当波士顿或斯德哥尔摩的气温徘徊在0摄氏度上下时，我们得到的天气预报往往是不确定的：下雨还是下雪完全依赖最终的气温是在零上还是零下。其间的差别是非常大的——前者不过是一场阵雨，而后者却可能造成城市灾害，因为雪占据的体积大约是雨的十倍，并且不像雨水那样容易流走。
When the temperature hovers near 32 degrees Fahrenheit in Boston, or 0 degrees Celsius in Stockholm, we get unstable weather reports: There may be rain or snow, depending on exactly where the temperature lands. That can make the difference between a passing shower and acity-stopping calamity, since snow occupies around ten times the volume of rain and doesn’t flow away so easily.
对我们这些常年在寒冷气候中生活的人来说，这种不确定性可谓司空见惯。然而仔细想想，它其实是很奇怪的：如果不是借助于长期的生活经验，我们通常会预期细小改变只会对结果产生微弱的影响。
Those of us who live in cold climates are used to this uncertainty, but on reflection it is strange. If we didn’t know better from experience, we might expect that a small change in conditions would lead to a small change in results.
当温度经过某个临界值时水突然会变成冰。这类现象被物理学家称之为相变，结冰只是一个典型例子。 在20世纪，如何理解相变一直是基础物理面临的一个让人头疼的挑战，它引导物理学家们在众多领域获得了深邃且崭新的洞察——小到夸克的性质、大到宇宙的演化。
The abrupt shift from water to iceas the temperature goes through a specific value is a familiar example of a much wider category that physicists call phase transitions. Phase transitions stood as a vexing challenge to the fundamental understanding of physics well into the 20th century, and they led physicists to develop deep new insights about many subjects, from the properties of quarks to the evolution of the universe.
最简单的相变与磁铁相关。我们所熟悉的条形磁铁或马蹄形磁铁，它们的磁性源于其内部做自旋运动的电子的排列。每个电子好比一个微型的地球，它的磁场的南北极之间的连线正好是自旋旋转轴。 当所有电子的旋转轴都沿着同一个方向排列时，它们的磁场相加增强产生磁引力。
One of the easiest phase transitions to think about involves magnets. The magnetism of a familiar bar or horseshoe magnet arises from the alignment of the spinning electrons within them. Each electron acts like a miniature Earth, with a magnetic field whose poles are aligned with the axis of rotation. When the axes align, those fields can add together, creating magnetic attraction.
如果你加热磁铁，那么电子的自旋轴就会不断摇动，使它们难以形成有序的排列，导致磁性在温度足够高时消失。这种磁性的改变跟冰与水之间的转变一样，是在某个温度下突然发生的。比如，磁铁矿的磁性大约在570摄氏度的时候突然消失。铁磁性消失的临界温度被称为居里温度（以皮埃尔·居里——玛丽·居里的丈夫、杰出物理学家、诺贝尔奖得主——的名字命名）。
But if you heat the magnet, the spins of the electrons get agitated, making alignment difficult, and at a high enough temperature, the magnetism disappears. This transition, like the transition between ice and water, takes place abruptly at 570 degrees Celsius in magnetite, which is known as the Curie temperature (after Pierre Curie—Marie’s husband, a remarkable physicist and Nobel Prize winner in his own right).
我们如何理解这种突然的改变呢？粗略地说，当我们加热磁铁时，电子自旋轴的摆动越来越厉害，从而越来越难形成相互锁定的整齐排列。当一个电子的自旋运动脱离束缚获得自由时，它就不再帮助邻近的电子自旋保持排列整齐，使得下一个电子的自旋更容易挣脱束缚，以此类推。也就是说，一旦能量达到了某个临界值，自旋的解放就不可避免了。
加热磁铁
How can we understand that abrupt change? Roughly speaking, as we heat up the magnet and the spins of the electrons are increasingly jostled, the lockstep alignment among them becomes less strict. When one spin breaks free, and can stay free, it no longer helps to align its neighbors. That makes it easier for the next spin to break free, and so forth. Once there is a critical amount of energy available, that liberating transition is inevitable.
今晨波士顿的气温降到了零度以下。看着阳光照在雪上反射出的耀眼光芒，我任由脑海里关于相变的思绪飞翔，最后停留在著名的鸭兔错觉上：面对这个可鸭可兔的图形，我们的大脑神经元必须同时达成一致，来决定我们看到的到底是鸭子还是兔子——虽然这两种选择都是合理的。当选择改变时，我们看到的图像就突然改变了。
鸭兔错觉图
Inspired today by the sun’s dazzling reflectionin the snow—for that’s the way the temperature landed this morning in Boston—I let my thoughts of phase transitions expand, and my mind’s eye rested on the famous optical illusion of the rabbit/duck. With such dual images, our brain’s neurons must come to agreement collectively, deciding between alternative interpretations that both make good sense. When the choice changes, it changes abruptly.
通过类比和隐喻，我们可以进一步地拓展相变的概念。例如，有时候我们会看到少数人对传统认知发起的挑战会引发整体舆论的突然变化。
And we can extend the idea of phase transitions even further through analogy and metaphor. For instance, we sometimes see sudden changes in the climate of opinion initiated by a few defectors from conventional wisdom.
在20世纪，物理学家们已经理解了简单材料中因温度变化所导致的相变。而当今的物理前沿则是在动力驱动的物理系统中研究因为驱动的微小变化所导致的系统性质的巨大变化。例如，当温度升高时，地球上的冰逐渐融化，使被反射的太阳热量减少，这又进一步加剧温度的升高…… 这也许会导致一个剧烈的灾难性的改变。所以，我很珍爱冬天的雪，庆幸还能够享受有雪的冬天。
Twentieth-century physics mastered phase transitions that occur in simple materials, as a function of temperature. Drastic changes in the behavior of dynamically driven systems, in response to small changes in the drive, are today’s frontier of research. As the Earth’s ice melts in response to rising temperatures, for instance, there is less reflection of the sun’s heat, which encourages a further rise in temperatures, and so on, perhaps toward a dramatic and catastrophic change. So I relish the winter snow, glad that there still are snowy winters to enjoy.
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。因在夸克粒子理论（强作用）方面所取得的成就，他在2004年获得了诺贝尔物理学奖。
本文英文原题为When Small Changes Make a Big Difference，中文翻译版经授权转载自「蔻享科普」。
撰文 | 弗兰克·维尔切克（Frank Wilczek）（麻省理工学院教授、2004年诺贝尔奖得主）
翻译 | 胡风、梁丁当
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