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百年相对论:一个等式为宇宙立法

A Century Ago, Einstein’s Theory of Relativity Changed Everything
百年相对论:一个等式为宇宙立法

PRINCETON, N.J. — By the fall of 1915, Albert Einstein was a bit grumpy.

新泽西普林斯顿——1915年秋天,阿尔伯特‧爱因斯坦的心情不太好。

And why not? Cheered on, to his disgust, by most of his Berlin colleagues, Germany had started a ruinous world war. He had split up with his wife, and she had decamped to Switzerland with his sons.

当然好不了。德国发动了一场毁灭性的战争,他的柏林同事大多在欢呼雀跃,这让他感到厌恶。他的妻子与他离异,而后带着他的儿子逃到了瑞士。

He was living alone. A friend, Janos Plesch, once said, “He sleeps until he is awakened; he stays awake until he is told to go to bed; he will go hungry until he is given something to eat; and then he eats until he is stopped.”

他现在是孤家寡人了。他的朋友雅诺什‧普雷施(Janos Plesch)曾说:“他会睡到没有人叫就不醒;醒着时,没有人叫就不去睡;没有人给他吃的他就一直饿着;没有人拦着,他就不停地吃。”

Worse, he had discovered a fatal flaw in his new theory of gravity, propounded with great fanfare only a couple of years before. And now he no longer had the field to himself. The German mathematician David Hilbert was breathing down his neck.

更糟的是,他在自己几年前大张旗鼓发表的引力新理论中,发现了一个致命缺陷。而如今他在这个领域已无法独领风骚,德国数学家大卫‧希尔伯特(David Hilbert)正对他穷追不舍。

So Einstein went back to the blackboard. And on Nov. 25, 1915, he set down the equation that rules the universe. As compact and mysterious as a Viking rune, it describes space-time as a kind of sagging mattress where matter and energy, like a heavy sleeper, distort the geometry of the cosmos to produce the effect we call gravity, obliging light beams as well as marbles and falling apples to follow curved paths through space.

于是,爱因斯坦回到了黑板前。1915年11月25日,他写下了那个支配寰宇的方程式。它仿佛古维京文字一般的简洁与神秘,把时空描述成一张松垮的床垫,物质与能量好似沉睡的人,扭曲了宇宙的几何形态,进而创造出我们称为引力的效应,迫使光线像弹珠或掉落的苹果那样,沿着弯曲的路径穿越空间。

This is the general theory of relativity. It’s a standard trope in science writing to say that some theory or experiment transformed our understanding of space and time. General relativity really did.

这就是广义相对论。科学文章所用的标准修辞会说,有些理论或实验彻底改变了我们对空间与时间的理解。广义相对论真的是这样。

Since the dawn of the scientific revolution and the days of Isaac Newton, the discoverer of gravity, scientists and philosophers had thought of space-time as a kind of stage on which we actors, matter and energy, strode and strutted.

自科学革命的发端和艾萨克‧牛顿发现万有引力以来,科学家与哲学家无不以为时空就像一座舞台,物质与能量如同演员,在上面高视阔步。

With general relativity, the stage itself sprang into action. Space-time could curve, fold, wrap itself up around a dead star and disappear into a black hole. It could jiggle like Santa Claus’s belly, radiating waves of gravitational compression, or whirl like dough in a Mixmaster. It could even rip or tear. It could stretch and grow, or it could collapse into a speck of infinite density at the end or beginning of time.

有了广义相对论之后,舞台本身一跃而起,参与了表演。时空可以弯曲、折叠、在死去的恒星周围把自己包覆起来,消失成一个黑洞。它可以像圣诞老人的肚皮一样抖动,放射出一波波的引力压缩,或是像食物搅拌器里的面团一样旋转。它甚至可以四分五裂。可以延伸扩大,或是在时间的起点或尽头,坍缩成一个有无限密度的小点。

Scientists have been lighting birthday candles for general relativity all year, including here at the Institute for Advanced Study, where Einstein spent the last 22 years of his life, and where they gathered in November to review a century of gravity and to attend performances by Brian Greene, the Columbia University physicist and World Science Festival impresario, and the violinist Joshua Bell. Even nature, it seems, has been doing its bit. Last spring, astronomers said they had discovered an “Einstein cross,” in which the gravity of a distant cluster of galaxies had split the light from a supernova beyond them into separate beams in which telescopes could watch the star exploding again and again, in a cosmic version of the movie “Groundhog Day.”

科学家已为广义相对论点了一整年的生日蜡烛,在普林斯顿高等研究院(Institute for Advanced Study)这里也不例外。爱因斯坦就在这座研究院里度过了他人生最后的22载光阴。11月,科学家聚在这里回顾了引力理论百年来的发展,还观赏了哥伦比亚大学物理学家、世界科学节主持人布赖恩·格林(Brian Greene)和小提琴家约书亚‧贝尔(Joshua Bell)的表演。就连自然界都好像出了一份力。今年春天,天文学家称他们发现了一个“爱因斯坦十字”,也就是某个遥远星簇的引力将一个超新星发出的光分成了几束,透过望远镜看来,那颗星星就像在不断反复地爆炸,仿若在上演一部宇宙版的《偷天情缘》(Groundhog Day)。

Hardly anybody would be more surprised by all this than Einstein himself. The space-time he conjured turned out to be far more frisky than he had bargained for back in 1907.

对于这一切,几乎没人会比爱因斯坦本人更惊讶。他所描述的时空,远比他自己1907年时所预料的更调皮。

It was then — perhaps tilting too far back in his chair at the patent office in Bern, Switzerland — that he had the revelation that a falling body would feel weightless. That insight led him to try to extend his new relativity theory from slip-siding trains to the universe.

就是在那年,他领悟到,下落的物体或许会感到失重——可能他当时在瑞士伯尔尼专利局的椅子上,向后仰得太多了。这个发现促使他尝试把新提出的相对论,从发生侧偏的火车,推广到整个宇宙。

According to that foundational theory, now known as special relativity, the laws of physics don’t care how fast you are going — the laws of physics and the speed of light are the same. Einstein figured that the laws of physics should look the same no matter how you were moving — falling, spinning, tumbling or being pressed into the seat of an accelerating car.

根据现在被称作狭义相对论的基础理论,物体运动的速度不影响物理定律的适用,光速和物理定律都是一样的。爱因斯坦认为,不管人如何移动——坠落、旋转、打滚或是被摁到一辆正在加速的汽车的座位上,物理定律应该是一样的。

One consequence, Einstein quickly realized, was that even light beams would bend downward and time would slow in a gravitational field. Gravity was not a force transmitted across space-time like magnetism; it was the geometry of that space-time itself that kept the planets in their orbits and apples falling.<-->纽约时报中英文网 http://www.qqenglish.com<-->

爱因斯坦很快便意识到,其中一个后果是,在引力场里,即便是光束也会向下弯曲,时间也会变慢。引力不是一种可以像磁力那样跨时空传输的力。正是时空本身的几何结构,让行星停留在各自的轨道上,让苹果落到地上。

It would take him another eight difficult years to figure out just how this elastic space-time would work, during which he went from Bern to Prague to Zurich and then to a prestigious post in Berlin.

他又花了艰苦卓绝的八年时间,才弄明白这个弹性时空的运行原理。在此期间,他先是从伯尔尼搬到布拉格,后来又去了苏黎世,最后在柏林得到了一个颇具声望的职位。

In 1913, he and his old classmate Jerome Grossmann published with great fanfare an outline of a gravity theory that was less relative than they had hoped. But it did predict light bending, and Erwin Freundlich, an astronomer at the Berlin Observatory, set off to measure the deflection of starlight during a solar eclipse in the Crimea.

1913年,他和老同学耶罗默·格罗斯曼(Jerome Grossmann)发表了一篇备受关注的引力理论的概要,但该理论的相对论特性不及他们的预期。但这个理论的确预言了光的弯曲。柏林天文台(Berlin Observatory)的天文学家埃尔温·弗罗因德利希(Erwin Freundlich)动身前往克里米亚,去观测日食期间星光的折射幅度。

When World War I started, Freundlich and others on his expedition were arrested as spies. Then Einstein discovered a flaw in his calculations.

一战开始时,弗罗因德利希和团队里的其他人,被当做间谍抓了起来。后来,爱因斯坦在自己的计算中发现了一个缺陷。

“There are two ways that a theoretician goes astray,” he wrote to the physicist Hendrik Lorentz. “1) The devil leads him around by the nose with a false hypothesis (for this he deserves pity) 2) His arguments are erroneous and ridiculous (for this he deserves a beating).”

“理论家出错有两种情况,”他给物理学家昂德里克·洛伦茨(Hendrik Lorentz)写信说。“1) 魔鬼用一个错误的假说牵着他的鼻子走(这种情况值得同情);2) 他的论证是错误、荒谬的(这种情况该打)。”

And so the stage was set for a series of lectures to the Prussian Academy that would constitute the final countdown on his quest to grasp gravity.

于是,在普鲁士科学院做一系列讲座的条件已经出现了。这些讲座是他为攻克引力奥秘而进行的探索中最后的倒计时。

A Breakthrough Moment

突破的时刻

Midway through the month, he used the emerging theory to calculate a puzzling anomaly in the motion of Mercury; its egg-shaped orbit changes by 43 seconds of arc per century. The answer was spot on, and Einstein had heart palpitations.

当月中旬,他用新理论计算了水星在运动中出现的一个令人费解的反常现象。水星的椭圆形轨道角度,每过一个世纪就会改变43秒。答案完全正确,爱因斯坦心跳加速。

The equation that Einstein wrote out a week later was identical to one that he had written in his notebook two years before but had abandoned.

一周后,爱因斯坦写下了一个等式。它和他两年前写在笔记本里,但后来又放弃了的那个等式一模一样。

On one side of the equal sign was the distribution of matter and energy in space. On the other side was the geometry of the space, the so-called metric, which was a prescription for how to compute the distance between two points.

等号的一边是物质和能量在空间中的分布。另一边是空间的几何结构,即所谓的度规。度规是指计算两点之间距离的方式。

As the Princeton physicist John Wheeler later described it, “Space-time tells matter how to move; matter tells space-time how to curve.” Easy to say, but hard to compute. The stars might be actors on a stage set, but every time they moved, the whole stage rearranged itself.

正如普林斯顿大学物理学家约翰·惠勒(John Wheeler)后来所说,“时空告诉物质如何移动;物质告诉时空如何弯曲。”说起来容易,计算起来难。各个恒星可能是舞台背景上的演员,但随着它们的每次运动,整个舞台都会发生变化。

It wasn’t long before Einstein received his first comeuppance.

不久后,爱因斯坦遭遇了第一个打击。

In December 1915, he received a telegram from Karl Schwarzschild, a German astrophysicist serving at the front in the war, who had solved Einstein’s equation to describe the gravitational field around a solitary star.

1915年12月,他收到了在战场前线服役的德国天体物理学家卡尔·施瓦茨希尔德(Karl Schwarzschild)发来的电报。施瓦茨希尔德解开了爱因斯坦用来描述一个孤星周围的引力场的方程。

One strange feature of his work was that at a certain distance from the star — to be known forever as the Schwarzschild radius — the equations would go kerblooey.

他的解有个奇怪的特性:当与恒星达到一定距离时——被称为史瓦西半径——这个方程就会坍塌。

“If this result were real, it would be a true disaster,” Einstein said. This was the beginning of black holes.

“如果结果是真的,这将是一场真正的灾难,”爱因斯坦说。这就是黑洞的开始。

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That Einstein’s equations could be solved at all for a single star baffled him. One of his guiding lights had been the Austrian physicist and philosopher Ernst Mach, who taught that everything in the universe was relative. Einstein took Mach’s Principle, as he called it, to mean that it should be impossible to solve his equations for the case of a solitary object.

让他感到困惑的是,爱因斯坦的方程式针对一个单一的恒星能否得解。奥地利物理学家、哲学家恩斯特·马赫(Ernst Mach)是爱因斯坦的指路明灯之一,马赫教导称,宇宙里的一切都是相对的。爱因斯坦称之为马赫原理,他认为这个原理意味着对于单独的物体而言,他的方程式不可能得到解答。

“One can express it as a joke,” he told Schwarzschild. “If all things were to disappear from the world, then according to Newton Galilean inertial space remains. According to my conception, however, nothing is left.”

“大家可以说这是个笑话,”他告诉史瓦西。“如果所有东西都将从这个世界消失,根据牛顿和伽利略的理论,惯性空间仍然存在。然而,按照我的想法,什么也留不下。”

And yet here was a star, according to his equations, bending space all by itself, a little universe in a nutshell.

可是,根据他的方程式,有一颗恒星在完全凭借自己的力量扭曲空间,简单地说就是一个小宇宙。

Designing a Universe

设计一个宇宙

Like most of his colleagues at the time, Einstein considered the universe to consist of a cloud of stars, the Milky Way, surrounded by vast space. What was beyond? Was the universe infinite? And if so, what stopped a star from drifting so far that it would have nothing to relate to?

就像他当时的大多数同事一样,爱因斯坦认为宇宙由大量恒星、银河及周围的广阔空间组成。宇宙之外有什么?宇宙是无限的吗?如果是这样的话,什么能阻止一颗恒星漂移到与所有物体脱离联系的距离?

To avoid such problems, Einstein set out in 1917 to design a universe without boundaries. In his model, space is bent around to meet itself, like the side of a tin can.

为了避免此类问题,爱因斯坦在1917年建立了无限宇宙模型。在他设立的模型中,空间就像锡罐的侧面一样,能够弯曲触碰到自己。

“I have committed another suggestion with respect to gravitation which exposes me to the danger of being confined to the nut house,” he confided to a friend.

他向一名朋友倾诉,“我提出另一个有关引力的建议,这使我面临被关进疯人院的风险。”

This got rid of the need for troublesome boundaries. But this universe was unstable, and the cylinder would collapse if something didn’t hold its sides apart.

这就不需要设置令人烦恼的边界了。但这个宇宙并不稳定,如果某种东西没有将两边撑住,这个圆柱就会坍缩。

That something was a fudge factor added to the equations Einstein called the cosmological constant. Physically, this new term, denoted by the Greek letter lambda, represented a long-range repulsive force.

这种东西就是爱因斯坦在自己的公式中插入的一种被他称为“宇宙常数”的容差系数。从物理学来看,这个由希腊字母“兰布达”(λ)指代的新名词代表着远距离的排斥力。

The happy result, Einstein thought, was a static universe of the type nearly everybody believed they lived in and in which geometry was strictly determined by matter.

爱因斯坦认为,皆大欢喜的结果就是一个静态宇宙,几乎所有人都认为他们生活在这样一个宇宙中,其中的几何形态完全由物质决定。

But it didn’t last. Willem de Sitter, a Dutch astronomer, came up with his own solution describing a universe that had no matter at all and was flying apart.

但这没能站住脚。荷兰天文学家威廉·德西特(Willem de Sitter)提出了自己的解答,他描述了一个根本不存在物质且正在飞散的宇宙。

“It would be unsatisfactory, in my opinion,” Einstein grumbled, “if a world without matter were possible.”

“我认为,如果说一个没有物质的世界是可能存在的,”爱因斯坦抱怨称。“这是无法令人满意的。”

And then Edwin Hubble discovered that the universe really was expanding.

后来,埃德温·哈勃(Edwin Hubble)发现,宇宙确实在不断膨胀。

If the cosmological constant couldn’t keep the universe still, then forget about it and Mach’s Principle, Einstein said. “It dates back to the time in which one thought that the ‘ponderable bodies’ are the only physically real entities,” he later wrote to the British cosmologist Felix Pirani.

爱因斯坦表示,既然这个宇宙常数不能使宇宙保持静态,那就别考虑它以及马赫原理了。他后来给英国宇宙学家费利克斯 ·皮拉尼(Felix Pirani)写信称,“这可以追溯到人们认为‘有重量的物质’是唯一真实存在的实体的时候。”

But it was too late. Quantum mechanics soon invested empty space with energy. In 1998 astronomers discovered that dark energy, acting just like the cosmological constant, seems to be blowing space-time apart, just as in de Sitter’s universe.

但为时已晚。量子力学很快就表明,真空中存在很多能量。1998年,天文学家发现暗能量就像宇宙常数一样,似乎将空间与时间分离,与德西特描述的宇宙相似。

In fact, most cosmologists agree today that not quite all motion is relative and that space-time does have an existence independent of matter, though it is anything but static and absolute. The best example are gravitational waves, ripples of compression and stretching speeding through empty space at the speed of light.

实际上,大多数宇宙学家如今同意这个观点,即并不是所有运动都是相对的,时空的确独立于物质存在,尽管它不是静态和绝对的。最好的例子就是引力波——以光速超速穿过真空的一波波引力压缩和伸展。

Einstein was back and forth on this. In 1916, he told Schwarzschild they did not exist, then published a paper saying they did. In 1936, he and his assistant did the same flip-flop again.

爱因斯坦在整个问题上摇摆不定。他在1916年告诉史瓦西,引力波并不存在,后来又发表论文称它存在。他和助手在1936年再次改变观点。

Nobody said this was easy, even for Einstein.

没人认为这很简单,即使是对爱因斯坦来说。

He set out to do one thing, namely make all motion relative, Michel Janssen, a science historian at the University of Minnesota, told a Princeton gathering this month. He failed, but in the process succeeded in doing something very interesting, unifying the effects of acceleration and gravity.

明尼苏达大学(University of Minnesota)科学史学家米歇尔·詹森(Michel Janssen)本月在普林斯顿大学参加聚会时表示,爱因斯坦开始做一件事情,就是使所有运动成为相对的。他失败了,但他在这个过程中成功地做了一些有趣的事情,将加速度与引力的效应统一起来。

The story goes to show, he said, that Bob Dylan was right when he sang “there’s no success like failure,” but wrong that “failure is no success at all.”

他表示,这个故事说明,鲍勃·迪伦(BobDylan)那句“没有像失败这样的成功”是对的,但“失败根本不是成功”是错误的。

Einstein’s greatest success came in 1919, when Arthur Eddington did the experiment that Freundlich had set out to do, and ascertained that lights in the heavens were all askew during an eclipse, bent by the sun’s dark gravity, just as Einstein had predicted.

爱因斯坦在1919年取得了巨大成功,当时亚瑟·爱丁顿(Arthur Eddington)做了弗罗因德利希之前开始做的实验,他发现,正如爱因斯坦预测的那样,出现日食时,天空中的光线在太阳的暗引力下发生弯曲,出现偏斜。

Asked what he would have done if general relativity had failed, Einstein said, “Then I would have been sorry for the dear Lord. The theory is correct.”

被问及如果广义相对论失败了,他会做什么时,爱因斯坦曾说,“那我会替敬爱的主感到难过。这个理论是正确的。”

And still the champ.

而且直到今天还是最棒的。

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