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宇宙中有多少粒子?

How many particles in the Universe? - Numberphile

Brady 我们讨论一下宇宙中有多少粒子
So, Brady, we’re gonna talk about how many particles there are in the universe.
我们在可观测的宇宙范围内计算粒子的数量
We gonna calculate the number of particles in the observable universe.
你知道那是宇宙中我们可见的部分
So that’s, you know, the section of the universe that we can see,
从那光能触及到我们
where light could have reached us from.
我们在这谈论的粒子是什么?
What are the particles that we’re talking about here?
我们将专注于我们所知道的粒子
So we’re gonna be interested in particles that’s, that are particles that we know exist,
那些基本的 有质量的粒子
that are fundamental, and we’re interested in the ones that have mass.
所以我们并不谈论诸如光子
So, we’re not really talking about photons, for example.
我们将要谈论的是夸克 电子之类的粒子
What we’re gonna be talking about are things like quarks, electrons, those sorts of things.
夸克 当然 存在于质子 中子之中
So the quarks, of course, are gonna live inside protons, neutrons,
而电子盘旋于那些在原子之中的质子和中子
and the electrons are gonna be in orbit around those, those protons and neutrons in atoms.
其他相当多的事物是可忽略的
Pretty much everything else is insignificant.
我们该如何做到?我们将用到四个数据
So, how do we do this? So we’re gonna use four bits of data.
宇宙学数据的一部分
Part of it’s gonna be cosmological data.
从测量宇宙微波背景辐射的普朗克卫星得来的数据
Data from the Planck satellite, which measures the cosmic microwave background radiation.
人们称之为宇宙大爆炸遗留下的辐射
People call it the radiation that’s left over from the big bang.
这是第一种中性原子形成后我们所观测到的辐射
It’s the radiation that you get, after, you know, when the first sort of neutral atoms began to form.
我们需要 我们将用从那得来的数据
So, we’re gonna need, we’re gonna use data from that.
和一点点粒子物理学的数据
And a little bit of particle physics data, as well.
所以这些是我们将使用的四个数据
So these are the four bits of information we’re gonna use.
首先是宇宙的临界密度
So the first of these is the critical density of the universe.
这是一个测量完全静止的宇宙的能量密度的好方法
So this is a good measure for what is the energy density of the universe, full stop.
这是因为我们知道宇宙空间非常接近于平坦
This is because we, we know that the universe is very close to being spatially flat.
它的形状不像球体或马鞍
So, it’s, it’s not shaped like a sphere or a saddle,
它介于两者之间
it’s somewhere in between the two.
因此 我们得知它的密度
And because of that, we know its density
是非常接近事实上相当轻的临界密度的
is very close to the critical density, which is a really really really light density, actually.
如果你把它与水的密度相比较
If you look at it, if you compare this to the density of water,
水的密度是一克每立方厘米
the density of water is one gram per centimeter cubed.
宇宙的密度是它的百万百万百万百万百万分之一 嗯?
And this is a million million million million million times less than that, right?
它超级稀疏的 对不?因为它就是我们正在讨论的宇宙
So it’s super undense, right? Because this is the universe we’re talking about.
我们需要的下一个数据
The next bit of information that we’re gonna need
是宇宙中能源收支平衡分数
is the fraction of that energy budget in the universe
储存于重子中 嗯 为什么是重子?
that’s stored in baryons. Now, why baryons?
重子 就此而言 它们就是
Well, baryons, really, in this context, they’re just
存在夸克的质子和中子
the protons and the neutrons, which is where the quarks live.
另外 可观测宇宙的尺度 同样来自普朗克的数据
The other thing the size of the observable universe. Again, coming from Planck data,
得到的数字大约是10的28次方厘米
we get this figure of about ten to the twenty-eight centimeters.
一个1后有二十八个0
A one with twenty-eight zeroes after it.
嗯 很多个厘米 但是宇宙很大 对不?
So, lots of centimeters, but the universe is big, right?
为什么用厘米啊?
Brady: “Why is it in centimeters?”
嗯 我用厘米是因为这个用的是厘米 我不想把
Well, I put it in centimeters, because this one was in centimeters, and I don’t want to start getting,
把单位弄得混乱 所以我想最好用同一套单位
getting all my units messed up. So I thought it safest to, to just be, keep one set of units in there.
最后 我们需要的是光子的质量
And the last thing is, that I’m gonna need is the mass of the proton.
我们关注的重子是质子和中子
The baryons that we’re interested in are protons and neutrons,
它们的质量大致相等 非常接近
they have got about the same mass, very close, you know, the mass is pretty much identical.
而光子的质量大概是10∧-24克
And so the mass of the proton is ten to the minus twenty-four grams, roughly.
这些是我们计算所需的四个数据
These are the four things that we’re gonna need to work out, you know,
也就是在宇宙中有多少个粒子
how many particles there are in the universe.
嗯 首先我们要算一下宇宙中有多少重子
So, to start off with, we’re gonna work out how many baryons there are in the universe,
也就是 那里总计有多少质子和中子
i.e., how many protons and neutrons, in total, there are.
我们计算这个所要做的第一件事是
First thing we’re gonna do to calculate that is, we’re gonna say,
重子中储存的或者说质子与中子中储存的
what is the energy density stored in baryons?
临界密度是多少?
Or stored in protons and neutrons?
嗯 就是把重子分数
Well, that’s just the fraction of baryons
乘上整体密度 这会得出储存在重子中的能量密度
times the overall density. This gives us the energy density stored in baryons.
我们要知道总能量 以及重子的总质量
We want to know the total energy, so the total mass stored in the baryons,
我们要乘上宇宙的体积
we need to multiply by the volume of the universe.
我们知道宇宙多大 对不?
But we know how big the universe is, right?
可由这个半径得到 宇宙体积就是这个半径的球的体积
It’s given by this radius. So the volume is just the size of the sphere
也就是三分之四π乘以半径的立方
of that radius, which is four, pi by three, and then that radius cubed.
由此可得重子中的总能量
That gives us the total energy stored in baryons.
如我所言这些重子基本是质子和中子 本质上质量相同
All right, these baryons, like we said, they’re basically protons and neutrons, which have the same mass, essentially.
想知道有多少重子
So if you want to know how many baryons there are,
我们只要将它除以一个重子的质量 对吧?
we just divide by the mass of one baryon, okay?
所以我们除以一个光子的质量
So we divide by the mass of a proton.
这将得出重子的数量
And this gives us the number of baryons.
这并不是我们想要的 我们想要的是粒子的数量
That’s not what we want, no. So we want to know the number of particles.
因此我们要知道那些粒子是怎样分布的
So we’ve gotta think about how those particles are distributed.
嗯 我们所知道的一件事是
Now, one thing we know is that the universe is, on average,
宇宙平均来说是电中性的
electrically neutral, okay?
正电荷与负电荷的数量是一致的
So the number of posi- positive charges balances the number of negative charges.
对我们来说 这就意味着质子与电子的数量是一致的
For our purposes, that means the number of protons is gonna balance the number of electrons.
我们需要的另一信息是
The other bit of information we can use is,
嗯 这些重子在哪呢?
we know, where are these baryons stored?
嗯 我们知道75%的重子存在于氢原子中
Well, we know that 75% of them are stored in hydrogen atoms,
25%存在于氦原子 还有其他原子 但是是可忽略的
and 25% in helium atoms. There’s other atoms as well, but it’s insignificant.
“对我们来说 可不能忽略”
Brady: “Not to us.”
是 你说的对 但往大了说可以忽略
Yeah, not to us, but in the broader scheme of things, it’s insignificant.
绝大多数是这样 75%在氢原子 25%在氦原子
By far the vast majority, so 75% in hydrogen, 25% in helium,
它们全都存在于那里
that’s where all this is stored.
我们通过观测遥远的气体云得知
And we know that from, from looking at, you know, distant gas clouds.
我们同样通过宇宙学的大胜利 也就是核合成得知
We also know it from one of the great triumphs of cosmology, which is nucleosynthesis.
有了这个信息 可以推想取四个原子的样本
So, given that information, let’s suppose we took a sample of four atoms,
那些原子中将三个是氢 一个是氦 对不?
and we know that three of those atoms are gonna be hydrogen, and one of them is gonna be helium, right?
嗯 氢原子含有一个质子和一个电子
Well, the hydrogen atom contains one proton and one electron.
所以这三个氢原子含有三个质子和三个电子
So these three contain three protons and three electrons.
氦原子含有两个质子 两个中子 两个电子
The helium atom contains two protons, two neutrons, two electrons.
嗯 现在我们将它们分开 因为每个质子含有三个夸克
So, now, well, we can split this up, because each of these protons contains three quarks.
每个中子含有三个夸克 这些原子中
Each neutron contains three quarks. So altogether, how many particles
总计有多少个粒子?26个
do we get from these four atoms? Twenty-six particles.
得到这26个粒子我们需要多少个重子?
How many baryons did we need to get those twenty-six particles?
嗯 我们要三个质子
Well, we’ve got three protons,
另两个质子 还有两个中子 七个重子 对不?
another two protons, and two neutrons, that’s seven baryons, okay?
因此从7个重子中可得到26个粒子
So we get twenty-seven particles from seven baryons.
因此我们知道总计有多少个重子
So we know how many baryons there are in total.
我们知道每7个重子可得26个粒子
We know for every seven baryons we get twenty-six particles,
如果我们想要知道粒子的总数
so if we want the total number of particles,
我们只要将这个数乘上七分之二十六
we just need to multiply this number by twenty-six over seven.
代入所有数字 嘛哩嘛哩哄
So we just plug in all the numbers, yadda yadda yadda,
见证奇迹 你得到了什么?
magic, and what do you get?
你会得到3.28乘以10的80次方这个神奇的数字
You get 3.28 times, and then the magic figure, ten to the eighty.
因此这就是宇宙中粒子的数量
So that’s how many particles there are in the universe.
似乎很多 对不?
Seems like a lot, right?
10^80 1后有八十个0 是个大数
Ten to the eighty, that’s like a one with eighty zeroes after, that’s a big number, right?
但实际上宇宙是个大地方 大约每立方米只有一个粒子
But actually, the universe is a big place, that’s about one particle every cubic meter.
几乎空无一物 但当然宇宙大部分是空的
Hardly anything, right? But of course, you know, most of space is
空荡荡的宇宙
space, it’s empty space.
不是每立方米一个原子 是一个粒子
Brady: “That’s not even one atom per cubic meter, that’s one particle.”
每立方米一个粒子 对 准确的说
One particle per cubic meter, yeah, exactly.
另一件很酷的事是你可以问
So the other, the other cool thing to think about is you could ask,
一个典型的人类身上有多少个粒子
how many particles are there in a typical human body?
嗯 人类身体大约三分之二是氢 四分之一是氧
Well, we know the human body is about two thirds hydrogen, about a quarter oxygen.
通过我们的所有信息 你可以算出粒子的数量
So from all our information, you can work out, the number of particles
一个人类的身体中大约有1.46×10^29个粒子
in a human body, about 1.46 times ten to the twenty-nine.
好 似乎很多
Okay, so that seems like a lot of particles,
但当然这不像整个宇宙的粒子那么多
but of course, it’s not as many as there are in the entire universe, right?
要构建多少个人类
So how many humans would you need to
才能用光宇宙中所有的粒子呢?
use up all the particles in the entire universe?
嗯 当然你只要将这两个数比一下
Well, of course, you just take the ratio of these, these two, right?
所以你需要2.25×10^51个人类
So you’d need 2.25 times ten to the fifty-one humans
才能用光所有粒子
to use up all the particles in the universe.
当今有75亿个人类 对不?
So, there’s about 7.5 billion humans alive today, right?
目前的人口增长率大约是每年增长1.11%
The population growth rate at the moment is about 1.11 percent per year.
我觉得算出我们需要多久才能用光所有粒子
So I thought it would be fun to work out how long it would take for us to, uh,
一定很有趣 对不?
given that rate of growth, for us to sort of use up all the particles in the universe, right?
我们算一下
So we can work this out.
如果我们将当用光所有粒子的人口数
If we take the population when it’s using up all the particles,
除以这个数 这是对应这个数字的人口
dividing this number, so this is the population corresponds to this number,
除以现在的人口
divided by the population now,
大约75亿
which is about 7.5 billion,
现人口是7.5×10^9
P now is 7.5 times ten to the nine.
然后这与增长率R
Then that’s related, by an exponential,
通过指数关联
to the rate of growth R, which is
R是每年增长1.11%
1.11 percent per year.
我们代入所有数字 重排这个方程
I can plug in all these numbers, I can rearrange this equation.
得到T=1/R × ln(Pall/Pnow)
I get T is one over R log P all over P now.
我们将所有数字代入 然后就会得到
So I just plug in the numbers, and it turns out that we will have used up,
人口以相同的比率持续增长
carry on, the population keeps growing at the same rate,
直到用光所有宇宙中粒子
we will have used up all the particles in the universe,
用于构建人类
in humans,
只要8604年
in 8604 years.
不怎么多
Which is not that much.
我还以为会是……
Brady: “I thought it was gonna be…”
我懂这难以置信 这是指数
I know, it’s amazing. This is exponential.
忘了化石燃料的事吧 我们要用光粒子了
Forget using up the fossil fuels, we’re gonna use all the particles.
是的 我的意思是 就忘了吧
Yeah, exactly. I mean, just forget, just forget what,
还是谈谈人口增长对地球 对宇宙的影响吧
what, talk about impact on the planet, impact on the universe, right?
不到一万年 我们将用光所有粒子
Population growth, this is. Within less than ten thousand years, we’ll have
我们以相同的比率保持增长
used up, and we keep growing at the same rate, we’ll have
将用尽所有的粒子来构建人类的身体
used up all the particles of the universe, in the form of humans.
在此之前有些事情必须要做
Surely somethings gotta give before that happens, right?
嗯 在这个宇宙中我们也许只剩下8604年
Well, there might be only 8604 years left for us here in the universe,
幸运的是对学习新技能来说时间很多
but luckily that’s plenty of time to learn a new skill.
有技能共享的地方是学习新技能的好地方
And a great place to learn new skills is with skill share.
他们赞助了这个视频 他们有一万六千个在线视频课程
They’re the sponsor of this video, and they’ve got something like 16,000 online video lessons,
来教你所有的事 从制作视频 到烹饪 设计
to teach you all sorts of stuff, from making videos, to cooking, design.
以及我很热衷于学的更多的一些东西
And something that I’m quite keen to learn a bit more about,
也就是操控遥控飞机来摄影
and that’s filming with, and flying drones.
那里他们有全部系列的课程
They’ve got a whole series of lessons on that.
这是我开始更深入思考的东西
And it’s something I’ve started looking at in a lot more depth.
当我用遥控飞机拍摄这个数学狂视频我得到了好灵感
I got pretty inspired when we made this numberphile video using a drone.
所以最终我剁手为自己买了一个会员
So finally I’m splashing out and getting one for myself.
不管怎样 十美刀一个月你可以在技能共享上成为会员
Anyway, from around ten dollars a month, you can get premium membership on skill share,
你可以观看所有视频 包括离线功能
you get access to all the videos, including offline.
如果你是个数学狂的观众 你用这个URL
And if you’re a numberphile viewer, and you use this URL here,
skl.sh/numberphile
skl.sh/numberphile
可在数学狂上免费得到两个月会员
you can get two free months on there.
都看看 看有什么想法
Check it all out. See what you think.
很早的时候 我印象深刻的一件事是
One of things that’s impressed me very early on was how well-made
这些课程制作得如此精良
the lessons themselves are.
它们真的是专业且时髦
They’re really kind of professional and modern.
这使它们看起来很有趣 因此更容易学会他们所教你的
It makes them a lot more enjoyable to watch, and therefore a lot easier to learn what they’re teaching you.
不管怎样相信我 再说一遍URL
Anyway, don’t take my word for it. There’s that website again,
skl.sh/numberphile
skl.sh/numberphile
这样他们知道你从这儿去的
That’s so they know you came from here.
感谢他们支持此视频
And our thanks to them for supporting this video.

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吾日三省吾身:宇宙中有多少粒子?宇宙中有多少粒子?宇宙中有多少粒子?

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