How Many Elementary Particles Are There, Really?
Kristina Armitage/ Quanta Magazine
克里斯蒂娜·阿米蒂奇/广达杂志
E very time I write about particle physics, I encounter a moment of uncertainty about a quantity that, at first glance, ought to be clear.
每次我写关于粒子物理学的文章时，我都会遇到一个对某个乍一看应该很清楚的量的不确定时刻。
How many kinds of elementary particles should I say there are?
我应该说基本粒子有多少种？
In experiments at the Large Hadron Collider, physicists smash together beams of protons, breaking them up into all possible elementary bits and pieces.
在大型强子对撞机的实验中，物理学家将质子束粉碎在一起，将它们分解成所有可能的基本碎片。
Meanwhile, they have an incredibly accurate set of mathematical equations for describing these building blocks and all the ways they fit together.
同时，他们有一套极其精确的数学方程来描述这些构建块以及它们组合在一起的所有方式。
So, since the known particles of nature can be both empirically observed and theoretically described, you would think they could also be counted.
因此，由于已知的自然界粒子既可以通过经验观察也可以通过理论描述，因此您可能会认为它们也可以被计算。
But alas not.
但可惜没有。
I knew that, for reasons we’ll see, the census is not so easy as it seems.
我知道，出于我们将会看到的原因，人口普查并不像看起来那么容易。
We have a full tally of the elementary particles, but the deeper you go into that count, the more complicated — and weirder — the answer becomes.
我们对基本粒子有完整的统计，但你越深入地统计，答案就会变得越复杂，也越奇怪。
So I recently emailed a few physicists to ask how each of them personally tallies nature’s fundamental constituents.
因此，我最近给几位物理学家发了电子邮件，询问他们每个人如何亲自计算自然的基本成分。
The first indicator of just how complicated the issue is came in a reply from David Tong , the University of Cambridge physicist and textbook author, when we were scheduling a video call: “P.S.
当我们安排视频通话时，剑桥大学物理学家兼教科书作者 David Tong 的回复首次表明了这个问题的复杂性：
I think the true answer to your question is not an integer!”
我认为你问题的真正答案不是整数！”
We’ll get to that (it comes from a mysterious calculation from 2011 ), but let’s enter this rabbit hole from the top.
我们会谈到这一点（它来自 2011 年的一项神秘计算），但让我们从顶部进入这个兔子洞。
The known elementary particles and their interactions obey a set of equations called the Standard Model of particle physics .
已知的基本粒子及其相互作用遵循一组称为粒子物理标准模型的方程。
The Standard Model is a “quantum field theory,” a mathematical description of reality in which entities called quantum fields permeate the universe.
标准模型是一种“量子场论”，是对现实的数学描述，其中称为量子场的实体遍布宇宙。
Ripples moving through these fields are what we call elementary particles; some behave like matter, while others impart forces.
穿过这些场的涟漪就是我们所说的基本粒子。有些行为像物质，而另一些则赋予力量。
The quantum fields and associated particles in the Standard Model underlie all known physical phenomena other than gravity, dark matter, and dark energy (all of which take unknown forms at a fundamental level).
标准模型中的量子场和相关粒子是除重力、暗物质和暗能量（所有这些在基本层面上都采取未知形式）之外的所有已知物理现象的基础。
I n philosophy, “qualia” refers to the subjective qualities of our experience: what it’s like for Alice to see blue or for Bob to feel delighted.
在哲学中，“感受性”指的是我们体验的主观品质：爱丽丝看到蓝色或鲍勃感到高兴是什么感觉。
Qualia are “the ways things seem to us,” as the late philosopher Daniel Dennett put it.
正如已故哲学家丹尼尔·丹尼特所说，感受性是“事物在我们看来的方式”。
In these essays, our columnists follow their curiosity, and explore important but not necessarily answerable scientific questions.
在这些文章中，我们的专栏作家追随他们的好奇心，探索重要但不一定可以回答的科学问题。
In posters on classroom walls, the Standard Model displays 17 particles.
在教室墙上的海报中，标准模型显示了 17 个粒子。
There are 12 matter particles, or fermions: the electron, muon, and tau; three neutrinos; and six quarks.
有 12 种物质粒子或费米子：电子、μ 子和 τ；三个中微子；和六个夸克。
Each of them has a distinct set of sensitivities to various forces.
他们每个人对各种力量都有一套独特的敏感性。
There are also four force-carrying particles, or “bosons”: the photon (which imparts the electromagnetic force), the W and Z bosons (the weak force), and the gluon (the strong force).
还有四种携带力的粒子或“玻色子”：光子（赋予电磁力）、W 和 Z 玻色子（弱力）和胶子（强力）。
Finally, there’s the Higgs boson, a so-called scalar particle that’s neither matter nor force; rather, it imbues other particles with mass through its interactions with them.
最后，还有希格斯玻色子，一种所谓的标量粒子，既不是物质也不是力。相反，它通过与其他粒子的相互作用而赋予它们质量。
Samuel Velasco/ Quanta Magazine
塞缪尔·贝拉斯科/广达杂志
It may just be this simple.
事情可能就是这么简单。
“I think 17 is the right answer,” Melissa Franklin , a professor of particle physics at Harvard University, told me.
“我认为 17 是正确的答案，”哈佛大学粒子物理学教授梅丽莎富兰克林告诉我。
But every particle physicist, Franklin included, recognizes that there are caveats.
但包括富兰克林在内的每一位粒子物理学家都认识到存在一些警告。
From 17, you can keep counting.
从17开始，你可以继续数。
Where you stop depends on your taste for complexity and mystery.
您停在哪里取决于您对复杂性和神秘性的品味。
The question of how many particles there are brings us to the edge of what’s known about the most basic levels of stuff.
粒子数量的问题将我们带到了对物质最基本水平的了解的边缘。
There is one glaring problem with 17.
17 有一个明显的问题。
To satisfy special relativity, each of the Standard Model’s matter fields supports both a particle and an “antiparticle,” which is identical to the particle except for having the opposite electric charge.
为了满足狭义相对论，每个标准模型的物质场都支持粒子和“反粒子”，“反粒子”除了具有相反的电荷之外与粒子相同。
This is what we popularly know as antimatter.
这就是我们俗称的反物质。
So instead of 12 matter particles, there are really 24.
所以物质粒子不是 12 个，而是 24 个。
Likewise, W bosons come in oppositely charged types known as W+ and W−.
同样，W 玻色子也有带相反电荷的类型，称为 W+ 和 W−。
(This doesn’t happen to the Z bosons, photons, or gluons; they’re electrically neutral.)
（Z 玻色子、光子或胶子不会发生这种情况；它们是电中性的。）
Franklin excludes antiparticles from her census, she said, because mathematically they more or less mirror their particle versions.
她说，富兰克林将反粒子排除在她的普查之外，因为从数学上讲，它们或多或少反映了它们的粒子版本。
(Bizarrely, antiparticles are equivalent to particles moving backward in time, and vice versa.) Neither is possible without the other, so they shouldn’t be counted twice.
（奇怪的是，反粒子相当于在时间上向后移动的粒子，反之亦然。）两者缺一不可，因此不应将它们计算两次。
But I find that rationale unconvincing.
但我觉得这个理由缺乏说服力。
Particles and antiparticles are undeniably distinct, even if they are secret twins.
无可否认，粒子和反粒子是不同的，即使它们是秘密双胞胎。
They can’t transform into each other (with the possible exception of neutrinos, which may or may not be their own antiparticles), and far from being functionally equivalent, they play totally different roles in reality.
它们不能相互转化（中微子可能是例外，中微子可能是也可能不是它们自己的反粒子），而且它们在功能上远非等效，在现实中扮演着完全不同的角色。
Matter is so dominant in our universe that any antimatter typically encounters matter quickly and annihilates.
物质在我们的宇宙中占据主导地位，任何反物质通常都会很快遇到物质并湮灭。
The reason for the cosmos’s matter-antimatter asymmetry is a major physics mystery.
宇宙物质与反物质不对称的原因是一个重大的物理谜团。
Antiparticles bring the total up to 30.
反粒子使总数达到 30。
But the notion that there’s only one gluon is another oversimplification.
但只有一个胶子的想法又是一种过于简单化的说法。
Really, the strong force is conveyed by eight gluons (and their associated fields), each possessing a distinct blend of charges known as “colors” and “anticolors.” The different gluons are impossible to distinguish experimentally, so Franklin, being an experimentalist, scoffed and shook her head when I asked if all eight should be tallied individually.
实际上，强力是由八个胶子（及其相关场）传递的，每个胶子都具有独特的电荷混合，称为“颜色”和“反色”。不同的胶子是不可能通过实验来区分的，所以富兰克林，作为一名实验者，当我问是否应该单独计算所有八个胶子时，她嘲笑并摇了摇头。
Yet in the mathematical equations that define the Standard Model, the eight gluons are distinct from one another in the same way that the W and Z bosons differ.
然而，在定义标准模型的数学方程中，八个胶子彼此不同，就像 W 和 Z 玻色子之间的不同一样。
For consistency’s sake, we probably have to count all eight.
为了保持一致性，我们可能必须计算全部八个。
So now we’re at 37.
现在我们已经37岁了。
From 17, you can keep counting.
从17开始，你可以继续数。
Where you stop depends on your taste for complexity and mystery.
您停在哪里取决于您对复杂性和神秘性的品味。
Quarks come in colors, too — the three possibilities are dubbed red, green, and blue — and antiquarks have anticolors, called anti-red, anti-green, and anti-blue.
夸克也有颜色——这三种可能性被称为红色、绿色和蓝色——反夸克也有反颜色，称为反红色、反绿色和反蓝色。
(Don’t try too hard to picture anti-red; these aren’t our familiar optical colors, though they combine in a manner that’s analogous mathematically.) The colors reflect how gluons and quarks interact with each other.
（不要太努力地想象反红色；这些不是我们熟悉的光学颜色，尽管它们以类似于数学的方式组合。）这些颜色反映了胶子和夸克如何相互作用。
For matter to exist in stable isolation, it must be color-neutral.
为了使物质以稳定的隔离状态存在，它必须是中性的。
So, just as red light, green light, and blue light blend to make white, so do red, blue, and green quarks form color-neutral protons and neutrons (the building blocks of atoms).
因此，正如红光、绿光和蓝光混合形成白色一样，红夸克、蓝夸克和绿夸克也形成色中性质子和中子（原子的组成部分）。
So there aren’t six quarks and six antiquarks but rather 36 in total.
所以并不是有 6 个夸克和 6 个反夸克，而是总共 36 个。
And that makes 61 elementary particles.
这就产生了 61 个基本粒子。
But there’s more.
但还有更多。
Matter particles also come in left-handed and right-handed varieties, a quality known as chirality — arguably a crucial distinction.
物质粒子也有左旋和右旋之分，这种性质被称为手性——可以说是一个至关重要的区别。
“I insist on left- and right-handed particles,” Chris Quigg , a senior particle theorist at the Fermi National Accelerator Laboratory, told me.
“我坚持左手和右手粒子，”费米国家加速器实验室的高级粒子理论家克里斯·奎格告诉我。
“I can’t account for this.
“我无法解释这一点。
Blame my parents.” (Far more idiosyncratically, Quigg leaves the force-carrying particles off his list, as he considers them to be transformations of matter particles rather than particles themselves.)
都怪我父母。” （更奇特的是，奎格将携带力的粒子从他的列表中剔除，因为他认为它们是物质粒子的转变而不是粒子本身。）
Chirality is a quantum version of the handedness that chemists see in molecules or that we see at the ends of our arms.
手性是化学家在分子中看到的或我们在手臂末端看到的手性的量子版本。
It is not a geometric arrangement like those, but mathematically the two states are mirror images of one another; you can’t rotate one to turn it into the other, any more than you can with left and right hands.
它不是像那些那样的几何排列，但从数学上来说，这两种状态是彼此的镜像；你无法旋转一个将其变成另一个，就像你无法用左手和右手一样。
The force-carrying particles have an analogous distinction, known as a polarization state.
承载力的粒子具有类似的区别，称为极化态。
Photons and gluons can be either left- or right-polarized, while the W+, W−, and Z bosons have a third, “longitudinal” polarization state as well.
光子和胶子可以是左偏振或右偏振，而 W+、W− 和 Z 玻色子也有第三种“纵向”偏振态。
(That extra state has a complicated origin connected to the Higgs field and events during the Big Bang.)
（这个额外的状态有一个复杂的起源，与希格斯场和大爆炸期间的事件有关。）
Not everyone counts these different chiral and polarization states as distinct particle types.
并不是每个人都将这些不同的手性和偏振态视为不同的粒子类型。
Yet it’s logical to do so, because they affect how particles behave and interact.
然而这样做是合乎逻辑的，因为它们影响粒子的行为和相互作用。
The weak force, for example, affects only left-handed matter particles.
例如，弱力仅影响左手物质粒子。
For related reasons, neutrinos appear only in a left-handed form in the Standard Model.
由于相关原因，中微子在标准模型中仅以左手形式出现。
These are physically distinct states with different roles in nature.
这些是物理上不同的状态，在自然界中具有不同的作用。
Counting each chirality and polarization state separately gets us to 118 particles — from a right-handed, anti-red, anti-charm quark to a green–anti-blue, left-polarized gluon, to a longitudinal W− boson.
分别计算每个手性和偏振态，我们得到 118 个粒子——从右旋、反红、反粲夸克到绿-反蓝、左偏振胶子，再到纵向 W− 玻色子。
“Now,” Tong said, “comes the weird stuff.”
“现在，”童说，“奇怪的事情来了。”
Physicists call all the ways that particles can vary “degrees of freedom” — with a different degree of freedom for each state a particle can hold.
物理学家将粒子变化的所有方式称为“自由度”——粒子可以保持的每种状态都有不同的自由度。
Color, for example, comprises three degrees of freedom: red, green, and blue.
例如，颜色包括三个自由度：红色、绿色和蓝色。
But those differences go beyond the states we have already described.
但这些差异超出了我们已经描述的状态。
We might consider the tally of all these degrees of freedom as a more precise, mathematical version of the question of how many elementary particles there can be.
我们可以将所有这些自由度的统计视为基本粒子数量问题的更精确的数学版本。
Physicists have long noticed a pattern in the degrees of freedom: The number of them depends on the scale at which you count them.
物理学家很早就注意到自由度的一种模式：自由度的数量取决于你计算它们的尺度。
On the scale of our everyday reality, objects are describable with fewer variables than it takes to specify the states of all the microscopic constituents.
在我们日常现实的规模上，描述物体所用的变量比指定所有微观成分的状态所需的变量要少。
When you zoom in on, say, a proton, and reveal its constituent quarks with their colors and various other properties, you’ll observe more ways of moving or varying — more degrees of freedom.
当你放大一个质子，并揭示它的组成夸克及其颜色和各种其他属性时，你会观察到更多的移动或变化方式——更多的自由度。
This is one of the main reasons it’s so difficult to pin down the particle population.
这是很难确定粒子数量的主要原因之一。
The closer you get, the more their categories splinter.
你越接近，他们的类别就越分裂。
Furthermore, the beginning of the Big Bang might have abounded with additional, high-energy particles that can’t form in our current, low-energy universe and aren’t part of the Standard Model.
此外，大爆炸的开始可能富含额外的高能粒子，这些粒子无法在我们当前的低能宇宙中形成，也不属于标准模型的一部分。
For instance, many extensions of the model to the high-energy early universe posit the existence of heavy right-handed neutrinos, but these would never arise now.
例如，该模型对高能早期宇宙的许多扩展都假设重右手中微子的存在，但这些现在永远不会出现。
“As you go down in energy scale,” Tong said, “you’re losing particles as you go, because they’re so heavy,” and therefore only possible at much higher energies.
童说：“当你的能量尺度下降时，你就会失去粒子，因为它们太重了”，因此只有在更高的能量下才有可能。
“As you go down in energy scale you lose knowledge of those particles.” If we continue to follow this idea, at very low energies only one particle is left: the photon.
“当你的能量等级下降时，你就会失去对这些粒子的了解。”如果我们继续遵循这个想法，在非常低的能量下只剩下一个粒子：光子。
Because they’re massless, photons can approach zero energy.
因为光子没有质量，所以能量可以接近零。
It’s natural to wonder if a full accounting is possible.
人们很自然地想知道是否可以进行全面的核算。
How many fundamental degrees of freedom are there, including all of those at the very highest energies and most microscopic distances that we can’t possibly detect?
存在多少个基本自由度，包括所有我们无法检测到的最高能量和最微观距离的自由度？
This brings us to the fascinating 2011 calculation Tong told me about, by Adam Schwimmer and Zohar Komargodski .
这给我们带来了 Adam Schwimmer 和 Zohar Komargodski 向我讲述的 2011 年令人着迷的计算。
Komargodski, a theoretical physicist at Stony Brook University, walked me through it.
石溪大学的理论物理学家 Komargodski 向我介绍了这一切。
I just mentioned the trend in which, as we zoom out in the universe, we’re able to detect fewer effective degrees of freedom.
我刚刚提到了这样的趋势：当我们缩小宇宙时，我们能够检测到的有效自由度越来越少。
In 1989, the physicist John Cardy conjectured that this is an inviolable rule that any quantum field theory must follow.
1989年，物理学家约翰·卡迪猜想，这是任何量子场论都必须遵循的不可侵犯的规则。
The rule had already been mathematically proved true of quantum field theories with one space and one time dimension, which describe particles moving along lines.
这一规则已经在数学上被证明对于具有一个空间和一个时间维度的量子场论是正确的，量子场论描述了沿直线运动的粒子。
But what about theories like the Standard Model, which involves three spatial dimensions plus time (called 3 + 1D)?
但是像标准模型这样涉及三个空间维度加上时间（称为 3 + 1D）的理论呢？
Schwimmer, an emeritus professor of physics at the Weizmann Institute of Science, and Komargodski proved Cardy’s conjecture.
魏茨曼科学研究所物理学名誉教授施维默和科马尔戈斯基证明了卡迪的猜想。
Their “ a theorem,” acclaimed among quantum field theorists, says that in 3 + 1D quantum field theories, the number of effective degrees of freedom must always decrease as you zoom out.
他们的“定理”在量子场论学家中广受好评，该定理指出，在 3 + 1D 量子场论中，有效自由度的数量必须始终随着缩小而减少。
They showed that this is universally true by exploring how quantum fields must respond to gravity tugging on them in four different places.
他们通过探索量子场如何响应四个不同地方的引力，证明了这是普遍正确的。
Their proof also yielded a strange conclusion about how many fundamental degrees of freedom there must be in 3 + 1D quantum field theories such as the Standard Model.
他们的证明还得出了一个奇怪的结论，即标准模型等 3 + 1D 量子场论中必须有多少个基本自由度。
Quantum fields, the proof showed, cannot have just any number of variations.
证据表明，量子场不可能有任意数量的变化。
To the contrary, only specific values are allowed: Scalar fields such as the Higgs field have just one degree of freedom.
相反，只允许特定值：诸如希格斯场之类的标量场只有一个自由度。
Matter fields must each have 5.5 degrees of freedom.
每个物质场必须有 5.5 个自由度。
And force fields each have 62 degrees of freedom.
每个力场都有 62 个自由度。
These figures emerge mathematically, without regard to the specific particle states we’ve been discussing to this point.
这些数字是在数学上出现的，而不考虑我们到目前为止所讨论的具体粒子状态。
“And nothing else works,” Komargodski said.
“其他方法都不起作用，”科马尔戈斯基说。
K omargodski’s tally started with the quantum fields as they existed before a reshuffling of degrees of freedom in the early moments of the universe, when the Higgs field became energized and imbued particles with mass.
科马戈斯基的统计从量子场开始，因为它们在宇宙早期自由度重新洗牌之前就已经存在，当时希格斯场变得充满能量，并为粒子注入了质量。
Initially, there were four scalar fields (one of which became the present-day Higgs field), 45 fermions (left-handed electrons, muons, tau particles, and their neutrino counterparts; right-handed electrons, muons, and tau particles; and left- and right-handed blue, green, and red quarks of all six types), and 12 force-carrying bosons: eight gluons plus four primordial bosons that subsequently became the W+, W−, Z, and photon.
最初，有 4 个标量场（其中一个成为现在的希格斯场）、45 个费米子（左手电子、μ 子、tau 粒子及其中微子对应物；右手电子、μ 子和 tau 粒子；以及所有六种类型的左手和右手蓝夸克、绿夸克和红夸克）和 12 个载力玻色子：8 个胶子加 4 个胶子原初玻色子随后成为 W+、W−、Z 和光子。
Antimatter isn’t counted separately but rather is included in each fermion field’s 5.5 degrees of freedom.
反物质不单独计算，而是包含在每个费米子场的 5.5 个自由度中。
Thus: (4 × 1) + (45 × 5.5) + (12 × 62) = 995.5 degrees of freedom in the Standard Model.
因此：标准模型中的 (4 × 1) + (45 × 5.5) + (12 × 62) = 995.5 个自由度。
“One, 5½, 62 — they pop out of the theorem,” he added.
“一、5.5、62——它们是从定理中跳出来的，”他补充道。
“I have no idea why this is what nature chose.”
“我不知道为什么大自然会做出这样的选择。”
Tong explained that fractional degrees of freedom (like that extra half degree possessed by matter fields) are variations that aren’t fully independent from those of other fields.
Tong解释说，分数自由度（就像物质场所拥有的额外半度）是不完全独立于其他场的变化。
What’s possible with one particle might depend on the state of another.
一个粒子的可能性可能取决于另一个粒子的状态。
“You kick that way, and suddenly all hell breaks loose, and the field is oscillating all over the place,” he said.
“你朝那个方向踢，突然间一切都乱了套，整个场域都在震荡，”他说。
So assuming the respective number of degrees of freedom for each scalar, matter, and force field in the Standard Model, how many does that make?
那么假设标准模型中每个标量、物质和力场各自的自由度数是多少？
Komargodski paused our conversation to ask ChatGPT, providing the relevant numbers, and then checked its work.
Komargodski 暂停了我们的谈话，询问 ChatGPT，提供了相关号码，然后检查了其工作。
The answer: 995.5.
答案：995.5。
That’s apparently how many degrees of freedom there are in the Standard Model.
这显然就是标准模型中的自由度。
I can’t help but feel flummoxed.
我不禁感到困惑。
And apparently that’s the general reaction.
显然这就是普遍的反应。
“Underlying all of this is the statement that quantum field theory is unbelievably hard and we’re not very good at it,” Tong said.
“这一切的背后是这样一个说法：量子场论非常困难，而我们并不擅长，”童说。
“There’s still a lot we don’t understand.”
“我们还有很多不明白的地方。”
Personally, I find myself to be a maximalist on the question of how many particles there are, even though (or because) it is a path to mystery.
就我个人而言，我发现自己在粒子数量问题上是一个极端主义者，尽管（或因为）这是一条通往神秘的道路。
But I also see the appeal of 17.
但我也看到了17的吸引力。
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