一个集中的地方
The singularity becomes a future time, not a central place.
事实上 史瓦西度量真的
In fact the Schwarzschild metric really
在单个方程里给出了两个独立的时空映射
gives two separate spacetime maps in a single equation,
一个在视界之上 另一个在视界之下
one for above and one for below the event horizon.
在这些区域里 坐标r和t扮演
The coordinates r and t play different roles
不同的角色
in those regions.
还有其他坐标系
There are other coordinate systems in which
它们从未发生过转换
that switch never happens.
但这神秘的三维翻转
But this mysterious dimensional flip
确实给了我们一些独特的见解
does give us some fascinating insight
即关于如何将时间和空间融合在一起
into how time and space blend together
可能是在所有时空中最奇怪的地方发生
in what is perhaps the strangest place in all of spacetime.
感谢Crunchyroll赞助本集
Thanks to crunchyroll for sponsoring this episode.
Crunchyroll给你带来日本的新动漫
Crunchyroll brings you new anime from Japan
在它们仅仅播出一小时之后
just one hour after its aired.
所有的剧集都是1080p高清的
All episodes are in 1080p HD and can
并且能在所有设备上观看
be viewed across all devices.
我觉得Space Time的观众们一定会
I think Space Time viewers would really
享受星际牛仔 一部科幻小说
enjoy Cowboy Bebop, a Sci-fi noir that
讲述了一帮太空赏金猎人的冒险故事
follows the adventures of a gang of space bounty hunters.
所以 怎么可以不爱呢?
So what’s not to love?
只要你登录Crunchyroll.com/spacetime
Crunchyroll is offering Space Time viewers a 30 day free
Crunchyroll为Space Time的观众们提供了为期30天的免费观看
trial if you go to Crunchyroll.com/spacetime.
再说一次 crunchyroll.com/spacetime
Again that’s crunchyroll.com/spacetime.
嘿 伙计们 在我们最近的时空之旅俱乐部
Hey guys, in our recent Space Time journal club,
我们谈到一篇论文 它描述了
we talked about a paper describing a recipe
制造一种不可思议的东西——时间晶体的方法
for making these weird things called time crystals
和关于研究者们如何成功创造出它们
and about how some researchers have now successfully created them.
让我们继续讨论
Let’s continue the discussion.
你们中只有少数几个人才知道时间水晶由什么构成
A few of you are unsure of what constitutes a time crystal.
在这一点上 该术语的使用是不够严谨的
At this point, the use of the term is pretty loose.
它指的是任何量子系统内部的相互作用
It refers to any quantum systems whose internal interactions
导致了从一个状态转变为另一个状态的周期变化
result in a periodic change from one state to another and then
然后又返回去
back again.
这个系统在测试阶段使用电子自旋
The systems that were tested use electron spins, which
即电子们彼此拉扯来形成一个级联流
pull on each other to cause a cascading flow of flipping
该级联流是翻转旋转的且呈周期性
spins the cycles back and forth.
真的 术语 时间晶体
Really though, the term time crystal
只是用来指代任何
is just used to refer to anything
有着内部状态随着时间推移而重复的模式的事物
that has a pattern of internal states that repeats over time.
它不一定得是规则的晶体
It doesn’t also have to be a regular crystal that has
即那些有着重复空间模式的晶体
a repeating spatial pattern.
事实上 它通常不是
In fact, it typically won’t be.
科林·布朗问 自旋翻转振荡是否
Colin Brown asks if the spin flip oscillation
仅依赖于电磁场
is only dependent on the electromagnetic field
振荡
oscillation.
并且他还问 那为什么如此特别
And he also asks why that’s so special.
首先是啊 这些时间晶体
Firstly yeah, these time crystals
在整数倍的电磁场频率下
oscillate at an integer multiple of the electromagnetic field
振荡
frequency.
因此 时间晶体振荡和电磁场振荡
So the time crystal oscillation and the EM field oscillation
在共振的状态
are in resonance.
对于时间晶体的每一个、两个、三个
For every one, two, three, et cetera cycles
等等周期 电磁场给出轻轻的一推
of the time crystal, the EM field gives a little push.
它必须是整数因素 因为如果磁场
It has to be an integer factor, because if the EM field were
通过时间晶体的周期推动到一半
pushing halfway through the time crystal period,
它会往错误的方向推动
it would be pushing in the wrong direction.
这就像你推秋千一样
It’s like when you’re pushing a swing,
你不需要通过每时每刻的推动来让它继续运动
you don’t need to push every time to keep it going.
但是你需要在正确的时间点推动它
But you do need to push at the right time
不然秋千会慢下来
or you’ll slow it down.
科林和其他人还问了 为什么这那么特殊?
Colin and others also ask why this is so special.
毕竟 很多东西都在振荡
After all, lots of things oscillate, especially when
尤其是当你推动它们的时候
you push them.
因此 在弗兰克·威尔采克一开始的想法中
So in Frank Wilczek’s initial idea,
他假设的时间晶体并不需要任何输入能量
his hypothetical time crystals didn’t require any input energy
来保持它们振荡
to keep them oscillating.
对于威尔采克的时间晶体 振荡状态
For Wilczek’s time crystals, the oscillating state
呈现平衡状态
is an equilibrium state.
并且振荡理应在没有任何能量输入的
And the oscillations were supposed to go on forever
情况下永远持续下去
without any energy inputs.
那将是特殊且怪异的 即使原期是
That would be special and weird, even if the original period
由外部磁场频率决定
was defined by an external EM field frequency.
现在在数学上已被证实
It’s now been proved mathematically
时间晶体可以平衡存在
that time crystals can exist in equilibrium.
为了使它们持续振荡 你需要不断地投入能量
To keep them oscillating, you need to keep putting in energy.
然而 实验结果
However, the experimental results
仍然是激动人心的 因为系统
are still exciting, because the system
确实产生了它们自身内部的振荡
did develop their own internal oscillations that
该振荡会抵抗来自外部强迫电磁场振荡的变化
resisted changes from the outside forcing EM field oscillation.
所以振荡 在某种意义上
So the oscillations were, in a sense,
是根本性的 只是不能持续
fundamental, just not sustainable.
这是不是比一个摇晃的钟摆更有趣?
Is this more interesting than, say, a swinging pendulum?
好 钟摆的确很酷
Well pendulums are pretty cool.
所以我不知道
So I don’t know.
它们是一种新型振荡系统
They’re a new type of oscillating system
它们可能有自己的用途
that could have their own uses.
我想感谢丹库洛斯·麦姆罗德
I’d like to thank Dankulous Memelord for what,
因为对我们来说 刺激了一个有益的探讨
for us, spurred a useful discussion
即在这一集的可理解性上的探讨
on the comprehensibility of this episode.
我们一直在监控反馈来增强
We’re always monitoring feedback to improve
视频的可理解性
the clarity of the show.
值得一说的是 我们对Space Time的目标
It’s worth commenting here that our goal on Space Time
和大多数科普节目有一点点不同
is a little bit different to most science media.
我们感兴趣的是去提供一个桥梁来理解
We’re interested in providing a bridge to understanding
真正的科学 即比入门级
the real science that goes a bit further
更深入一点点
than an introductory level.
时空之旅俱乐部尤其如此
That’s especially true of Space Time Journal Club.
如果你发现在第一次观看时有比较多看不懂的地方
If you’re finding an episode a bit much on first viewing,
有个好主意是去查找其他资源
it’s often a good idea to also check out
它们可能会提供更好的介绍
some other sources, which might give a better intro.
但请坚持 因为理解我们的宇宙
But please persist, because understanding our universe
非常值得我们为之付出的所有工作
is well worth all of the work.
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视频概述

本集介绍了在黑洞中的时间与空间关系 是一集上佳的科普类作品,黑洞视界的两边,时空完全倒反,本视频告诉你为什么

听录译者

收集自网络

翻译译者

Cassic

审核员

Y

视频来源

https://www.youtube.com/watch?v=KePNhUJ2reI

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