有人眼中是弦，她眼中却是分形构成的时空。
内容总结：
探索时空分形本质：物理学家挑战量子引力理论新前沿
在微观尺度的最深处，物理定律是否会彻底改写？海德堡大学物理学家阿斯特丽德·艾希霍恩与团队正通过“渐近安全”理论，提出一个颠覆性的构想：在普朗克尺度上，时空可能具有分形结构，物理规律将在此停止变化。
突破传统理论的困境
当研究尺度小到原子如同可观测宇宙般广阔时，经典物理理论完全失效。引力在此尺度以不可预测的方式增强，而量子场论在描述引力与时空结构耦合时，因无法处理极高能标的量子涨落而崩溃。对此，学界主流提出弦理论或圈量子引力等方案，认为时空连续性可能瓦解。
艾希霍恩团队则另辟蹊径，继承诺贝尔奖得主史蒂文·温伯格的思想，探索“渐近安全”的可能性：在极微观尺度上，所有作用力的强度将趋于稳定，时空与物质形成自相似的分形结构，使得量子场论仍能适用。“她是渐近安全理论中引力-物质系统的专家，”合作者、哥本哈根大学物理学家阿莱西亚·普拉塔尼亚评价道。
从数学到物理的验证之路
团队通过数学上的“重正化群”方法，模拟不断放大时空尺度的过程，寻找物理规律停止变化的“固定点”。2013年，艾希霍恩在博士后阶段发表论文《物质至关重要》，首次证实引入已知物质场后固定点依然存在。2023年夏季的最新研究更完整纳入所有场的相互作用，初步构建出包含物质与引力的自洽图像。
理论预测开始与实验数据吻合：研究显示，从固定点出发向外“放大”时，希格斯玻色子、顶夸克、底夸克等粒子的质量预测值与实测误差仅在10%以内。团队曾因计算结果与底夸克质量惊人匹配而将其图表命名为“OMG图”。艾希霍恩回忆道：“我们震惊地发现，这个理论竟能以定量方式解释现实。”
对未知领域的启示与局限
该理论已排除部分流行暗物质模型（如最简单版本的弱相互作用大质量粒子、轴子类粒子等）与分形时空的兼容性，但艾希霍恩强调，实验探测仍至关重要：“如果明天轴子实验发现了暗物质，我们的理论将面临压力。这些探索间接揭示了时空的量子结构。”
尽管渐近安全理论尚无法解释所有粒子性质，但迄今未发现与之矛盾的观测证据。艾希霍恩认为，不同量子引力理论可能并非互斥，而是对同一物理现实的不同视角描述。“在量子引力研究中，保持谦逊总是明智的。”
这项研究不仅挑战了人们对时空本质的认知，也为统一量子力学与引力提供了新的可能路径。在微观世界的分形图景中，物理学家正在重新书写宇宙最深层的运行法则。
中文翻译：
在有些人眼中是弦，在她眼中却是分形时空
引言
阿斯特丽德·艾希霍恩终日思考着物理定律在微观尺度如何变化。
想象一下，将你阅读本文的屏幕不断放大。看似平滑的屏幕会迅速分解为晃动的分子晶格，继而显现出围绕原子核运动的电子云。当你潜入原子核，进入夸克领域时，原子便消失了。正是在质子如太阳系般庞大的尺度上，艾希霍恩的探索开始了。
越过这个尺度，基本作用力本身开始转变。电磁力和弱相互作用增强，而强相互作用减弱。这些变化以相当规律的方式发生，因此物理学家对其机制有较好的把握……直到规律失效。
当一个原子显得如同可观测宇宙般辽阔时，既定的物理定律便无法解释相隔一个原子宽度的粒子间会发生什么。在原子尺度微弱到难以察觉的引力，会以难以捉摸的方式增强。此时你已跨越到"普朗克"领域。
粒子物理学在这个尺度上的明显失效催生了一些颠覆性理论。有物理学家认为，这种认知断层昭示着宇宙的基本构成并非粒子，而是振动的弦与膜。另一些学者主张，在最小尺度上，时空本身必然分解为圈状结构。
艾希霍恩与同事们正在探索另一种可能性。1976年，后来荣获诺贝尔奖的理论物理学家史蒂文·温伯格指出，若持续放大到足够微观的尺度，或许会抵达物理规则停止演变的临界点。新领域将不再涌现，作用力强度趋于稳定，而引力终将显现出完美的自洽性。
过去十年间，这位德国海德堡大学的物理学家已成为研究"渐进安全"理论的领军人物。艾希霍恩特别强调物质与时空相互影响的重要性。"她是渐进安全理论中引力-物质系统的专家，"曾与艾希霍恩合作的哥本哈根大学物理学家阿莱西亚·普拉塔尼亚如是说。
近十年来，艾希霍恩在证明量子定律很可能如温伯格推测那样，于普朗克尺度停止变化方面取得重大进展。她还将普朗克尺度物理与更易研究的尺度物理相联结——这对任何研究微观引力理论的学者而言都是著名的挑战。《量子》杂志近期就这些探索与艾希霍恩进行了对话，以下为经过精简和编辑的访谈内容。
核心难题是什么？若在最小尺度上将引力与其他作用力同等对待，会出现什么问题？
我们处理大多数作用力的方法称为量子场论。该理论假设宇宙充满量子场，场的涟漪表现为点状粒子。这些粒子在连续时空中运动，并通过作用力相互影响。
根本问题在于，若以最直接的方式将量子引力视为涨落的量子场，这种方法将失效。
简而言之，对于电磁力这类已被充分理解的作用力，我们需要考虑场在所有尺度上的涨落。随着观察尺度不断缩小，这些涨落永无止境。它们如同携带越来越高能量的虚粒子。我们知道如何在计算中处理这些高能虚粒子的效应：作用力强度会改变，仅此而已。
但当你尝试引入阿尔伯特·爱因斯坦与时空结构相联系的引力时，涨落就变得棘手了。在更短距离上，更高能量的虚粒子会以全新方式相互作用。我们无法解释这些持续变化的效应，因此量子场论无法预测微观尺度的现象。
物理学家认为量子场论的失效说明了什么？
这告诉我们，随着观察尺度缩小，新现象必然出现。关于这些现象的本质，我认为大致存在三种思路。
其一是量子场论可能彻底失效。基本粒子并非我们设想中的点状结构，而是呈现弦状特性。这就是弦理论。
其二是需要摒弃时空连续性的假设。就像我手中的水杯看似连续，本质上却由原子构成。时空或许也是如此。这是圈量子引力或因果集理论阐述的观点。
或者我们可以认为场与粒子持续存在，时空持续存在，而新特性在于时空呈现出广义上的分形结构：包括引力在内的作用力强度停止变化，你开始反复看到相同的图景，以及粒子相互作用的相同规则。这就是我所探索的渐进安全理论。若这种自相似领域存在，时空与其他场的涨落将足够稳定，使我们能运用经典的量子场论进行预测。
分形时空听起来很酷，但也显得颇为玄妙。为何这种设想具有合理性？
原因之一是对称性在众多自然理论中极为普遍。例如时空本身具有对称性：不存在特殊方向、特殊位置或特殊时刻。但我们确实拥有特殊尺度：世界在人类、细菌和电子眼中呈现不同面貌。这很奇特。因此我认为一个自然的假设是：在基础层面或许不存在特殊尺度，尺度之间可能存在对称性，即尺度对称性。
另一个原因是这是研究量子引力非常保守的路径。你采用实验室中从未失效的量子场论，然后追问：需要如何调整才能使其对所有尺度都具有预测力？据我们所知，引入尺度对称性是我们唯一能做的尝试。
如何验证这个理论？
首先需要验证量子场是否能以特定方式涨落，从而实现某种特殊平衡，使所有尺度呈现相同面貌。我们采用类似数学显微镜的方法：建立场及其相互作用的数学表征，计算场中涟漪的相互作用随观察尺度缩小的变化规律，继而寻找变化停止的临界点——我们称之为不动点。
你们找到不动点了吗？
我们拥有大量包含不动点的理想化简化理论案例。学界已在纯引力真空时空领域做了大量工作。实际上，大多数研究采用更简化的设定，仅考虑空间量子涨落而非时空共同涨落。尽管如此，数百篇论文已验证了变化停止的不动点确实稳固存在。
接下来的问题是：引入物质场会发生什么？这是我2013年作为博士后撰写的最早论文之一。我与合作者纳入所有已知物质场与作用力场，发现不动点依然存在——尽管是在仅考虑空间的特殊设定中。我们将论文命名为《物质至关重要》，这个醒目标题后来成了我的研究口号。
去年夏天，我们通过证明即使纳入所有已知场的相互作用方式（2013年论文未涉及这部分），不动点仍可能存在，从而完善了理论框架。这是首次审视完整图景。
目前这听起来主要是数学问题。物理意义如何体现？怎样验证我们的宇宙是否真的如此运行？
为验证理论，我们反转逻辑链条：不再通过缩小尺度在模型中寻找不动点的数学证据，而是假设不动点存在并放大尺度，追问：分形领域会对宏观世界产生何种物理影响？
会产生什么影响？
有充分迹象表明，这将迫使宏观世界呈现我们所见的面貌。2009年，米哈伊尔·沙波什尼科夫和克里斯托夫·韦特里希证明，从不动点放大尺度会迫使赋予质量的希格斯玻色子质量值精确符合我们的测量结果。
2018年，我与博士生亚伦·赫尔德经历了一个难忘时刻。前一年我们已发现不动点会迫使顶夸克质量接近测量值。当时我们正在研究该理论是否能解释顶夸克兄弟——底夸克的质量。在引力视角中它们本应是完全相同的双胞胎，因为引力不敏感于它们独特的量子特性，但实验却发现二者质量不同。
那个下午我记忆犹新。亚伦和我在办公室笔记本电脑前，通过Mathematica软件查看结果图表。我们清楚地看到存在一个预测误差在10%以内的匹配点。
在没有不动点的世界里，质量可以是任意值。但若存在不动点，引力与弱电力之间会产生特殊"对话"，而这场对话的结果就是这两种夸克必须具有实际观测到的不同质量。
至今我们仍称其为"天呐图表"。这个理论能以定量方式实现，实在令人震撼。
能否从不动点存在性预测所有粒子特性？
自2017年以来我们取得更多进展。我们成功将不动点与若干中微子特性联系起来，包括其诡异的轻质量——这项发现与另一个研究组同时独立获得。
但我们也清楚渐进安全理论远未达到解释一切的程度。例如真实质子质量虽与不动点相容，但也可能重达10倍或100倍。
不过据我们目前所知，尚无任何粒子特性与渐进安全理论相悖。若存在矛盾，我们便可证伪该理论。但现阶段所有数据都吻合，我们似乎能比以往多解释一些粒子特性及其相互作用。这或许是种进步，也让我感到欣慰。
若有人在1980年代顶夸克质量测量之前完成这项工作，你认为当今量子引力研究版图会是何种面貌？
我们完成了这些"回溯预测"，这很好。但有时我会想："唉，我们太迟了！"若当时有人做出真正的预测，或许渐进安全理论已成为量子引力的主流观点。
又或许他们能超越我们当前的认知，发现渐进安全理论失效的临界点。那样他们可能会毅然转向弦理论等更激进的理论，确信这种颠覆性转变是必要的。
那么你们能否对未知粒子做出真正的预测？
我们研究了各种暗物质模型，可以明确告知哪些设想可能与渐进安全理论不相容。
比如哪些？
实际上包括几种主流暗物质模型。例如弱相互作用大质量粒子的最简版本、多数人寻找的最简类轴子粒子，以及可能影响未来核钟的超轻暗物质——这些似乎都与分形世界不相容，尽管我们无法绝对排除它们。
那么你认为寻找WIMP、轴子和超轻暗物质的研究都是在浪费时间吗？
绝非如此！实验物理学家正勇敢推进研究，尽可能进行检验。这些检验可视为对渐进安全理论的测试。如果轴子实验明天就发现暗物质，反而会给我们的理论带来压力。因此这些探索间接揭示了时空的量子结构，我认为这是实验产生的绝妙副产品。
若有朝一日你能预测特定暗物质候选者并获得实验证实，这对其他量子引力理论意味着什么？
或许有人认为这会证伪其他理论，但事实未必如此。渐进安全理论可能与其他理论框架相容。或许在基础尺度上存在弦、圈或其他结构，但随着尺度放大，你会进入变化极其缓慢的领域，使其看似处于不动点。这种可能性意味着不同的量子引力研究方法或许并非竞争关系，而是对同一物理现实的不同视角。
听起来人们对任何时空理论都应保持谦逊。
在量子引力研究中，保持谦逊总是明智的。
英文来源：
Where Some See Strings, She Sees a Space-Time Made of Fractals
Introduction
Astrid Eichhorn spends her days thinking about how the laws of physics change at the tiniest scales.
Imagine zooming in closer and closer to the device on which you’re reading this article. Its apparently smooth screen quickly dissolves into a jiggling lattice of molecules, which in turn resolve into clouds of electrons buzzing around atomic nuclei. You dive into a nucleus, and atoms disappear as you enter the domain of quarks. It is here, where protons loom as large as solar systems, that Eichhorn’s explorations begin.
Past this point, the fundamental forces themselves shift. Electromagnetism and the weak interaction intensify, while the strong force slackens. The changes happen in a fairly regular way, so physicists have a good sense of how they work … until they don’t.
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. Gravity, a force that’s too weak to notice at the scale of atoms, grows strong in an erratic way. You’ve just crossed over into the “Planck” realm.
The apparent breakdown of particle physics at this scale has inspired some dramatic theories. 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. Others argue that at these smallest scales, space and time themselves must dissolve into structures such as loops.
Eichhorn and her colleagues are pursuing a different possibility. 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. New realms would stop appearing; the intensities of the forces would stabilize; and gravity would turn out to make perfect sense after all.
Eichhorn, a physicist at Heidelberg University in Germany, has over the last decade become a leading theorist investigating this idea, called asymptotic safety. In particular, Eichhorn has emphasized the importance of taking into account the ways in which matter affects space-time, and vice versa. “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.
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. 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. Quanta recently spoke with Eichhorn about these efforts. The interview has been condensed and edited for clarity.
What’s the big problem? If we treat gravity like the other forces at the smallest scales, what goes wrong?
So, the approach we use with most of the forces is called quantum field theory. It assumes the universe is full of quantum fields. Fields have ripples that manifest as pointlike particles. These particles move through a continuous space-time and interact via forces.
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.
Very roughly, for a well-understood force like electromagnetism, we need to consider fluctuations in the field at all scales. And these fluctuations never stop coming as you zoom in. They act like virtual particles with higher and higher energies. 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.
But when you try to add gravity, which Albert Einstein linked with the structure of space-time, the fluctuations become problematic. At shorter distances, the higher-energy virtual particles interact in new and different ways. We can’t account for these ever-changing effects, so quantum field theory fails to predict what will happen at those tiny scales.
What do physicists think this failure of quantum field theory is telling us?
It tells us that something new happens as we zoom in. And I would say there are roughly three lines of thinking as to what that might be.
One is that maybe quantum field theory breaks down, full stop. The objects are not points, in the way that we think of elementary particles as points. Instead, they become stringy. That’s string theory.
Another is that we need to remove the assumption that space-time is continuous. I take my glass of water, and it looks continuous to me, but fundamentally it’s atomic. Maybe it’s the same with space-time. This is the idea spelled out in loop quantum gravity, or in causal sets.
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. That’s the idea I’m pursuing, asymptotic safety. 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.
A fractal-like space-time sounds cool, but it also sounds pretty out there. Why is this a sensible thing to expect?
One reason is that symmetries are very common in many theories of nature. Space-time itself has symmetries, for instance. There are no special directions, no special places, and no special times. But we do have special scales: The world looks one way to humans, another way to bacteria, and yet another way to electrons. That’s peculiar. So I think it’s a natural assumption to say that at the fundamental level, maybe there are no special scales. Maybe there is a symmetry between scales, a scale symmetry.
Another is that this is a very conservative approach to quantum gravity. 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? And as far as we know, adding scale symmetry is the only thing we can do.
How can you test this idea?
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. 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. Then we look for a place where that change stops, a place we call a fixed point.
Have you found any?
We have tons of simplified examples of idealized theories with fixed points. The community at large has worked a lot on empty space-time, just pure gravity. 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. But nevertheless, people have tested this in literally hundreds of papers and found very robustly that this fixed point where things stop changing exists.
And then the next question to ask is: What happens when I throw in matter fields? This is one of my earliest papers that I wrote as a postdoc in 2013. 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. We gave the paper this catchy title, “Matter Matters,” and it became a bit of a slogan for me.
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. We have now looked at the complete picture for the first time.
So far, this sounds like mainly a math question. Where does the physics come in? How can you test whether our universe really works this way?
To test it, we turn the logic around. 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?
And what implications would it have?
We have good indications that it would force the macroscopic world to look a lot like the world we see. 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.
And in 2018, my Ph.D. student Aaron Held and I had a memorable moment. The previous year, we had already found that a fixed point would force the top quark to have close to the measured mass. And we were investigating whether it could also account for the mass of the top quark’s sibling, the bottom quark. 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.
I remember this afternoon distinctly. 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. We saw that indeed there is this point where the predictions match up to within 10%.
In a world with no fixed point, the masses could be anything. 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.
To this day we call it the OMG plot. It was just so mind-blowing to us that this idea really works out in a quantitative way.
Can you predict all particle properties from the existence of a fixed point?
We’ve made more progress since 2017. 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.
But we also know that asymptotic safety is quite far from explaining everything. The real proton mass is consistent with a fixed point, for instance, but it could also be 10 or 100 times as heavy.
As far as we can tell, though, there are no particle properties that are incompatible with asymptotic safety. If there were, we could rule the theory out. 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. That might be progress. That makes me happy.
If someone had done this work in the 1980s, before anyone had measured the mass of the top quark, what do you think the quantum gravity landscape would look like today?
We’ve made these “retrodictions,” and that’s nice. 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.
Or maybe they would have advanced beyond where we are now and found a point where asymptotic safety doesn’t work out. Then they might have abandoned it for strings and other exotic theories with a complete confidence that such a drastic move is necessary.
Well, are there any bona fide predictions you can make about unknown particles?
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.
Like what?
Several of the popular dark matter models, actually. 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.
So do you think hunters looking for WIMPs, axions, and ultralight dark matter are all wasting their time?
Definitely not! Experimentalists are bravely going forward and testing as much as they can. And those tests can be seen as tests of asymptotic safety. If an axion experiment finds dark matter tomorrow, that would actually put our theory under pressure. 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.
If you could predict a specific dark matter candidate someday and then someone found it, what would that mean for the other theories of quantum gravity?
You might think it would rule them out, but this is not necessarily the case. Asymptotic safety could be compatible with these other approaches. 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. That’s possible, and it means that distinct quantum gravity approaches may actually not be competitors, but rather different perspectives on the same physics.
It sounds like one should be humble about any picture of space-time.
In quantum gravity research, it’s always a good idea to be humble.