Theory of Fluids Enters the 21st Century
I n the second half of the 20th century, a conceptual tsunami swept through physics.
20世纪下半叶，一场概念海啸席卷了物理学界。
The discovery that our world emerges from a microscopic world of molecules, which emerges from an even more microscopic world of subatomic particles (which in turn emerges from even stranger stuff) triggered the rewriting of our theories of matter.
我们的世界源于微观的分子世界，而分子的微观世界又源于更微观的亚原子粒子世界（而亚原子粒子又源于更奇怪的物质）这一发现引发了我们物质理论的重写。
But the revolution didn’t reach fluids.
但这场革命并未波及流体。
Their governing equations remained in their simple, vintage form: the Navier-Stokes equations, first developed in the 19th century.
他们的控制方程仍然保持着简单、老式的形式：纳维-斯托克斯方程，最早于 19 世纪提出。
The Navier-Stokes equations are enormously successful at predicting how fluids flow and swirl.
纳维-斯托克斯方程在预测流体如何流动和漩涡方面非常成功。
But they fail to account for the existence of swarms of microscopic bits that make up matter.
但他们未能解释构成物质的大量微观颗粒的存在。
A strange connection between black holes and quantum soups helped scientists to understand the elusive math behind fluid dynamics.
黑洞和量子汤之间的奇怪联系帮助科学家们理解了流体动力学背后难以捉摸的数学。
Now physicists have a theory that does.
现在物理学家有一个理论可以做到这一点。
It is the fruit of a 20-year effort to rebuild the theory of fluids from the ground up.
这是我们从头开始重建流体理论 20 年努力的成果。
Along the way, physicists have come up with a whole new way of defining what it means to be a fluid, based on fundamental properties known as symmetries, and have shown that the Navier-Stokes equations are a consequence of symmetries, which explains why the equations take the forms that they do.
在此过程中，物理学家基于称为对称性的基本属性，提出了一种全新的方法来定义流体的含义，并证明纳维-斯托克斯方程是对称性的结果，这解释了为什么方程采用它们的形式。
By understanding the origins of the Navier-Stokes equations, researchers have found a way to go beyond them, redefining what it means to be a fluid and predicting new behaviors that stem from the motions of microscopic particles.
通过了解纳维-斯托克斯方程的起源，研究人员找到了一种超越它们的方法，重新定义了流体的含义，并预测了源于微观粒子运动的新行为。
The trail to understanding fluids as the product of the microscopic world was blazed, ironically, by physicists thinking about some of reality’s biggest scales.
具有讽刺意味的是，物理学家对现实中一些最大尺度的思考开辟了将流体理解为微观世界产物的道路。
It would take insights from researchers studying black holes and the universe at large to finally bring fluids into the modern era.
最终将流体带入现代需要研究黑洞和整个宇宙的研究人员的见解。
For centuries, scientists have understood the basics of fluids.
几个世纪以来，科学家们已经了解了流体的基础知识。
In the 1750s, the mathematician Leonhard Euler adapted Newton’s second law of motion — the same one that gives us F = ma — to predict the motion of liquids.
1750 年代，数学家莱昂哈德·欧拉 (Leonhard Euler) 采用牛顿第二运动定律（该定律给出了 F = ma）来预测液体的运动。
Euler’s equations work perfectly for “perfect” fluids, in which a current can flow forever because the fluid has no viscosity — a sort of intrinsic stickiness — to slow it down.
欧拉方程非常适用于“完美”流体，其中电流可以永远流动，因为流体没有粘度（一种内在的粘性）来减慢速度。
In the early 1800s, Claude-Louis Navier and George Gabriel Stokes gave Euler’s equations an upgrade.
1800 年代初，克洛德-路易斯·纳维和乔治·加布里埃尔·斯托克斯对欧拉方程进行了升级。
The new Navier-Stokes equations could handle any fluid, perfect or not.
新的纳维-斯托克斯方程可以处理任何流体，无论完美与否。
They could handle the way one fluid dissipates in another, like an ink drop spreading out to fill a glass of water, and the way fluids (including air, which is technically a fluid) experience friction.
他们可以处理一种流体在另一种流体中消散的方式，就像墨滴扩散到充满一杯水的方式，以及流体（包括空气，从技术上讲是一种流体）经历摩擦的方式。
George Gabriel Stokes (left), an Irish mathematician and physicist, and Claude-Louis Navier, a French engineer, developed their theory of fluids in the 1800s.
爱尔兰数学家和物理学家乔治·加布里埃尔·斯托克斯（左）和法国工程师克劳德·路易斯·纳维尔在 1800 年代发展了流体理论。
Archivio storico dell’Accademia delle Scienze; Public Domain
科学学院历史档案；公共领域
Today physicists and engineers use Navier-Stokes to shape aircraft wings and yacht propellers; to forecast where a hurricane will make landfall; to model how climate change will increase the risk of drought; and to predict the behavior of flows of lava, clouds of ash, and even the interiors of stars.
如今，物理学家和工程师使用纳维-斯托克斯模型来塑造飞机机翼和游艇螺旋桨；预测飓风将在何处登陆；模拟气候变化将如何增加干旱风险；并预测熔岩流、火山灰云、甚至恒星内部的行为。
They also know that there’s more to fluids than Euler, Navier, and Stokes appreciated.
他们还知道流体的意义远超出欧拉、纳维和斯托克斯的想象。
The Navier-Stokes equations presume that fluids are continuous substances that flow perfectly smoothly, no matter how much you zoom in on a point.
纳维-斯托克斯方程假定流体是连续的物质，无论将一个点放大多少，它们都可以完美平滑地流动。
But in fact, fluids are amalgamations of molecules and atoms.
但事实上，流体是分子和原子的混合物。
As you zoom in, you’ll eventually discern tiny blips in the flow due to this grainy nature, blips that the classic fluid equations lop off.
当你放大时，你最终会发现由于这种颗粒状性质而导致的流动中的微小斑点，这些斑点是经典流体方程所消除的。
“Navier-Stokes is very much an approximation,” said Michael Landry , a physicist at the Massachusetts Institute of Technology.
“纳维-斯托克斯在很大程度上是一个近似值，”麻省理工学院的物理学家迈克尔·兰德里说。
“It’s not an exact equation.”
“这不是一个精确的方程。”
In this way, our theory of fluids is an outlier.
这样，我们的流体理论就显得异常了。
In the 1900s, as we uncovered the structure of the world at smaller and smaller scales, physicists revamped many of their theories of matter to take the existence of atoms and the like into account.
在 1900 年代，随着我们在越来越小的尺度上揭示世界的结构，物理学家修改了他们的许多物质理论，以考虑原子等的存在。
The new theories were also approximations, because tracking the motion of every last atom is impossible.
新理论也是近似值，因为追踪每一个原子的运动是不可能的。
But over the decades, physicists found a way to rewrite the theories and re-derive them in a more atom-friendly way.
但几十年来，物理学家找到了一种方法来重写这些理论，并以一种对原子更友好的方式重新推导它们。
In the 1970s, Kenneth Wilson, a physicist at Cornell University, gathered up all the pieces and put them into one mathematical package.
20 世纪 70 年代，康奈尔大学的物理学家肯尼思·威尔逊 (Kenneth Wilson) 将所有的碎片收集起来，并将它们放入一个数学包中。
Wilson showed, with rigorous calculations, why the smaller scales bleed through to our level in mercifully few ways.
威尔逊通过严格的计算证明了为什么较小的尺度会以很少的方式渗透到我们的水平。
He developed a whole new method for building high-level theories, called effective field theories, that would form the new foundation for much of physics.
他开发了一种构建高级理论的全新方法，称为有效场论，它将为大部分物理学奠定新的基础。
The work would win him a Nobel prize.
这项工作为他赢得了诺贝尔奖。
Since the 1960s, physicists had been puzzling over a common property of metals.
自 20 世纪 60 年代以来，物理学家一直对金属的一个共同特性感到困惑。
When a metal is cooled, its atoms eventually align, causing it to magnetize.
当金属冷却时，其原子最终排列，导致其磁化。
Mysteriously, this collective alignment always happens at precisely the same speed, whether the metal is iron, nickel, cobalt, or another material.
神秘的是，这种集体排列总是以完全相同的速度发生，无论金属是铁、镍、钴还是其他材料。
Wilson’s approach would eventually show why.
威尔逊的方法最终会说明原因。
The key was to look at a material’s symmetries.
关键是观察材料的对称性。
Kenneth Wilson, a physicist at Cornell University, won the Nobel Prize in Physics in 1982.
肯尼思·威尔逊（Kenneth Wilson）是康奈尔大学的物理学家，1982年获得诺贝尔物理学奖。
Keystone Pictures USA/ZUMAPRESS
美国梯形影业/ZUMAPRESS
You can think of a symmetry as a change that doesn’t matter.
您可以将对称性视为无关紧要的变化。
A square has some symmetry; you can rotate it by 90 degrees, and no one will notice.
正方形具有一定的对称性；你可以将它旋转 90 度，没有人会注意到。
A circle has more symmetry; you can rotate it by any angle you like without consequences.
圆形更具有对称性；您可以将其旋转任意角度，而不会产生任何后果。
Wilson used symmetries to calculate exactly how the math that describes any material will change as you zoom in and out.
威尔逊使用对称性来准确计算描述任何材料的数学随着放大和缩小将如何变化。
He laid out a two-step process.
他制定了一个两步流程。
The first step is to identify the symmetries of your system at the most microscopic level you understand.
第一步是在您理解的最微观层面上识别系统的对称性。
Take magnets, for example.
以磁铁为例。
Their atoms are laid out in some kind of grid, breaking the underlying continuous symmetry of space.
它们的原子排列在某种网格中，打破了空间的连续对称性。
(You have to move the magnet by one space on the lattice for it to look the same.) The atoms also have the freedom to point in any direction — another symmetry.
（你必须在晶格上将磁铁移动一个空间才能使其看起来相同。）原子还可以自由地指向任何方向——这是另一种对称性。
Symmetries like these determine exactly which mathematical terms belong in your theory.
像这样的对称性准确地确定了哪些数学术语属于你的理论。
The second step is to zoom out toward the macroscopic level.
第二步是把视野拉近到宏观层面。
Wilson’s mathematical machinery tells you whether each term in your theory will grow or shrink as you do so.
威尔逊的数学机制告诉您理论中的每一项是否会随着您的操作而增大或缩小。
What he found was that as you zoom out, most terms shrink nearly to zero.
他发现，当你缩小时，大多数项都会缩小到几乎为零。
This has to do with the fact that as you zoom out, your mathematical vision blurs.
这与当你缩小时，你的数学视野变得模糊有关。
Details related to individual atoms, or small groups of atoms, become too small to care about.
与单个原子或小原子团相关的细节变得太小而无需关心。
Only the terms tracking broad trends survive, and you land on a short and sweet theory of magnetism — an effective field theory — disconnected from almost all the atomic details.
只有追踪大趋势的术语才能生存下来，你就会得到一个简短而甜蜜的磁理论——一种有效的场论——与几乎所有原子细节脱节。
“This is the power of Wilson’s understanding,” Landry said.
“这就是威尔逊理解力的力量，”兰德里说。
“You can just skip to the answer.”
“你可以直接跳到答案。”
Wavelike Kelvin-Helmholtz clouds illustrate that vastly different substances act like liquids.
波浪状的开尔文-亥姆霍兹云表明，截然不同的物质表现得像液体。
With this machinery, Wilson solved the mystery of why many magnets magnetize at the same rate.
通过这种机器，威尔逊解决了为什么许多磁铁以相同的速率磁化的谜团。
The zooming-out step passes through a point at which all magnets look the same, whether their atoms are arranged in cubes or tetrahedra.
缩小步骤经过一个点，在该点所有磁铁看起来都一样，无论它们的原子排列成立方体还是四面体。
All that matters is that the atoms have a symmetry that lets them point in any direction.
重要的是原子具有对称性，可以让它们指向任何方向。
(Magnets whose atoms are pinned down to spin in a plane, for instance, magnetize at a different rate.)
（例如，原子被固定在平面上旋转的磁铁，会以不同的速率磁化。）
Wilson’s work also clarified why a few properties, like the temperature at which the magnetization takes place, vary wildly from magnet to magnet, even when they have the same spin symmetry.
威尔逊的工作还阐明了为什么磁体之间的一些特性（例如磁化发生的温度）差异很大，即使它们具有相同的自旋对称性。
These properties are related to the size of the few surviving terms.
这些属性与少数幸存项的大小有关。
The symmetries tell you the overall shape of the terms that stay large, but not exactly how large they are.
对称性告诉您保持较大的项的整体形状，但不能准确说明它们有多大。
The sizes of these terms act like threads lightly tethering the macroscopic world to the microscopic one.
这些术语的大小就像一根线，轻轻地将宏观世界与微观世界联系在一起。
Over the following decades, Wilson’s machinery seeped into many areas of physics.
在接下来的几十年里，威尔逊的机器渗透到物理学的许多领域。
Physicists used Wilson’s calculations to justify the previously murky mechanics of quantum field theory, which treats each particle as a wave while washing out the less significant effects of the smallest vibrations.
物理学家利用威尔逊的计算来证明之前模糊的量子场论力学的合理性，该理论将每个粒子视为波，同时消除了最小振动的不太显着的影响。
Wilson’s contributions also shaped modern theories of certain phases of matter, like solids.
威尔逊的贡献还塑造了物质某些相（例如固体）的现代理论。
But when it came to fluids, scientists remained stuck.
但当谈到液体时，科学家们仍然陷入困境。
Their defining symmetries weren’t yet clear.
它们的对称性尚不清楚。
The first break in the case came in the 2000s, when a group of cosmologists was using Wilsonian thinking to develop an effective field theory for the universe as a whole.
这个案例的第一次突破出现在 2000 年代，当时一群宇宙学家正在利用威尔逊思想为整个宇宙发展一种有效的场论。
As they did so, they stumbled upon a key insight: The universe’s expansion breaks a crucial symmetry in space-time.
当他们这样做时，他们偶然发现了一个重要的见解：宇宙的膨胀打破了时空的一个重要的对称性。
In general, space and time have no reference point against which you can measure speed.
一般来说，空间和时间没有可以衡量速度的参考点。
If you’re in a windowless spaceship, you can’t tell whether you’re moving quickly, slowly, or not at all.
如果你在一艘没有窗户的宇宙飞船里，你无法判断自己是在快速移动、缓慢移动，还是根本没有移动。
Space-time has a symmetry with respect to speed.
时空相对于速度具有对称性。
But in the expanding universe, there is a special reference point against which you can discern a motion: It’s the one in which the expansion of space itself moves galaxies uniformly away from you.
但在膨胀的宇宙中，有一个特殊的参考点，你可以根据它辨别运动：在这个参考点中，空间本身的膨胀使星系均匀地远离你。
If you were to leave your galaxy in a spaceship and travel against this cosmic recession in a particular direction, you would see the galaxies in front of you recede more slowly than the galaxies behind you.
如果你乘坐宇宙飞船离开你的星系，逆着宇宙衰退向一个特定的方向旅行，你会看到你前面的星系比你后面的星系退缩得更慢。
Fluids, the group noted, break the same symmetry.
该小组指出，流体打破了同样的对称性。
If you’re immersed in a resting liquid, you can tell you’re at rest.
如果您浸入静止液体中，则可以看出您处于静止状态。
And if you start to swim, you’ll feel the drag of the fluid as it moves past you.
如果您开始游泳，您会感觉到液体流过您时的阻力。
The resting fluid, like the expanding universe, lacks the underlying speed symmetry of space-time.
静止的流体，就像膨胀的宇宙一样，缺乏潜在的时空速度对称性。
Meanwhile, it has other standard space-time symmetries; rotations and translations don’t change the fluid.
同时，它还有其他标准的时空对称性；旋转和平移不会改变流体。
“At the level of the symmetries, they are the same,” said Alberto Nicolis , a physicist now at Columbia University, who worked on the effective field theory of the cosmos.
“在对称性层面上，它们是相同的，”哥伦比亚大学物理学家阿尔贝托·尼科利斯（Alberto Nicolis）说，他致力于宇宙有效场论的研究。
Alberto Nicolis, a physicist at Columbia University, took inspiration from cosmology to help devise a new theory of fluids.
哥伦比亚大学物理学家阿尔贝托·尼科利斯从宇宙学中获得灵感，帮助设计了一种新的流体理论。
The resemblance got the group thinking, but they needed one more ingredient.
这种相似性引起了团队的思考，但他们还需要一种成分。
They found it by considering what changes they could make to a fluid without changing its energy — another set of symmetries.
他们通过考虑在不改变流体能量的情况下可以对流体进行哪些改变而发现了这一点——另一组对称性。
They realized you could always swap two parcels of a fluid for free.
他们意识到你总是可以免费交换两包液体。
You could also shuffle three parcels, or four, or any number.
您还可以洗三个、四个或任意数量的包裹。
In contrast, you can’t exchange any regions of a solid without paying an energy toll, through rupture or serious internal stress, so solids lack these swapping symmetries.
相比之下，如果不付出能量代价，通过破裂或严重的内应力，就无法交换固体的任何区域，因此固体缺乏这些交换对称性。
The group had identified an unlimited number of fluid symmetries.
该小组已经确定了无限数量的流体对称性。
They considered what terms these symmetries would require in the theory and then, channeling the spirit of Wilson, zoomed out and watched the microscopic details wash away.
他们考虑了这些对称性在理论中需要什么术语，然后，秉承威尔逊的精神，缩小并观察微观细节被冲走。
They landed right on the Euler equations, perfect for perfect fluids, derived from fundamental symmetry principles.
他们直接找到了欧拉方程，该方程非常适合完美流体，源自基本对称原理。
The resulting theory — initially buried in a cosmology paper in 2005 and highlighted in a hydrodynamics paper in 2012 — was the first to apply the full effective field theory treatment to fluids.
由此产生的理论——最初被埋藏在 2005 年的一篇宇宙学论文中，并在 2012 年的一篇流体动力学论文中得到强调——是第一个将全面有效的场论处理应用于流体的理论。
“It’s the foundational text of all of this,” Landry said.
“这是所有这一切的基础文本，”兰德里说。
The next step would be to include the imperfect fluids, too.
下一步将包括不完美的流体。
The new effective field theory accelerated an effort within a community of scientists studying black holes, which have their own strange connection to fluids.
新的有效场论加速了科学家们研究黑洞的努力，黑洞与流体有着奇怪的联系。
A theoretical breakthrough from the late 1990s had established that, under special conditions, you could view a spherical black hole as a flat quantum soup.
20 世纪 90 年代末的理论突破表明，在特殊条件下，你可以将球形黑洞视为扁平的量子汤。
Theorists had connected the viscosity of the soup, which enabled it to dissipate energy, to the black hole’s ability to gobble up energy and hide it.
理论家将汤的粘度（使其能够耗散能量）与黑洞吞噬能量并隐藏能量的能力联系起来。
“Things can fall into the black hole,” Nicolis said.
“东西可能会掉进黑洞，”尼科利斯说。
“That’s a form of dissipation.”
“这是一种消散形式。”
Physicists already had an effective field theory of black holes: Einstein’s theory of gravity.
物理学家已经有了有效的黑洞场论：爱因斯坦的引力理论。
If a black hole had a secret identity as an imperfect, energy-dissipating, viscous fluid, then an effective field theory for imperfect, energy-dissipating, viscous fluids should exist, too.
如果黑洞的秘密身份是不完美的耗能粘性流体，那么对于不完美的耗能粘性流体的有效场论也应该存在。
Multiple teams raced to find it.
多个团队竞相寻找它。
At the Massachusetts Institute of Technology, Hong Liu led a team that used black holes as a jumping-off point to understand fluids at a deeper level.
在麻省理工学院，刘红领导的团队以黑洞为起点，更深层次地了解流体。
Hong Liu , a physicist at MIT, led one of the groups.
麻省理工学院的物理学家刘红领导了其中一个小组。
The group noticed that the surface of a black hole had a swapping symmetry akin to the one Nicolis and company had used to define a fluid; you could exchange patches of a black hole with each other without disturbing the black hole’s structure.
研究小组注意到黑洞的表面具有交换对称性，类似于尼科利斯和他的公司用来定义流体的对称性。你可以在不破坏黑洞结构的情况下互相交换黑洞的碎片。
But that symmetry wasn’t enough to describe an imperfect fluid.
但这种对称性不足以描述不完美的流体。
To achieve that, Liu’s group — which included the researchers Michael Crossley and Paolo Glorioso — resorted to an old trick from quantum mechanics.
为了实现这一目标，刘的团队（包括研究人员迈克尔·克罗斯利和保罗·格洛里索）诉诸了量子力学的老把戏。
They duplicated the substance in their theory, effectively adding a second fluid with a clock that ticked backward while the first fluid’s clock ticked forward.
他们在理论中复制了这种物质，有效地添加了第二种液体，其时钟向后滴答作响，而第一种液体的时钟向前滴答作响。
Comparing the two fluids at any given moment let the researchers keep track of random variations.
在任何给定时刻比较两种流体可以让研究人员跟踪随机变化。
(The real physical fluid was essentially an average of the two mathematical fluids.)
（真正的物理流体本质上是两种数学流体的平均值。）
The team had one last problem.
该团队还有最后一个问题。
They knew that a zoomed-out fluid must obey the laws of thermodynamics: It has to have a temperature that varies from place to place, and a tendency for any hot patches to blend with cold patches as time ticks along.
他们知道，缩小的流体必须遵守热力学定律：它的温度必须随地点而变化，并且随着时间的推移，任何热斑都会与冷斑混合。
At the same time, they knew that at the zoomed-in level, the buzzing of atoms makes no distinction between past and future.
同时，他们知道，在放大的水平上，原子的嗡嗡声无法区分过去和未来。
(You wouldn’t be able to tell if a video of atomic motion was playing forward or backward.) Was there a way to tie the thermodynamics of the fluid to the two ways that time worked?
（你无法判断原子运动的视频是向前还是向后播放。）有没有办法将流体的热力学与时间运行的两种方式联系起来？
After some trial and error, the group found a symmetry that did the trick.
经过一番尝试和错误后，研究小组发现了一种对称性，可以达到目的。
The transformation switched the two fluids, reversed their clocks, and fiddled with the temperature in a particular way.
这种转变改变了两种流体的方向，颠倒了它们的时钟，并以一种特殊的方式改变了温度。
If it happened a second time, the fluid would return to its original state.
如果发生第二次，液体就会恢复到原来的状态。
The different notions of time, and their ultimate compatibility, flowed from this symmetry, which was unlike any that physicists had seen before.
不同的时间概念及其最终的兼容性源于这种对称性，这与物理学家以前见过的任何对称性都不同。
“It’s a funny symmetry,” said Kristan Jensen , a physicist now at the University of Victoria in Canada, who also contributed to the black-holes-to-fluids effort.
“这是一个有趣的对称性，”加拿大维多利亚大学的物理学家克里斯坦·詹森 (Kristan Jensen) 说，他也为黑洞到流体的研究做出了贡献。
“And it’s essential.
“这很重要。
Before that, there are a ton of terms.
在此之前，有大量的术语。
And then [everything] collapses down and you just get known phenomena, nothing more and nothing less.”
然后[一切]崩溃了，你只得到已知的现象，仅此而已。”
They were done.
他们完成了。
From these symmetries they could write down a theory and zoom out to derive the Navier-Stokes equations.
根据这些对称性，他们可以写下一个理论并缩小范围以推导出纳维-斯托克斯方程。
In 2015, Liu and his group posted their new effective field theory .
2015年，刘和他的团队发布了他们新的有效场理论。
It was a magnum opus, spanning 110 pages.
这是一部长达 110 页的巨著。
“It blew my mind,” Landry said.
“这让我大吃一惊，”兰德里说。
Next, physicists would put the theory to work.
接下来，物理学家将把这个理论付诸实践。
It wasn’t immediately obvious how to harness the highly technical theory for specific applications.
如何利用高科技理论来实现特定的应用还不是很明显。
But Liu and Glorioso rewrote the equations in a more accessible way in 2018, and the calculations started to trickle out.
但刘和格洛里索在 2018 年以一种更容易理解的方式重写了方程，计算结果开始慢慢流出。
The new work allowed theorists to work more efficiently and push their calculations further.
这项新工作使理论家能够更有效地工作并进一步推动他们的计算。
In particular, they were able to ferret out tiny terms in Navier-Stokes equations that had previously been ignored, terms that capture some of the effects of random molecular motion.
特别是，他们能够找出纳维-斯托克斯方程中以前被忽略的微小项，这些项捕获了随机分子运动的一些影响。
“The stuff that we’re doing is more than just sort of an alternate version [of fluid dynamics],” Landry said.
“我们正在做的事情不仅仅是[流体动力学]的替代版本，”兰德里说。
“It is actually strictly more correct.”
“实际上严格来说更正确。”
Luca Delacrétaz at the University of Chicago used the new theory to calculate more precisely how heat spreads through a liquid — and found that it moves more slowly than expected during its first few moments, due to random jitters.
芝加哥大学的卢卡·德拉克雷塔兹 (Luca Delacrétaz) 使用新理论更精确地计算热量如何通过液体传播，并发现由于随机抖动，液体在最初的几分钟内移动速度比预期慢。
The effect is far too small to measure in water, but it becomes more substantial in quantum systems made from a limited number of particles.
这种效应太小，无法在水中测量，但在由有限数量的粒子组成的量子系统中，它变得更加明显。
“Doing precision physics in chaotic quantum many-body systems sounds crazy, but now it’s possible,” Delacrétaz said.
“在混沌量子多体系统中进行精密物理学听起来很疯狂，但现在这是可能的，”德拉克雷塔兹说。
Other researchers used the theory to derive Navier-Stokes analogues for exotic states of matter, like fracton matter .
其他研究人员利用该理论推导出奇异物质态（例如分形物质）的纳维-斯托克斯类似物。
Roughly speaking, fracton matter is composed of groups of particles that collectively act like one particle .
粗略地说，分形物质是由一组粒子组成的，这些粒子的行为就像一个粒子一样。
Individual “fractons” stay trapped in place; only when fractons band together can they move about.
单个“分形”被困在原地；只有当分形结合在一起时，它们才能移动。
In 2020, Andrew Lucas, a physicist at the University of Colorado, Boulder, and his collaborators spotted new symmetries in the fracton phase and used the effective field theory framework to derive a fracton version of the Navier-Stokes equations .
2020 年，科罗拉多大学博尔德分校的物理学家安德鲁·卢卡斯 (Andrew Lucas) 和他的合作者在分形相中发现了新的对称性，并使用有效场论框架推导了纳维-斯托克斯方程的分形版本。
The work opened the door to understanding whole new classes of liquidlike phases of matter.
这项工作为理解全新的类液态物质相打开了大门。
“It’s just a few lines of algebra to kind of plug it into the formalism that [Liu] developed and ask what’s possible,” Lucas said.
“这只是几行代数，可以将其插入[刘]开发的形式主义中，并询问什么是可能的，”卢卡斯说。
In 2024, Lucas and his group built on Liu’s theory by making explicit the basis for some of its construction.
2024 年，卢卡斯和他的团队以刘的理论为基础，明确了其某些构建的基础。
They used a newly discovered “strong” symmetry , related to the fact that the total number of particles in a fluid is always the same.
他们使用了新发现的“强”对称性，该对称性与流体中粒子总数始终相同的事实有关。
That symmetry is partially broken, becoming a “weak” symmetry, due to the fact that the exact number of particles in a specific region of a fluid can vary from moment to moment.
这种对称性被部分破坏，成为“弱”对称性，因为流体特定区域中粒子的确切数量可能随时变化。
The consequence of this broken symmetry, they found, is a long, slow diffusion.
他们发现，这种对称性破缺的结果是漫长而缓慢的扩散。
This helps explain why it takes many seconds for an ink drop to spread through a fluid made of particles furiously colliding from picosecond to picosecond.
这有助于解释为什么墨滴需要很多秒才能在由皮秒到皮秒激烈碰撞的粒子组成的流体中扩散。
Lucas and his collaborators integrated this symmetry into Liu’s effective field theory in 2024 .
卢卡斯和他的合作者在 2024 年将这种对称性整合到刘的有效场理论中。
“Our main contribution was to justify what Liu was doing,” Lucas said.
“我们的主要贡献是证明刘的所作所为是合理的，”卢卡斯说。
“To me it’s a closure of a story.”
“对我来说，这是一个故事的结局。”
While the effective field theory framework has catalyzed new calculations, the real prize may be more conceptual: a new definition of what makes a fluid a fluid.
虽然有效场论框架催生了新的计算，但真正的奖励可能更具概念性：对流体为何成为流体的新定义。
A fluid is any material with a particular set of symmetries, no matter what it’s made of.
流体是具有一组特定对称性的任何材料，无论它是由什么制成的。
“There’s something magical about fluid dynamics,” Nicolis said.
“流体动力学有一些神奇之处，”尼科利斯说。
“There’s oil, water, mercury.
“有油、水、汞。
These are all very different, microscopically, very different things that, in practice, behave very similarly when you look at how they flow.”
从微观上看，这些都是非常不同的东西，但实际上，当你观察它们的流动方式时，它们的行为非常相似。”
Get highlights of the most important news delivered to your email inbox
获取发送到您的电子邮件收件箱的最重要新闻的摘要
Quanta Magazine moderates comments to facilitate an informed, substantive, civil conversation.
《Quanta》杂志对评论进行审核，以促进知情、实质性、文明的对话。
Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected.
辱骂、亵渎、自我推销、误导、语无伦次或偏离主题的评论将被拒绝。
Moderators are staffed during regular business hours (New York time) and can only accept comments written in English.
版主在正常工作时间（纽约时间）有工作人员，并且只能接受英文评论。