引言:寻找暗物质的地下之旅
我正在墨尔本市郊的一座金矿里。
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I am at a gold mine a couple hours outside of Melbourne,
因为在地下一公里深处,他们正在安装一个探测器来寻找暗物质(Dark Matter: 宇宙中不发光、不吸收光,也不反射光,只能通过引力效应被探测到的物质)。
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because, one kilometer underground, they're putting in a detector to look for dark matter.
我们走吧。
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Let's go.
(史诗般的音乐)
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(epic music)
下到地下一公里需要30分钟。
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It's gonna take 30 minutes to go down a kilometer underground.
暗物质被认为构成了宇宙中85%的物质。
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Dark matter is thought to make up 85% of all the matter in existence.
它可能形成一个比我们能看到的一切物质重五倍的“影子宇宙”。
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It could form a shadow universe five times more massive than everything we can see.
在过去的几十年里,超过50个实验试图直接探测暗物质,但除了一个之外,都没有发现任何东西。
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Over the past several decades, over 50 experiments have tried to make a direct detection of dark matter, but none of them has found anything, except one.
暗物质的周期性信号之谜
在意大利阿尔卑斯山下,有一个名为DAMA/LIBRA(Dark Matter / Large Sodium Iodide Bulk for RAre processes: 一个位于意大利格兰萨索国家实验室的暗物质探测实验)的暗物质探测器。
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Under a mountain in the Italian Alps, there is a dark matter detector called DAMA/LIBRA.
它已经收集了大约20年的数据,每年都看到同样的奇特结果。
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It's been collecting data for around 20 years and, every year, it sees the same peculiar results.
探测率在六月达到峰值,然后在十一月降至最低。
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The rate of detections increases to a peak in June and then decreases to a minimum in November.
一些科学家认为这可能是暗物质存在的第一个直接证据。
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Some scientists think this could be the first direct evidence of dark matter.
但为什么暗物质会产生一个周期性的年度信号呢?
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But why would dark matter create a periodic annual signal?
嗯,这就是我们的星系,或者至少是它在可见光下看起来的样子。
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Well, this is our galaxy, or at least what it looks like with visible light.
天文学家怀疑它被一个巨大的暗物质球体包围并渗透,这些看不见的粒子在各个随机方向上快速移动。
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Astronomers suspect it is surrounded and permeated by a huge sphere of dark matter, invisible particles that are zipping around all in random directions.
根据大多数理论,暗物质除了通过引力之外,不与任何东西(包括它自身)发生相互作用。
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According to most theories, dark matter doesn't interact with anything including itself, except through gravity.
我们认为暗物质的量应该是普通物质的五倍。
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We think there should be five times as much dark matter as there is ordinary matter.
现在,我们的太阳系正以每秒220公里的速度绕着星系运动。
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Now, our solar system is moving around the galaxy at 220 kilometers per second.
这意味着我们也在以这个速度穿过暗物质,但地球绕太阳公转的速度是每秒30公里。
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That means we're also moving through dark matter at this rate, except earth orbits the sun at 30 kilometers a second.
所以,一年中的一半时间,我们与太阳同向运动,穿过暗物质的速度更快。
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So, for half the year, we're moving with the sun, going faster through dark matter.
而另一半时间,我们则向相反方向运动,所以穿过暗物质的速度较慢。
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And, the other half the year, we're moving in the opposite direction, so going slower through dark matter.
其想法是,当我们穿过暗物质最快的时候,我们会遇到更多的暗物质,这发生在六月;而当我们移动最慢的时候,遇到的暗物质较少,这发生在十一月。
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And, the idea is we encounter more dark matter when we're moving through it fastest, which happens to be in June, and less of it when we're moving slowest, which happens in November.
实际的几何结构要复杂一些。
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The actual geometry is a little more complicated.
太阳系相对于银河系平面倾斜了60度,但这个想法仍然成立。
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The solar system is tilted at 60 degrees relative to the plane of the galaxy, but the idea still works.
因此,DAMA/LIBRA观测到的信号可能是由于这种穿过暗物质的运动,也可能根本不是由于暗物质。
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So, the signal observed at DAMA/LIBRA may be due to this motion through dark matter or it might not be due to dark matter at all.
它可能只是像温度、湿度、土壤中的水分、山上的雪,或者意大利游客数量这样平凡的事情。
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It could just be something mundane, like the temperature, humidity, moisture in the soil, the snow on the mountain, or the number of tourists in Italy.
所有这些事物都以一年为周期波动。
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All of these things fluctuate with a period of one year.
这就是为什么他们将在南半球,也就是墨尔本市郊这座金矿的底部,建造一个几乎相同的实验。
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And, that is why they're gonna build an almost identical experiment in the Southern hemisphere, down the bottom of this gold mine outside of Melbourne,
因为在那里,季节是相反的,但我们穿过暗物质的运动仍然相同。
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because, there, the seasons are reversed, but our motion through dark matter is still the same.
所以,如果我们看到相同的信号,那将是暗物质存在的非常强有力的证据。
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So, if we see the same signal, it's pretty strong evidence for the existence of dark matter.
DAMA/LIBRA面临的一个大问题是,还有其他非常相似的实验没有发现任何东西。
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One of the big problems that DAMA/LIBRA has is that there are other very similar experiments that don't see anything.
这导致了对DAMA/LIBRA信号是否真的是暗物质的巨大不确定性。
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And, this has led to a lot of uncertainty about is the DAMA/LIBRA signal really dark matter?
所以,是的,我们不知道,对吧?
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So, yeah, we don't know, right?
这是科学中最喜欢的事情……
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The favorite thing in science...
暗物质存在的早期证据
但我们最初为什么会认为暗物质存在呢?
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But, why do we think dark matter exists in the first place?
1933年,瑞士天文学家弗里茨·兹威基(Fritz Zwicky)研究了后发星系团(Coma Cluster: 一个包含数千个星系的巨大星系团)。
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In 1933, Swiss astronomer, Fritz Zwicky, was studying the coma cluster, a collection of more than a thousand galaxies.
这些星系通过引力相互束缚,所以它们都围绕着它们的共同质心运行。
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These galaxies are gravitationally bound together. So, they all orbit around their collective center of mass.
兹威基测量了这些星系的轨道速度,发现有些星系的速度比他预期的要快得多。
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Zwicky measured the orbital speeds of these galaxies and found that somewhere moving way faster than he expected,
这就像星系团中存在着比他能看到的更多的物质,将一切向内拉。
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it was as if there was a lot more matter in the cluster than he could see, pulling everything inwards.
于是,他提出了看不见的物质的存在,他称之为“dunkle materie”,这便是“暗物质”一词的起源。
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So, he proposed the existence of invisible matter, which he called dunkle materie, the origin of the term dark matter.
没有人真正认真对待这个想法,但40年后,暗物质再次出现。
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No one really took this idea seriously, but 40 years later, dark matter turned up again.
维拉·鲁宾(Vera Ruben)和肯特·福特(Kent Ford)观测了仙女座星系(Andromeda Galaxy: 离银河系最近的大型螺旋星系)中恒星的运动。
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Vera Ruben and Kent Ford observed the motion of stars in the Andromeda Galaxy.
他们预期离中心越远,恒星的轨道速度就会越慢,但他们发现的并非如此。
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And, they expected that the further out from the center you go, the slower the stars would be orbiting, but this is not what they found.
随着离中心距离的增加,旋转速度几乎保持不变。
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The rotational velocity stays almost constant with increasing distance from the center.
如果没有星系中额外的质量将这些恒星拉住,它们应该会被甩入太空。
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Without additional mass in the galaxy to pull those stars in, they should be flung off into space.
在其他星系中也得到了相同的结果。
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The result was the same in other galaxies.
阿尔伯特·博斯马(Albert Bosma)等人使用射电望远镜测量了离星系中心更远的氢气,但旋转速度仍然保持不变。
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Using radio telescopes, Albert Bosma and others measured hydrogen gas even further out from a galaxy center, but the rotational velocity still stayed constant.
解释这一点的一种方法是假设存在我们看不见的物质,即暗物质,它将所有这些星系维系在一起。
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One way to explain this is to posit the existence of matter we can't see, dark matter, which holds all these galaxies together.
所以,假设你有一颗恒星,这代表了星系中心所有物质的质量,它将恒星向内拉。
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So, let's say you have a star and this represents the mass of everything in the center of the galaxy that's pulling the star in.
如果恒星的向心力等于它受到星系其余所有质量的引力吸引,它就能保持稳定的轨道。
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The star can maintain a stable orbit if it's centripetal force is equal to the gravitational attraction to all the mass in the rest of the galaxy.
所以你可以看到,在大约一米的距离处,这就是轨道的速度。
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And, so you can see that at about a distance of one meter, this is the speed of the orbit.
好的,但是如果我们添加一些暗物质会发生什么呢?
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Okay, but what happens if we add some dark matter?
所以,这个水瓶代表我们看不见的物质,现在有更多的质量将这颗恒星拉向中心。
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So, this water bottle represents the matter we can't see, now there is more mass pulling this star into the middle,
这意味着在相同的轨道上,它现在可以运行得更快,事实上,它必须运行得更快才能保持那个轨道。
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which means, at the same orbit, it can now go much faster, and, in fact, it must go faster to maintain that orbit.
这解释了观测结果。
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And, this explains the observation.
这就是我们所看到的。
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This is what we see.
(金属撞击声)
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(metal clanking)
(德里克笑声)
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(Derek laughing)
通过观察恒星的旋转速度,科学家们估计一个星系大约85%的质量是暗物质。
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By looking at the rotation speeds of stars, scientists estimate that about 85% of the mass of a galaxy is dark matter.
引力理论的修正与暗物质粒子假说
但是,还有另一种解释这些观测结果的方法,而无需引入暗物质。
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But, there's another way to explain these observations without invoking dark matter.
那就是修改我们的引力理论。
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And, that is to modify our theory of gravity.
有什么证据支持粒子理论完全是误导,我们实际上应该寻找修正的引力理论呢?
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What's the supporting evidence for thinking that the particle idea is totally misguided and we should actually be looking at a revised theory of gravity?
我们可以要么引入我们看不见的东西,要么就说,嗯,宇宙就是我们能看到的东西,我们需要一种方法来解释外面发生的事情。
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We can either invoke something we can't see or you just say, well, the universe is what we can see, and we need a way to explain what's going on out there.
我们能做到这一点的唯一方法是修改物理定律。
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And, the only way we can do that is by modifying the laws of physics.
所以,当你观察星系的外围时,它们有很大的向心加速度。
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So, when you look at the outskirts of galaxies, they've got a lot of centripetal acceleration.
暗物质理论认为,这种向心加速度是由于暗物质的引力效应。
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Dark matter says that well, that centripetal acceleration is due to the gravitational effect of dark matter.
而喜欢MOND(Modified Newtonian Dynamics: 修正牛顿动力学,一种替代暗物质的引力理论)的人会说,不,那个向心加速度,那只是它已经达到了这个下限,不能再低了。
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Whereas, the people who like MOND will say, no, that's centripetal acceleration, that's just the fact that it's now reached this floor and can't get any lower.
所以他们说,没有额外的力是由于暗物质造成的,而是加速度有一个下限。
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So, they, they're saying that there's not additional force due to dark matter, but there's a limit to how low the acceleration could go.
我认为共识强烈倾向于它是一种物理物质,因为它似乎很合理,宇宙中可能存在我们尚未见过的其他粒子。
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I think the consensus is hugely in favor of it being a physical substance, in that it just seems reasonable that is that it could be other particles out there that we haven't seen yet.
更多确凿证据:子弹星系团与宇宙微波背景
还有更多证据。
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And, there's more evidence.
这是子弹星系团(Bullet Cluster: 两个星系团碰撞后的产物,提供了暗物质存在的强有力证据),一个两个星系团碰撞的地点。
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This is the bullet cluster, a site where two clusters of galaxies collided.
这些星系团的大部分普通质量都在星际气体中。
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Most of the ordinary mass of these clusters is in the interstellar gas.
当碰撞发生时,星际气体相互作用,升温并减速。
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And, when the collision occurred, the interstellar gas interacted, heated up, and slowed down.
所以你可能会认为子弹星系团的大部分质量会集中在所有这些气体所在的中间。
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So, you'd expect that most of the mass of the bullet cluster would be in the middle where all of this gas is.
但是,如果你使用引力透镜(Gravitational Lensing: 光线在经过大质量物体附近时发生弯曲的现象),也就是引力弯曲光线的方式,你实际上可以测量这张图片中大部分质量在哪里。
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But, if you use gravitational lensing, the way that gravity bends light, you can actually measure where most of the mass in this picture is.
它不在中间。
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And, it isn't in the middle.
它实际上在两侧。
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It's actually on either side.
所以,解释这一点的最好方法是,当星系团碰撞时,所有气体都卡在了中间,但暗物质直接穿了过去,在我们能看到最少普通物质的地方产生了最大的引力透镜效应。
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So, the best way to explain this is that when the clusters collided, all that gas got stuck in the middle, but the dark matter passed right through, creating the most gravitational lensing where we can see the least ordinary matter.
更多关于暗物质的证据来自宇宙中最古老的光。
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Even more evidence for dark matter comes from the oldest light in the universe.
大爆炸后38万年,光终于可以不受阻碍地穿梭于宇宙中。
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380,000 years after the big bang, light could finally travel through the universe unimpeded.
这就是我们所看到的宇宙微波背景(Cosmic Microwave Background, CMB: 大爆炸遗留下来的辐射,是宇宙中最古老的光)。
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And, this is what we see as the cosmic microwave background or CMB.
红点显示早期宇宙稍热的地方,蓝点显示稍冷的地方,但这些温差非常微小。
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The red spots show where the early universe was a little hotter and the blue spots show where it was a little cooler, but these temperature differences were tiny.
只有0.01%,但它们确实存在。
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Just 0.01%, but they are there.
你可以通过计算不同大小的斑点数量,将这张图片转换为图表。
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And, you can turn this picture into a graph by counting up how many blobs there are of different sizes.
所以,最常见的斑点大小导致了这个峰值,但也有其他常见大小的斑点。
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So, there's the most common size blob, which results in this peak, but there are also other common size blobs.
因此,你会得到这些大小递减的其他峰值。
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And, so you get these other peaks of decreasing size.
这些峰的高度取决于暗物质的多少。
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Now, the height of these peaks depends on how much dark matter there is.
在一个没有暗物质的宇宙中,图表看起来是这样的,但随着暗物质的增加,偶数峰的振幅会减小。
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In a universe without dark matter, the graph looks like this, but as dark matter increases, the amplitudes of even numbered peaks decreases.
为了匹配CMB的测量结果,我们需要大约五倍于普通物质的暗物质。
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To match the measurements of the CMB, we need about five times as much dark matter as ordinary matter.
这个数字也与解释星系中恒星运动和星系团中星系运动所需的暗物质量相符。
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This figure also agrees with the amount of dark matter required to explain the motion of stars in galaxies and the motion of galaxies in clusters.
所以,暗物质假说用一个简单的理论框架解释了许多不同的观测结果,即宇宙中存在某种只通过引力相互作用的粒子。
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So, the dark matter hypothesis explains a lot of different observations with a simple theoretical framework, that there's some type of particle out there that only interacts through gravity.
但这种粒子到底是什么呢?
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But, what is this particle exactly?
WIMPs探测实验:原理与挑战
嗯,既然我们不知道,科学家们已经提出了许多不同的可能性。
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Well, since we don't know, scientists have proposed a whole bunch of different things that it could be.
现在我们必须尝试去找到它们。
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And, now we have to try to go out and find them.
方法因你试图寻找什么而异。
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The approach differs depending on what you're trying to find.
DAMA/LIBRA和金矿底部的探测器正在寻找WIMPs(Weakly Interacting Massive Particles: 弱相互作用重粒子,一种假想的暗物质粒子)。
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Dama Libra and the detector at the bottom of the gold mine are looking for WIMPs, weakly interacting massive particles.
这些粒子预计与质子质量相当,但与普通物质的相互作用极其微弱。
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These particles are expected to weigh about as much as a proton, but interact with ordinary matter extremely weakly.
探测器的核心是七个七公斤重的纯碘化钠(Sodium Iodide)晶体。
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At the heart of the detector, our seven seven kilogram crystals of pure sodium iodide.
所以,那里面实际上是碘化钠。
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So, that's actually sodium iodide in there.
是的。
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Yeah.
我没想到它会这么清晰。
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I didn't expect it to be so clear.
这个想法是,非常非常罕见地,一个暗物质粒子可能会撞击晶体中的原子核并转移其能量。
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The idea is that very, very rarely a dark matter particle may hit a nucleus in the crystal and transfer its energy.
这会产生一道光,称为闪烁(Scintillation: 某些物质在受到高能粒子或辐射激发时发出的短暂光脉冲),由光电倍增管(Photomultiplier Tubes: 极其灵敏的光探测器)探测到,这些管子位于每个晶体的上方和下方。
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This creates a flash of light called a scintillation, which is detected by photomultiplier tubes, very sensitive light detectors, which are positioned above and below each crystal.
但有一个问题,即使是最纯净的碘化钠晶体也含有放射性钾。
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But, there's a problem, even the purest sodium iodide crystal contains radioactive potassium.
当一个钾原子衰变时,它会发射一个电子和一个伽马射线。
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And, when a potassium atom decays, it emits an electron and a gamma ray.
现在,电子可以在晶体中引起闪烁,就像假想的暗物质粒子一样。
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Now, the electron can cause a scintillation in the crystal just like the hypothesized dark matter particle.
为了消除这些事件,碘化钠晶体被浸没在一个装有12吨直链烷基苯(Linear Alkylbenzene: 一种液体闪烁体,用于探测辐射)的罐中。
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So, to eliminate these events, the sodium iodide crystals are submerged in a tank full of 12 tons of linear alkylbenzene.
这是一种液体闪烁体,当暴露在伽马射线中时会发光,然后这些光可以被罐中的光电倍增管探测到。
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This is a liquid scintillator that emits light when exposed to a gamma ray and that light can then be detected by photo multiplier tubes in the tank.
所以,如果晶体和罐中同时探测到信号,那很可能是一个钾衰变事件,而不是暗物质事件。
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So, if there's a simultaneous detection in the crystal and in the tank, it was most likely a potassium decay, not a dark matter event,
但还有另一个问题,宇宙射线。
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but there's another problem, cosmic rays.
来自太阳和其他星系的高能粒子撞击地球大气层顶部,产生μ子(Muons: 一种基本粒子,本质上是重电子),它们以接近光速的速度流向地球。
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Energetic particles from the sun and other galaxies hit the top of Earth's atmosphere creating muons, essentially heavy electrons, which stream toward the earth at close to the speed of light.
μ子也可以在晶体中产生闪烁。
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Muons can also create flashes of light in the crystal.
这是μ子探测器,它有三块塑料板,中间隔着一些钢片。
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This is Muon detector, and it's got these three paddles of plastic here separated by some pieces of steel.
如果我们几乎同时在这三块板中都看到一道光,那么我们就知道有μ子穿过了它们。
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If we see a flash of light in all three, basically the same time, then we know that Muon has passed through them.
所以,如果我按下重置,我们可以看到,μ子的数量正在增加。
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So, if I hit reset, we can see, counting up the muons being seen.
所以至少每秒有几个。
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So, it's at least a few a second.
这就是为什么所有灵敏的粒子探测器都位于地下深处。
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This is why all sensitive particle detectors are located deep underground
在这里,我们有μ子探测器,现在在地下一公里处,它已经运行了大约15分钟,没有μ子计数。
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Here, we have the muon detector, now one kilometer underground, and it's been running for something like 15 minutes, and there have been no muon counts.
是的,我们必须让它运行很长时间,我想,即使我们想得到一个单一的撞击。
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Yeah, we have to leave this running for a long time, I think, even if we wanted to get a single hit.
我们预计这里的μ子数量会减少大约一百万倍。
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We expect the number of muons down here to be about a million less.
我们在顶部没有看到一百万个,所以我们可能在这里看不到任何一个。
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And, we didn't see a million at the top, so we're probably not gonna see any down here.
这就是将暗物质探测器置于地下的全部意义。
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And, this is the whole point of putting a dark matter detector underground.
你想要去除所有会在探测器中产生噪音的背景辐射。
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You wanna get rid of all the background that would create noise in the detector.
但即使这种屏蔽也不够。
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But, even this shielding is not enough.
我们所有的μ子探测器都直接位于罐体上方。
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We all have muon detectors immediately above the tank.
所以,如果晶体中看到闪烁的同时探测到μ子,就可以将其排除。
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So, if a flash is seen in a crystal at the same time a muon is detected, it can be ruled out.
位于地下也带来了自身的挑战。
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Being underground brings its own challenges.
矿井的墙壁含有微量的放射性元素,如铀和钍,它们会衰变为氡气(Radon Gas: 一种放射性惰性气体)。
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The walls of the mine contain trace amounts of radioactive elements like uranium and thorium, which decay into radon gas.
这里对暗物质实验的要求相当严格。
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The requirements here are fairly serious for dark matter experiments.
我们必须完全控制环境,特别是氡气水平。
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We have to completely control the environment, in particular, the radon level.
为了抵消这一点,洞穴的墙壁涂有特殊涂料以 containment 放射性粒子。
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To counteract this, the walls of the cavern are coated with special paint to contain radioactive particles.
晶体浸没在连续的纯氮气流中。
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The crystals are immersed in a continuous stream of pure nitrogen gas.
整个探测器由120吨钢和塑料屏蔽。
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And, the entire detector is shielded by 120 tons of steel and plastic.
哇,看看那个洞穴的大小。
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Wow, look at the size of that cavern.
实验的未来与暗物质的本质
这个实验承载着巨大的希望。
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There is a lot riding on this experiment.
它将验证或推翻物理学中最具争议的结果之一。
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It will validate or disprove one of the most contentious results in physics.
所以,如果我们什么也没看到,那么,这就是DAMA/LIBRA的终结;但如果我们看到了什么,那么,我们都会很高兴。
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So, if we see nothing, well, this is the death of DAMA/LIBRA but if we see something, well, we are all happy.
我其实喜欢这个想法,因为宇宙80%的质量是暗物质或“暗物质”,也许暗物质不止由一种粒子组成。
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I actually like the idea that because 80% of the mass of the universe is dark matter or dark stuff, maybe there's more than just one particle that dark matter is made of.
它可能是一个完整的“暗标准模型”,如果你愿意的话。
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It could be an entire dark standard model if you like.
一个我们能看到的一切的“暗”版本,或者也许是更复杂的东西,因为它实在太多了。
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A dark version of everything that we can see or maybe something more complex, 'cause there's so much more of it.
我真的希望是那样。
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Like I really hope it's that.
你认为暗物质与普通物质相互作用吗?
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- Do you think that dark matter interacts with ordinary matter?
如果我们想知道这些东西是什么,我们最好希望在实验中至少能探测到某种程度的相互作用。
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- If we want to find out what this stuff is, we better hope there's some level of interaction that we can at least probe when it comes to doing experiments.
如果上帝给了我一本伟大的物理学书,里面有A和B两部分,一部分是关于发光物质的,一部分是关于暗物质的,而且它们互不交流,我会说那是一个非常奇特的宇宙。
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If God gave me the great book of physics and there were two sections, section A and section B, one for the luminous matter and one for dark matter, and they didn't talk to each other, I would say that was a very peculiar universe.
但在科学中,我们必须接受这种可能性,即在某种程度上,我们可能永远找不到答案。
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But, in science, we have to live with the possibility that, at some level, we may never find the answer.
它可能会一直困扰我们,但至少我们尝试了。
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It may elude us, but at least we tried.
赞助商信息
本视频的赞助商Brilliant与暗物质恰恰相反。
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The sponsor of this video, Brilliant, is the opposite of dark matter.
你随处可见它,而且它具有高度互动性。
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You see it everywhere and it's highly interactive.
Brilliant是一个创新的STEM学习平台,通过引人入胜的动手课程指导你学习数学、科学和计算机科学。
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Brilliant is an innovative stem learning platform that guides you through engaging, hands on courses in math, science, and computer science.
他们有许多精彩的课程,涵盖从初级代数到概率论,再到计算机科学基础等众多主题。
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They have great courses on so many topics from pre-algebra to probability, to computer science fundamentals.
它是观看教育性YouTube视频的理想补充。
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It's the ideal compliment to watching educational YouTube videos.
在学习完一个主题后,你可以深入探索并亲自动手实践,这样你就能真正理解它。
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After learning about a topic, you can dive deeper and get your hands dirty, so you really understand it.
例如,如果你想了解更多关于暗物质、引力透镜和宇宙微波背景的知识,我强烈推荐他们的天体物理学课程。
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For example, if you wanna learn more about dark matter, gravitational lensing, and the cosmic microwave background, I highly recommend their astrophysics course.
他们所有的课程都投入了大量的精力和关注。
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A lot of care and attention goes into all their courses.
每一课和互动模拟都建立在你之前学到的知识之上。
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Every lesson and interactive simulation builds on what you've learned previously.
每一步,你的知识都会通过测验进行测试,这些测验会检查你的理解并巩固你所学到的知识。
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And, every step of the way, your knowledge is tested through quizzes, which check your understanding and reinforce what you've learned.
如果你遇到困难,总会有有用的提示。
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If you get stuck, there's always a helpful hint.
所以,我鼓励你访问 brilliant.org/veritasium 查看他们提供的课程。
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So, I encourage you to check out the courses on offer over at brilliant.org/veritasium.
我敢打赌你会在那里找到你想了解更多内容的东西。
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And, I bet you'll find something there that you wanna learn more about.
此外,如果你现在点击,Brilliant将为前200名注册者提供年度高级订阅20%的折扣。
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Plus, if you click through right now, Brilliant are offering 20% off an annual premium subscription to the first 200 people to sign up.
所以,我要感谢Brilliant对Veritasium的支持,也要感谢你的观看。
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So, I want to thank Brilliant for supporting Veritasium and I want to thank you for watching.
📌 文中提及的人物和组织
公司/组织: Brilliant