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撰文 | Frank Wilczek

翻译 | 胡风、梁丁当

中文版

4月7日，《自然》（Nature）和《物理评论快报》（Physical Review Letters）杂志分别刊登了关于缪子磁矩的最新实验测量结果与理论计算结果，轰动了整个物理学界。这项研究由来自全球多个研究机构的众多物理学家通过多年的合作完成，其精度达到了十亿分之一。或许你会觉得，进行如此高精度的测量与计算，在科学层面上没啥新意。其实不然。在这个过程中，可能有奇迹出现。

缪子是一种基本粒子。它具有一些与人们熟悉的电子类似的基本性质。比如，它们带有完全相同的电荷。但二者又有两点很大的区别：缪子比电子重约200倍，而且很不稳定，其平均寿命只有约2微秒。

相比其他奇异粒子，对缪子的探测异常容易。它能在高能加速器中大量产生。尽管一微秒听上去很短，但是快速运动的缪子在消失前能够穿越很长的距离，从而留下易被探测的轨迹。当人们在谈到缪子特定的质量和磁矩时，往往觉得理所当然。但在实际测量中，我们需要对数百万个不同的粒子进行取样，而测到的数据居然几乎相同，这个事实是极为深刻与神奇的。迄今为止的精密测量让我们更加确信，所有的缪子，就像所有电子一样，具有完全相同的性质。

缪子永远在旋转。正如物理学家所说，它们有“自旋”，这是解释它们许多行为的关键。如果缪子处于磁场中，它的旋转轴就会绕磁场旋转，类似于一个倾斜的陀螺绕着竖直方向旋转。这种类似陀螺的运动叫做进动。缪子在磁场中的进动率是磁场强度、一些已知的物理常数和一个被称为磁矩的物理量的乘积。

对缪子的磁矩进行粗略的估计是比较容易的（如果你学了一学期相对论量子场论的话）。但是，如果要达到超过千分之一的精度，就必须引入被称为虚粒子的奇异量子效应，更别提超过十亿分之一了。根据量子理论，看上去虚无的空间实则充满了生机——各种不同的粒子在极短的时间内产生与湮灭。这些所谓的虚粒子寿命太短，所以无法被探测器直接记录下来，但它们却会改变真实粒子的行为。

很多虚粒子在空间中分布得很稀疏。要精确地计算它们对缪子磁矩的影响，是一项耗时而复杂的工作。但经过几十年的发展，物理学家已经非常精通此道。而其他的虚粒子，如夸克、反夸克和胶子，却完全不同。它们在空间中密集分布，会产生强烈的相互作用。我们并不擅长计算它们的影响，这个瓶颈制约了目前理论预测的精度。

目前，解决这个问题的办法通常有两个。老办法是从真实粒子的实验数据进行外推，来估算需要的信息。新方法则是用超级计算机进行人力无法完成的第一性原理计算。这两种方法照理应该得到相同的结果，但目前它们并不一致。计算机算出来的缪子磁矩与最新的实验测量一致，而利用实验数据外推得到的结果却有十亿分之一的差异。

这个差异若被证实，就意味着有一种迄今为止未被发现的粒子在起作用，崭新的物理现象可能就在眼前。这个可能性太让人兴奋了，物理学家们蜂拥而上，提出各种猜想以抢占先机。新的实验结果刚一公布，一夜之间就冒出了几十个相互竞争的提议。物理学家知道将要宣布一个新的发现，所以有备而来。但正如计算机的结果所显示的那样，这个“差异”仍然有可能只是空欢喜一场。

但无论如何，对于物理学家来说，这是一个奇迹、一件幸事，因为我们竟然能够在如此微小的差异上发挥我们的聪明才智。精度所传达的最深刻的信息是：物体的真实世界和数学构造的理想世界，在令人难以置信的精度上，是同一个世界。

英文版

On April 7, the physics world was startled into glorious confusion by two announcements of a new measurement and a new calculation of the magnetic moment of the muon, published in the journals Physical Review Letters and Nature. The new results, accurate to the level of one part per billion, are the product of multiyear collaborations by large groups of physicists at institutions around the world. You might think that the work of making such precise measurements and calculations is as dull as science gets, but it can make magic happen.

Muons are elementary particles that in several fundamental ways resemble the more familiar electrons; for example, both carry exactly the same amount of electric charge. But there are two big differences: Muons are roughly 200 times heavier than electrons, and they are unstable, with a mean lifetime of roughly two microseconds.

As exotic particles go, muons are uncommonly user-friendly. They are easy to produce in large numbers at high-energy accelerators. And though a microsecond may not sound like a long time, fast-moving muons can travel a long way before they expire, leaving easily detectable tracks. Though it’s often taken for granted, the fact that we can talk about "the" mass and "the" magnetic moment of the muon, when in practice we sample millions of different particles, is both profound and amazing. Precision measurements so far reinforce our confidence that all It is painstaking and intricate work to calculate the influence of virtual particles precisely, but after decades of practice, physicists have gotten very good at it. muons, like all electrons, have exactly the same properties.

Muons are forever rotating—as physicists say, they have "spin"—which is key to many aspects of their behavior. If a muon is exposed to a magnetic field, its rotation axis circles around that field’s direction, similarly to how the axis of a tilted, spinning top circles around the vertical. This top-like motion is called precession. The rate of a muon's precession in a magnetic field is equal to the product of the strength of the magnetic field, some known physical constants and a number called the magnetic moment.

Making a rough prediction of the magnetic moment of a muon is child's play (for children who've taken a semester of relativistic quantum field theory). But to make it accurate beyond one part in a thousand, let alone one part in a billion, you've got to bring in the weird quantum effect known as virtual particles. According to quantum theory, apparently empty space is actually alive with activity, as particles of all different kinds briefly fluctuate into and out of existence. These so-called virtual particles are too fleeting to register directly in practical detectors, but they modify the calculated behavior of real particles.

Many kinds of virtual particles are distributed sparsely in space. It is painstaking and intricate work to calculate their influence on the muon's magnetic moment precisely, but after decades of practice, physicists have gotten very good at it. Other virtual particles like quarks, antiquarks and gluons are a different story. They are dense in space and they interact strongly with one another. We are nowhere near so skillful at calculating their effects, and at present this bottleneck limits the precision of theoretical predictions.

Two different approaches to this problem are currently on the market. The older approach extrapolates from data about real particles to estimate the required information. The newer approach uses supercomputer technology to do superhuman, first-principles calculations. Those two approaches should give the same answer, but presently they don't. The computer calculations give an answer for the muon magnetic moment that agrees with the new experimental measurement, while the data extrapolations leave a part-in-a-billion discrepancy.

A genuine discrepancy would signal that there are hitherto undiscovered particles at work. If so, other new phenomena could be right around the corner. That tantalizing possibility has triggered a gold rush of speculation and stake-claiming by physicists. Immediately after the new experimental result was announced, dozens of rival proposals materialized overnight. Physicists knew an announcement was coming, and they were prepared. But the "discrepancy" still might turn out to be fool’s gold, as the computer calculations suggest.

In any case, it's a miracle and a blessing for physicists that we get to exercise our wits over the mere possibility of such minute discrepancies. For the deepest message of precision is that the real world of physical objects and the ideal world of mathematical constructions turn out, with mind-boggling accuracy, to be the same world.

Frank Wilczek

弗兰克·维尔切克是麻省理工学院物理学教授、量子色动力学的奠基人之一。因发现了量子色动力学的渐近自由现象，他在2004年获得了诺贝尔物理学奖。

本文经授权转载自微信公众号“蔻享学术”。