Where Some See Strings, She Sees a Space-Time Made of Fractals
Astrid Eichhorn, a physicist at Heidelberg University in Germany, is a leader in the field of asymptotic safety — a conservative theory of quantum gravity.
阿斯特丽德·艾希霍恩 (Astrid Eichhorn) 是德国海德堡大学的物理学家，是渐近安全（一种保守的量子引力理论）领域的领导者。
Astrid Eichhorn spends her days thinking about how the laws of physics change at the tiniest scales.
阿斯特丽德·艾希霍恩 (Astrid Eichhorn) 整天思考物理定律如何在最微小的尺度上发生变化。
Imagine zooming in closer and closer to the device on which you’re reading this article.
想象一下，放大到越来越接近您正在阅读本文的设备。
Its apparently smooth screen quickly dissolves into a jiggling lattice of molecules, which in turn resolve into clouds of electrons buzzing around atomic nuclei.
它表面光滑的屏幕很快就会分解成一个摇晃的分子晶格，而分子晶格又分解成围绕原子核嗡嗡作响的电子云。
You dive into a nucleus, and atoms disappear as you enter the domain of quarks.
当你潜入原子核时，当你进入夸克领域时，原子就会消失。
It is here, where protons loom as large as solar systems, that Eichhorn’s explorations begin.
正是在这里，质子隐约可见，与太阳系一样大，艾希霍恩的探索由此开始。
Past this point, the fundamental forces themselves shift.
过了这个点，基本力量本身就会发生变化。
Electromagnetism and the weak interaction intensify, while the strong force slackens.
电磁力和弱相互作用增强，而强相互作用减弱。
The changes happen in a fairly regular way, so physicists have a good sense of how they work …
这些变化以相当规律的方式发生，因此物理学家对它们的工作原理有很好的了解……
until they don’t.
直到他们不这样做。
When an atom appears as large as the observable universe, the established laws of physics can no longer tell you what happens between particles separated by an atom’s width.
当原子看起来与可观测的宇宙一样大时，既定的物理定律就无法再告诉你由原子宽度分隔的粒子之间会发生什么。
Gravity, a force that’s too weak to notice at the scale of atoms, grows strong in an erratic way.
引力是一种在原子尺度上太弱而无法被注意到的力，但它却以一种不稳定的方式增强。
You’ve just crossed over into the “Planck” realm.
你刚刚进入了“普朗克”领域。
The apparent breakdown of particle physics at this scale has inspired some dramatic theories.
粒子物理学在这种规模上的明显崩溃激发了一些戏剧性的理论。
Some physicists argue that this failure point in our understanding tells us that the universe is fundamentally composed not of particles, but of vibrating strings and membranes .
一些物理学家认为，我们理解中的这个失败点告诉我们，宇宙从根本上来说不是由粒子组成，而是由振动的弦和膜组成。
Others argue that at these smallest scales, space and time themselves must dissolve into structures such as loops .
其他人则认为，在这些最小的尺度上，空间和时间本身必须分解成诸如循环之类的结构。
Eichhorn and her colleagues are pursuing a different possibility.
艾希霍恩和她的同事正在寻求一种不同的可能性。
In 1976, Steven Weinberg, a theorist who would eventually earn a Nobel Prize, pointed out that if you zoomed in far enough, you might reach a place where the rules of physics would stop changing.
1976 年，最终获得诺贝尔奖的理论家史蒂文·温伯格 (Steven Weinberg) 指出，如果你放大得足够远，你可能会到达物理规则停止变化的地方。
New realms would stop appearing; the intensities of the forces would stabilize; and gravity would turn out to make perfect sense after all.
新的领域将不再出现；力量的强度将会稳定；事实证明，万有引力是完全有道理的。
Eichhorn, a physicist at Heidelberg University in Germany, has over the last decade become a leading theorist investigating this idea, called asymptotic safety .
艾希霍恩是德国海德堡大学的物理学家，在过去的十年里，他成为研究这一被称为渐近安全的想法的领先理论家。
In particular, Eichhorn has emphasized the importance of taking into account the ways in which matter affects space-time, and vice versa.
艾希霍恩特别强调了考虑物质影响时空方式的重要性，反之亦然。
“She is the expert of gravity-matter systems in asymptotic safety,” said Alessia Platania, a physicist at the University of Copenhagen who has worked with Eichhorn.
“她是渐进安全重力-物质系统方面的专家，”曾与艾希霍恩合作过的哥本哈根大学物理学家阿莱西娅·普拉塔尼亚 (Alessia Platania) 说。
The quantum fields in nature have ripples that balance in just the right way to stabilize the laws of physics at shorter scales, Eichhorn’s work has suggested.
艾希霍恩的研究表明，自然界中的量子场具有以正确的方式平衡的涟漪，以稳定较短尺度的物理定律。
Over the last decade, Eichhorn has made significant strides toward showing that the quantum laws likely do stop changing around the Planck scale, just as Weinberg suspected.
在过去的十年里，艾希霍恩在证明量子定律可能确实在普朗克尺度上停止变化方面取得了重大进展，正如温伯格所怀疑的那样。
She has also connected Planck-scale physics with physics at scales that are easier to study — a famously challenging task for anyone working with a theory of gravity at the smallest levels.
她还将普朗克尺度的物理学与更容易研究的尺度的物理学联系起来——对于任何研究最小水平引力理论的人来说，这是一项众所周知的挑战性任务。
Quanta recently spoke with Eichhorn about these efforts.
广达最近与艾希霍恩谈论了这些努力。
The interview has been condensed and edited for clarity.
为了清晰起见，采访内容已经过精简和编辑。
So, the approach we use with most of the forces is called quantum field theory.
因此，我们对大多数力使用的方法称为量子场论。
It assumes the universe is full of quantum fields.
它假设宇宙充满量子场。
Fields have ripples that manifest as pointlike particles.
场上有波纹，表现为点状粒子。
These particles move through a continuous space-time and interact via forces.
这些粒子穿过连续的时空并通过力相互作用。
Ultimately the problem is that if we try to treat quantum gravity as a fluctuating quantum field in this most straightforward way, then this approach does not work.
最终的问题是，如果我们试图以这种最直接的方式将量子引力视为波动的量子场，那么这种方法就行不通。
Very roughly, for a well-understood force like electromagnetism, we need to consider fluctuations in the field at all scales.
非常粗略地讲，对于像电磁这样的众所周知的力，我们需要考虑所有尺度的场波动。
And these fluctuations never stop coming as you zoom in.
当你放大时，这些波动永远不会停止。
They act like virtual particles with higher and higher energies.
它们的行为就像具有越来越高能量的虚拟粒子。
We know how to account for the effects of these high-energy virtual particles in our calculations: The intensity of the force changes, but that’s it.
我们知道如何在计算中考虑这些高能虚拟粒子的影响：力的强度会发生变化，但仅此而已。
But when you try to add gravity, which Albert Einstein linked with the structure of space-time, the fluctuations become problematic.
但是，当你尝试添加引力（阿尔伯特·爱因斯坦将引力与时空结构联系起来）时，波动就会出现问题。
At shorter distances, the higher-energy virtual particles interact in new and different ways.
在较短的距离上，较高能量的虚拟粒子以新的不同方式相互作用。
We can’t account for these ever-changing effects, so quantum field theory fails to predict what will happen at those tiny scales.
我们无法解释这些不断变化的效应，因此量子场论无法预测在这些微小尺度上会发生什么。
Physicists use the machinery of renormalization, which Eichhorn describes as a “mathematical microscope,” to calculate how the world changes as you zoom in and out.
物理学家使用重整化机制（艾希霍恩将其描述为“数学显微镜”）来计算放大和缩小时世界如何变化。
It tells us that something new happens as we zoom in.
它告诉我们，当我们放大时，会发生一些新的事情。
And I would say there are roughly three lines of thinking as to what that might be.
我想说，关于这可能是什么，大致有三种思路。
One is that maybe quantum field theory breaks down, full stop.
一是量子场论也许会崩溃，句号。
The objects are not points, in the way that we think of elementary particles as points.
物体不是点，就像我们将基本粒子视为点一样。
Instead, they become stringy.
相反，它们变得粘稠。
That’s string theory.
这就是弦理论。
To this day we call it the OMG plot.
直到今天，我们仍称其为 OMG 情节。
It was just so mind-blowing to us, that this idea really works out in a quantitative way.
这对我们来说真是太令人兴奋了，这个想法确实能够以定量的方式发挥作用。
Another is that we need to remove the assumption that space-time is continuous.
另一个是我们需要消除时空连续的假设。
I take my glass of water, and it looks continuous to me, but fundamentally it’s atomic.
我拿起一杯水，对我来说它看起来是连续的，但从根本上来说它是原子的。
Maybe it’s the same with space-time.
也许时空也是如此。
This is the idea spelled out in loop quantum gravity, or in causal sets.
这是圈量子引力或因果集中阐述的想法。
Or you can say that fields and particles persist; space-time persists; and the new thing is that space-time takes on a structure that is, broadly speaking, like a fractal: The intensity of the forces, including gravity, stops changing, and you start seeing the same picture, the same rules for how particles talk to each other, over and over.
或者你可以说场和粒子持续存在；时空持续存在；新的事情是，时空呈现出一种广义上像分形的结构：包括重力在内的力的强度停止变化，你开始一遍又一遍地看到相同的画面，相同的粒子如何相互交谈的规则。
That’s the idea I’m pursuing, asymptotic safety.
这就是我追求的理念：渐近安全。
If this self-similar realm exists, then the fluctuations of space-time, and of the other fields, would become stable enough for us to make predictions using good old-fashioned quantum field theory.
如果这种自相似领域存在，那么时空和其他场的波动将变得足够稳定，使我们能够使用良好的老式量子场论进行预测。
One reason is that symmetries are very common in many theories of nature.
原因之一是对称性在许多自然理论中非常常见。
Space-time itself has symmetries, for instance.
例如，时空本身具有对称性。
There are no special directions, no special places, and no special times.
没有特别的方向，没有特别的地点，也没有特别的时间。
But we do have special scales: The world looks one way to humans, another way to bacteria, and yet another way to electrons.
但我们确实有特殊的尺度：世界对人类来说是一种方式，对细菌来说是另一种方式，对电子来说又是另一种方式。
That’s peculiar.
这很奇怪。
So I think it’s a natural assumption to say that at the fundamental level, maybe there are no special scales.
所以我认为，在基本层面上，也许不存在特殊的尺度，这是一个自然的假设。
Maybe there is a symmetry between scales, a scale symmetry.
也许尺度之间存在对称性，尺度对称。
Eichhorn also studies the ways in which asymptotic safety could be compatible with the picture of reality emerging from other approaches to quantum gravity, like string theory.
艾希霍恩还研究了渐近安全性与其他量子引力方法（如弦理论）所呈现的现实图景相兼容的方式。
Another is that this is a very conservative approach to quantum gravity.
另一个原因是，这是一种非常保守的量子引力方法。
You take quantum field theory, which has never failed in the lab, and you ask: What do you need to do to make it predictive for all scales?
你采用量子场论，它在实验室中从未失败过，你会问：你需要做什么才能让它预测所有尺度？
And as far as we know, adding scale symmetry is the only thing we can do.
据我们所知，增加尺度对称性是我们唯一能做的。
First we need to check whether quantum fields can actually fluctuate in such a way that they achieve a special balance between them that makes all scales look the same.
首先，我们需要检查量子场是否真的可以波动，从而在它们之间实现特殊的平衡，从而使所有尺度看起来都相同。
We work with a procedure that is sort of the mathematical version of a microscope: We set up a mathematical representation of the fields and their interactions, and we calculate how the interactions between the ripples in the fields change as we zoom in.
我们使用的程序有点像显微镜的数学版本：我们建立了场及其相互作用的数学表示，并计算当我们放大时场中波纹之间的相互作用如何变化。
Then we look for a place where that change stops, a place we call a fixed point.
然后我们寻找变化停止的地方，我们称之为固定点的地方。
We have tons of simplified examples of idealized theories with fixed points.
我们有大量具有固定点的理想化理论的简化示例。
The community at large has worked a lot on empty space-time, just pure gravity.
整个社区在空的时空、纯粹的引力方面做了很多工作。
Actually, most of us work in an even more simplified setting where there are only quantum fluctuations of space, rather than fluctuations of both space and time.
事实上，我们大多数人都在一个更加简化的环境中工作，其中只有空间的量子涨落，而不是空间和时间的涨落。
But nevertheless, people have tested this in literally hundreds of papers and found very robustly that this fixed point where things stop changing exists.
但尽管如此，人们在数百篇论文中对此进行了测试，并非常有力地发现，事物停止变化的固定点是存在的。
And then the next question to ask is: What happens when I throw in matter fields?
接下来要问的问题是：当我投入物质场时会发生什么？
This is one of my earliest papers that I wrote as a postdoc in 2013.
这是我 2013 年作为博士后撰写的最早的论文之一。
My collaborators and I included all the known matter and force fields and found that the fixed point was still there, albeit in this funny space-only setting.
我和我的合作者包括了所有已知的物质和力场，发现固定点仍然存在，尽管是在这个有趣的纯空间环境中。
We gave the paper this catchy title, “ Matter Matters ,” and it became a bit of a slogan for me.
我们给这篇论文起了一个朗朗上口的标题“重要”，这对我来说有点像一个口号。
Last summer we tied things up by showing that there is likely a fixed point even when we include all of the ways that the known fields can interact with each other — something we left out of the 2013 paper.
去年夏天，我们通过证明即使我们包含了已知场相互作用的所有方式，也可能存在一个固定点，从而将事情联系起来——这是我们在 2013 年论文中遗漏的。
We have now looked at the complete picture for the first time.
我们现在第一次看到了完整的情况。
Eichhorn and her collaborators make predictions by assuming scale symmetry and asking what kind of a world they will see when they zoom back out to our level.
艾希霍恩和她的合作者通过假设尺度对称性并询问当他们缩小到我们的水平时他们会看到什么样的世界来进行预测。
To test it, we turn the logic around.
为了测试它，我们扭转逻辑。
Instead of zooming in and looking for mathematical evidence of a fixed point in our models, we assume that a fixed point exists and zoom out, asking: What physical implications would a fractal-like realm have for our macroscopic world?
我们不是放大并寻找模型中固定点的数学证据，而是假设存在一个固定点并缩小，询问：类似分形的领域对我们的宏观世界有什么物理影响？
We have good indications that it would force the macroscopic world to look a lot like the world we see.
我们有充分的迹象表明，这将迫使宏观世界看起来与我们所看到的世界非常相似。
In 2009, Mikhail Shaposhnikov and Christof Wetterich showed that zooming out from a fixed point forces the mass of the Higgs boson , the particle that accounts for mass, to be almost exactly the value we measure.
2009 年，米哈伊尔·沙波什尼科夫 (Mikhail Shaposhnikov) 和克里斯托夫·韦特里奇 (Christof Wetterich) 证明，从固定点缩小会迫使希格斯玻色子（负责质量的粒子）的质量几乎与我们测量的值完全相同。
It’s a natural assumption to say that at the fundamental level, maybe there are no special scales.
很自然的假设是，在基本层面上，也许不存在特殊的尺度。
And in 2018, my Ph.D. student Aaron Held and I had a memorable moment.
2018 年，我的博士学位。学生 Aaron Held 和我度过了一个难忘的时刻。
The previous year, we had already found that a fixed point would force the top quark to have close to the measured mass.
去年，我们已经发现一个固定点会迫使顶夸克的质量接近测量值。
And we were investigating whether it could also account for the mass of the top quark’s sibling, the bottom quark.
我们正在研究它是否也可以解释顶夸克的兄弟姐妹底夸克的质量。
They’re supposed to be identical twins in the eyes of gravity, because their distinctive quantum properties are not things that gravity is sensitive to, but experiments have found that they have different masses.
在引力眼中它们应该是同卵双胞胎，因为它们独特的量子特性并不是引力敏感的东西，但实验发现它们具有不同的质量。
I remember this afternoon distinctly.
我清楚地记得今天下午。
Aaron and I sat together in my office in front of my laptop, and we were looking at plots of our results in the software Mathematica.
亚伦和我一起坐在办公室里的笔记本电脑前，我们正在 Mathematica 软件中查看结果图。
We saw that indeed there is this point where the predictions match up to within 10%.
我们发现确实存在预测匹配度在 10% 以内的点。
In a world with no fixed point, the masses could be anything.
在一个没有固定点的世界里，群众可以是任何东西。
But if there is a fixed point, a very particular conversation starts up between gravity and the electroweak force, and a result of that conversation is that these quarks basically have to have the two different masses that they do.
但如果存在一个固定点，引力和电弱力之间就会开始一种非常特殊的对话，而这种对话的结果是这些夸克基本上必须具有它们所具有的两种不同的质量。
To this day we call it the OMG plot.
直到今天，我们仍称其为 OMG 情节。
It was just so mind-blowing to us that this idea really works out in a quantitative way.
这个想法确实能够以定量的方式实现，这让我们非常兴奋。
If the world is fundamentally “scale symmetric,” Eichhorn says, then the textbook quantum theory may perfectly capture the behavior of gravity and the structure of space-time.
艾希霍恩说，如果世界从根本上来说是“尺度对称的”，那么教科书上的量子理论就可以完美地捕捉引力的行为和时空的结构。
We’ve made more progress since 2017.
自 2017 年以来，我们取得了更多进展。
We were able to connect the fixed point with a few neutrino properties, including their weirdly light mass , which we found simultaneously with another group .
我们能够将固定点与一些中微子特性联系起来，包括我们与另一组同时发现的中微子的奇怪的轻质量。
But we also know that asymptotic safety is quite far from explaining everything.
但我们也知道，渐近安全性还远远不能解释一切。
The real proton mass is consistent with a fixed point, for instance, but it could also be 10 or 100 times as heavy.
例如，真实的质子质量与某个固定点一致，但也可能是其质量的 10 倍或 100 倍。
As far as we can tell, though, there are no particle properties that are incompatible with asymptotic safety.
但据我们所知，不存在与渐近安全性不相容的粒子属性。
If there were, we could rule the theory out.
如果有的话，我们就可以排除这个理论。
But for now, everything works, and it looks like we might explain a little bit more about the properties of particles and their interactions than we could before.
但就目前而言，一切正常，看起来我们可以比以前更多地解释粒子的属性及其相互作用。
That might be progress.
这可能就是进步。
That makes me happy.
这让我很高兴。
We’ve made these “retrodictions,” and that’s nice.
我们做了这些“复古”，这很好。
But sometimes I think, “Man, we were too late!” If someone had made these as actual predictions back then, maybe asymptotic safety would be the largely established view of quantum gravity.
但有时我会想，“伙计，我们太晚了！”如果当时有人将这些作为实际的预测，也许渐近安全性将成为量子引力的广泛确立的观点。
Eichhorn suspects that if you zoom in far enough, the laws of physics may stop changing.
艾希霍恩怀疑，如果放大得足够远，物理定律可能会停止变化。
Or maybe they would have advanced beyond where we are now and found a point where asymptotic safety doesn’t work out.
或者也许他们会超越我们现在的水平，并找到渐近安全不起作用的点。
Then they might have abandoned it for strings and other exotic theories with a complete confidence that such a drastic move is necessary.
然后他们可能会放弃它而转向弦乐和其他奇异的理论，并完全相信这样一个激烈的举动是必要的。
We’ve looked at various proposals for dark matter, and I can tell you a number of things that probably don’t work in asymptotic safety.
我们已经研究了有关暗物质的各种建议，我可以告诉你一些在渐近安全下可能行不通的事情。
Several of the popular dark matter models, actually.
实际上，几种流行的暗物质模型。
The simplest versions of weakly interacting massive particles , for instance; the simplest type of axionlike particles most people look for; and the kind of ultralight dark matter that could influence upcoming nuclear clocks all don’t seem to be compatible with the fractal world, although we cannot exclude them with absolute certainty.
例如，弱相互作用的大质量粒子的最简单版本；大多数人寻找的最简单的类轴子粒子；尽管我们不能绝对肯定地排除它们，但可能影响即将到来的核钟的超轻暗物质似乎都与分形世界不兼容。
Definitely not!
绝对不是！
Experimentalists are bravely going forward and testing as much as they can.
实验者正在勇敢地前进并尽可能多地进行测试。
And those tests can be seen as tests of asymptotic safety.
这些测试可以被视为渐近安全性的测试。
If an axion experiment finds dark matter tomorrow, that would actually put our theory under pressure.
如果轴子实验明天发现暗物质，这实际上会给我们的理论带来压力。
So these hunts are indirectly informing us about the quantum structure of space-time, and I find that a rather cool by-product of these experiments.
因此，这些搜寻间接地告诉我们时空的量子结构，我发现这是这些实验的一个相当酷的副产品。
You might think it would rule them out, but this is not necessarily the case.
您可能认为这会排除它们，但事实并非一定如此。
Asymptotic safety could be compatible with these other approaches.
渐近安全性可以与这些其他方法兼容。
Perhaps at the fundamental scale there are strings or loops or something, but then as you zoom out you hit a realm where things change so slowly for a while that it looks as if you’re at a fixed point.
也许在基本尺度上存在字符串或循环之类的东西，但当你缩小时，你会遇到一个领域，其中事物在一段时间内变化得如此缓慢，以至于看起来好像你处于一个固定点。
That’s possible, and it means that distinct quantum gravity approaches may actually not be competitors, but rather different perspectives on the same physics.
这是可能的，这意味着不同的量子引力方法实际上可能不是竞争对手，而是对同一物理的不同观点。
In quantum gravity research, it’s always a good idea to be humble.
在量子引力研究中，保持谦虚总是个好主意。
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