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#### 宇宙中有多少粒子？

How many particles in the Universe? - Numberphile

So, Brady, we’re gonna talk about how many particles there are in the universe.

We gonna calculate the number of particles in the observable universe.

So that’s, you know, the section of the universe that we can see,

where light could have reached us from.

What are the particles that we’re talking about here?

So we’re gonna be interested in particles that’s, that are particles that we know exist,

that are fundamental, and we’re interested in the ones that have mass.

So, we’re not really talking about photons, for example.

What we’re gonna be talking about are things like quarks, electrons, those sorts of things.

So the quarks, of course, are gonna live inside protons, neutrons,

and the electrons are gonna be in orbit around those, those protons and neutrons in atoms.

Pretty much everything else is insignificant.

So, how do we do this? So we’re gonna use four bits of data.

Part of it’s gonna be cosmological data.

Data from the Planck satellite, which measures the cosmic microwave background radiation.

People call it the radiation that’s left over from the big bang.

It’s the radiation that you get, after, you know, when the first sort of neutral atoms began to form.

So, we’re gonna need, we’re gonna use data from that.

And a little bit of particle physics data, as well.

So these are the four bits of information we’re gonna use.

So the first of these is the critical density of the universe.

So this is a good measure for what is the energy density of the universe, full stop.

This is because we, we know that the universe is very close to being spatially flat.

So, it’s, it’s not shaped like a sphere or a saddle,

it’s somewhere in between the two.

And because of that, we know its density

is very close to the critical density, which is a really really really light density, actually.

If you look at it, if you compare this to the density of water,

the density of water is one gram per centimeter cubed.

And this is a million million million million million times less than that, right?

So it’s super undense, right? Because this is the universe we’re talking about.

The next bit of information that we’re gonna need

is the fraction of that energy budget in the universe

that’s stored in baryons. Now, why baryons?

Well, baryons, really, in this context, they’re just

the protons and the neutrons, which is where the quarks live.

The other thing the size of the observable universe. Again, coming from Planck data,

we get this figure of about ten to the twenty-eight centimeters.

A one with twenty-eight zeroes after it.

So, lots of centimeters, but the universe is big, right?

Brady: “Why is it in centimeters?”

Well, I put it in centimeters, because this one was in centimeters, and I don’t want to start getting,

getting all my units messed up. So I thought it safest to, to just be, keep one set of units in there.

And the last thing is, that I’m gonna need is the mass of the proton.

The baryons that we’re interested in are protons and neutrons,

they have got about the same mass, very close, you know, the mass is pretty much identical.

And so the mass of the proton is ten to the minus twenty-four grams, roughly.

These are the four things that we’re gonna need to work out, you know,

how many particles there are in the universe.

So, to start off with, we’re gonna work out how many baryons there are in the universe,

i.e., how many protons and neutrons, in total, there are.

First thing we’re gonna do to calculate that is, we’re gonna say,

what is the energy density stored in baryons?

Or stored in protons and neutrons?

Well, that’s just the fraction of baryons

times the overall density. This gives us the energy density stored in baryons.

We want to know the total energy, so the total mass stored in the baryons,

we need to multiply by the volume of the universe.

But we know how big the universe is, right?

It’s given by this radius. So the volume is just the size of the sphere

of that radius, which is four, pi by three, and then that radius cubed.

That gives us the total energy stored in baryons.

All right, these baryons, like we said, they’re basically protons and neutrons, which have the same mass, essentially.

So if you want to know how many baryons there are,

we just divide by the mass of one baryon, okay?

So we divide by the mass of a proton.

And this gives us the number of baryons.

That’s not what we want, no. So we want to know the number of particles.

So we’ve gotta think about how those particles are distributed.

Now, one thing we know is that the universe is, on average,

electrically neutral, okay?

So the number of posi- positive charges balances the number of negative charges.

For our purposes, that means the number of protons is gonna balance the number of electrons.

The other bit of information we can use is,

we know, where are these baryons stored?

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”

Yeah, not to us, but in the broader scheme of things, it’s insignificant.

By far the vast majority, so 75% in hydrogen, 25% in helium,

that’s where all this is stored.

And we know that from, from looking at, you know, distant gas clouds.

We also know it from one of the great triumphs of cosmology, which is nucleosynthesis.

So, given that information, let’s suppose we took a sample of four atoms,

and we know that three of those atoms are gonna be hydrogen, and one of them is gonna be helium, right?

Well, the hydrogen atom contains one proton and one electron.

So these three contain three protons and three electrons.

The helium atom contains two protons, two neutrons, two electrons.

So, now, well, we can split this up, because each of these protons contains three quarks.

Each neutron contains three quarks. So altogether, how many particles

do we get from these four atoms? Twenty-six particles.

How many baryons did we need to get those twenty-six particles?

Well, we’ve got three protons,

another two protons, and two neutrons, that’s seven baryons, okay?

So we get twenty-seven particles from seven baryons.

So we know how many baryons there are in total.

We know for every seven baryons we get twenty-six particles,

so if we want the total number of particles,

we just need to multiply this number by twenty-six over seven.

magic, and what do you get?

You get 3.28 times, and then the magic figure, ten to the eighty.

So that’s how many particles there are in the universe.

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?

But actually, the universe is a big place, that’s about one particle every cubic meter.

Hardly anything, right? But of course, you know, most of space is

space, it’s empty space.

Brady: “That’s not even one atom per cubic meter, that’s one particle.”

One particle per cubic meter, yeah, exactly.

So the other, the other cool thing to think about is you could ask,

how many particles are there in a typical human body?

Well, we know the human body is about two thirds hydrogen, about a quarter oxygen.

So from all our information, you can work out, the number of particles

in a human body, about 1.46 times ten to the twenty-nine.

Okay, so that seems like a lot of particles,

but of course, it’s not as many as there are in the entire universe, right?

So how many humans would you need to

use up all the particles in the entire universe?

Well, of course, you just take the ratio of these, these two, right?

So you’d need 2.25 times ten to the fifty-one humans

to use up all the particles in the universe.

So, there’s about 7.5 billion humans alive today, right?

The population growth rate at the moment is about 1.11 percent per year.

So I thought it would be fun to work out how long it would take for us to, uh,

given that rate of growth, for us to sort of use up all the particles in the universe, right?

So we can work this out.

If we take the population when it’s using up all the particles,

dividing this number, so this is the population corresponds to this number,

divided by the population now,

P now is 7.5 times ten to the nine.

Then that’s related, by an exponential,

to the rate of growth R, which is
R是每年增长1.11％
1.11 percent per year.

I can plug in all these numbers, I can rearrange this equation.

I get T is one over R log P all over P now.

So I just plug in the numbers, and it turns out that we will have used up,

carry on, the population keeps growing at the same rate,

we will have used up all the particles in the universe,

in humans,

in 8604 years.

Which is not that much.

Brady: “I thought it was gonna be…”

I know, it’s amazing. This is exponential.

Forget using up the fossil fuels, we’re gonna use all the particles.

Yeah, exactly. I mean, just forget, just forget what,

what, talk about impact on the planet, impact on the universe, right?

Population growth, this is. Within less than ten thousand years, we’ll have

used up, and we keep growing at the same rate, we’ll have

used up all the particles of the universe, in the form of humans.

Surely somethings gotta give before that happens, right?

Well, there might be only 8604 years left for us here in the universe,

but luckily that’s plenty of time to learn a new skill.

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And it’s something I’ve started looking at in a lot more depth.

I got pretty inspired when we made this numberphile video using a drone.

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Check it all out. See what you think.

One of things that’s impressed me very early on was how well-made

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They’re really kind of professional and modern.

It makes them a lot more enjoyable to watch, and therefore a lot easier to learn what they’re teaching you.

Anyway, don’t take my word for it. There’s that website again,
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That’s so they know you came from here.

And our thanks to them for supporting this video.