百年相對論：一個等式為宇宙立法

(Ajin 開口)

被選舉，軍宅，換柱，惡馬，笨豬，無罪毒油，頂新 - - - - 這些名詞包圍著的台灣，完全渾然不知，今年就是把人與神之間的距離，拉近一小公分的「相對論」之發表，100週年！

愛因斯坦於1915 11 25 在Princeton 發表相對論，迄今一百週年。這是人類何等偉大的文明路標！

然而，至今人類還沒有進步到知曉如何運用這偉大發現於現實生活當中。所以到今天，俺還是覺得 "抽水馬桶" 依然是頂著冠冕保持王座。

俺也在此也特地向這位頂著小圓帽的老可 -- 愛·亞伯特 (Albert) 彎幾個腰！

http://cn.nytimes.com/science/20151125/c25relativity/zh-hant/

百年相對論：一個等式為宇宙立法

DENNIS OVERBYE 2015年11月25日

新澤西普林斯頓——1915年秋天，阿爾伯特‧愛因斯坦的心情不太好。

當然好不了。德國發動了一場毀滅性的戰爭，他的柏林同事大多在歡呼雀躍，這讓他感到厭惡。他的妻子與他離異，而後帶着他的兒子逃到了瑞士。

他現在是孤家寡人了。他的朋友雅諾什‧普雷施(Janos Plesch)曾說：「他會睡到沒有人叫就不醒；醒着時，沒有人叫就不去睡；沒有人給他吃的他就一直餓着；沒有人攔着，他就不停地吃。」

更糟的是，他在自己幾年前大張旗鼓發表的引力新理論中，發現了一個致命缺陷。而如今他在這個領域已無法獨領風騷，德國數學家大衛‧希爾伯特(David Hilbert)正對他窮追不捨。

於是，愛因斯坦回到了黑板前。1915年11月25日，他寫下了那個支配寰宇的方程式。它彷彿古維京文字一般的簡潔與神秘，把時空描述成一張松垮的床墊，物質與能量好似沉睡的人，扭曲了宇宙的幾何形態，進而創造出我們稱為引力的效應，迫使光線像彈珠或掉落的蘋果那樣，沿着彎曲的路徑穿越空間。

這就是廣義相對論。科學文章所用的標準修辭會說，有些理論或實驗徹底改變了我們對空間與時間的理解。廣義相對論真的是這樣。

自科學革命的發端和艾薩克‧牛頓發現萬有引力以來，科學家與哲學家無不以為時空就像一座舞台，物質與能量如同演員，在上面高視闊步。

有了廣義相對論之後，舞台本身一躍而起，參與了表演。時空可以彎曲、摺疊、在死去的恆星周圍把自己包覆起來，消失成一個黑洞。它可以像聖誕老人的肚皮一樣抖動，放射出一波波的引力壓縮，或是像食物攪拌器里的麵糰一樣旋轉。它甚至可以四分五裂。可以延伸擴大，或是在時間的起點或盡頭，坍縮成一個有無限密度的小點。

科學家已為廣義相對論點了一整年的生日蠟燭，在普林斯頓高等研究院(Institute for Advanced Study)這裡也不例外。愛因斯坦就在這座研究院里度過了他人生最後的22載光陰。11月，科學家聚在這裡回顧了引力理論百年來的發展，還觀賞了哥倫比亞大學物理學家、世界科學節主持人布賴恩·格林(Brian Greene)和小提琴家約書亞‧貝爾(Joshua Bell)的表演。就連自然界都好像出了一份力。今年春天，天文學家稱他們發現了一個「愛因斯坦十字」，也就是某個遙遠星簇的引力將一個超新星發出的光分成了幾束，透過望遠鏡看來，那顆星星就像在不斷反覆地爆炸，仿若在上演一部宇宙版的《偷天情緣》(Groundhog Day)。

對於這一切，幾乎沒人會比愛因斯坦本人更驚訝。他所描述的時空，遠比他自己1907年時所預料的更調皮。

就是在那年，他領悟到，下落的物體或許會感到失重——可能他當時在瑞士伯爾尼專利局的椅子上，向後仰得太多了。這個發現促使他嘗試把新提出的相對論，從發生側偏的火車，推廣到整個宇宙。

根據現在被稱作狹義相對論的基礎理論，物體運動的速度不影響物理定律的適用，光速和物理定律都是一樣的。愛因斯坦認為，不管人如何移動——墜落、旋轉、打滾或是被摁到一輛正在加速的汽車的座位上，物理定律應該是一樣的。

愛因斯坦很快便意識到，其中一個後果是，在引力場里，即便是光束也會向下彎曲，時間也會變慢。引力不是一種可以像磁力那樣跨時空傳輸的力。正是時空本身的幾何結構，讓行星停留在各自的軌道上，讓蘋果落到地上。

他又花了艱苦卓絕的八年時間，才弄明白這個彈性時空的運行原理。在此期間，他先是從伯爾尼搬到布拉格，後來又去了蘇黎世，最後在柏林得到了一個頗具聲望的職位。

1913年，他和老同學耶羅默·格羅斯曼(Jerome Grossmann)發表了一篇備受關注的引力理論的概要，但該理論的相對論特性不及他們的預期。但這個理論的確預言了光的彎曲。柏林天文台(Berlin Observatory)的天文學家埃爾溫·弗羅因德利希(Erwin Freundlich)動身前往克里米亞，去觀測日食期間星光的折射幅度。

一戰開始時，弗羅因德利希和團隊里的其他人，被當做間諜抓了起來。後來，愛因斯坦在自己的計算中發現了一個缺陷。

「理論家出錯有兩種情況，」他給物理學家昂德里克·洛倫茨(Hendrik Lorentz)寫信說。「1) 魔鬼用一個錯誤的假說牽着他的鼻子走（這種情況值得同情）；2) 他的論證是錯誤、荒謬的（這種情況該打）。」

於是，在普魯士科學院做一系列講座的條件已經出現了。這些講座是他為攻克引力奧秘而進行的探索中最後的倒計時。

突破的時刻

當月中旬，他用新理論計算了水星在運動中出現的一個令人費解的反常現象。水星的橢圓形軌道角度，每過一個世紀就會改變43秒。答案完全正確，愛因斯坦心跳加速。

一周後，愛因斯坦寫下了一個等式。它和他兩年前寫在筆記本里，但後來又放棄了的那個等式一模一樣。

等號的一邊是物質和能量在空間中的分佈。另一邊是空間的幾何結構，即所謂的度規。度規是指計算兩點之間距離的方式。

正如普林斯頓大學物理學家約翰·惠勒(John Wheeler)後來所說，「時空告訴物質如何移動；物質告訴時空如何彎曲。」說起來容易，計算起來難。各個恆星可能是舞台背景上的演員，但隨着它們的每次運動，整個舞台都會發生變化。

不久後，愛因斯坦遭遇了第一個打擊。

1915年12月，他收到了在戰場前線服役的德國天體物理學家卡爾·施瓦茨希爾德(Karl Schwarzschild)發來的電報。施瓦茨希爾德解開了愛因斯坦用來描述一個孤星周圍的引力場的方程。

他的解有個奇怪的特性：當與恆星達到一定距離時——被稱為史瓦西半徑——這個方程就會坍塌。

「如果結果是真的，這將是一場真正的災難，」愛因斯坦說。這就是黑洞的開始。

讓他感到困惑的是，愛因斯坦的方程式針對一個單一的恆星能否得解。奧地利物理學家、哲學家恩斯特·馬赫(Ernst Mach)是愛因斯坦的指路明燈之一，馬赫教導稱，宇宙里的一切都是相對的。愛因斯坦稱之為馬赫原理，他認為這個原理意味着對於單獨的物體而言，他的方程式不可能得到解答。

「大家可以說這是個笑話，」他告訴史瓦西。「如果所有東西都將從這個世界消失，根據牛頓和伽利略的理論，慣性空間仍然存在。然而，按照我的想法，什麼也留不下。」

可是，根據他的方程式，有一顆恆星在完全憑藉自己的力量扭曲空間，簡單地說就是一個小宇宙。

設計一個宇宙

就像他當時的大多數同事一樣，愛因斯坦認為宇宙由大量恆星、銀河及周圍的廣闊空間組成。宇宙之外有什麼？宇宙是無限的嗎？如果是這樣的話，什麼能阻止一顆恆星漂移到與所有物體脫離聯繫的距離？

為了避免此類問題，愛因斯坦在1917年建立了無限宇宙模型。在他設立的模型中，空間就像錫罐的側面一樣，能夠彎曲觸碰到自己。

他向一名朋友傾訴，「我提出另一個有關引力的建議，這使我面臨被關進瘋人院的風險。」

這就不需要設置令人煩惱的邊界了。但這個宇宙並不穩定，如果某種東西沒有將兩邊撐住，這個圓柱就會坍縮。

這種東西就是愛因斯坦在自己的公式中插入的一種被他稱為「宇宙常數」的容差係數。從物理學來看，這個由希臘字母「蘭布達」(λ)指代的新名詞代表着遠距離的排斥力。

愛因斯坦認為，皆大歡喜的結果就是一個靜態宇宙，幾乎所有人都認為他們生活在這樣一個宇宙中，其中的幾何形態完全由物質決定。

但這沒能站住腳。荷蘭天文學家威廉·德西特(Willem de Sitter)提出了自己的解答，他描述了一個根本不存在物質且正在飛散的宇宙。

「我認為，如果說一個沒有物質的世界是可能存在的，」愛因斯坦抱怨稱。「這是無法令人滿意的。」

後來，埃德溫·哈勃(Edwin Hubble)發現，宇宙確實在不斷膨脹。

愛因斯坦表示，既然這個宇宙常數不能使宇宙保持靜態，那就別考慮它以及馬赫原理了。他後來給英國宇宙學家費利克斯 ·皮拉尼(Felix Pirani)寫信稱，「這可以追溯到人們認為『有重量的物質』是唯一真實存在的實體的時候。」

但為時已晚。量子力學很快就表明，真空中存在很多能量。1998年，天文學家發現暗能量就像宇宙常數一樣，似乎將空間與時間分離，與德西特描述的宇宙相似。

實際上，大多數宇宙學家如今同意這個觀點，即並不是所有運動都是相對的，時空的確獨立於物質存在，儘管它不是靜態和絕對的。最好的例子就是引力波——以光速超速穿過真空的一波波引力壓縮和伸展。

愛因斯坦在整個問題上搖擺不定。他在1916年告訴史瓦西，引力波並不存在，後來又發表論文稱它存在。他和助手在1936年再次改變觀點。

沒人認為這很簡單，即使是對愛因斯坦來說。

明尼蘇達大學(University of Minnesota)科學史學家米歇爾·詹森(Michel Janssen)本月在普林斯頓大學參加聚會時表示，愛因斯坦開始做一件事情，就是使所有運動成為相對的。他失敗了，但他在這個過程中成功地做了一些有趣的事情，將加速度與引力的效應統一起來。

他表示，這個故事說明，鮑勃·迪倫(BobDylan)那句「沒有像失敗這樣的成功」是對的，但「失敗根本不是成功」是錯誤的。

愛因斯坦在1919年取得了巨大成功，當時亞瑟·愛丁頓(Arthur Eddington)做了弗羅因德利希之前開始做的實驗，他發現，正如愛因斯坦預測的那樣，出現日食時，天空中的光線在太陽的暗引力下發生彎曲，出現偏斜。

被問及如果廣義相對論失敗了，他會做什麼時，愛因斯坦曾說，「那我會替敬愛的主感到難過。這個理論是正確的。」

而且直到今天還是最棒的。

翻譯：Kailin Hsiung（實習）、陳亦亭、許欣

http://cn.nytimes.com/science/20151125/c25relativity/en-us/

A Century Ago, Einstein’s Theory of Relativity Changed Everything

By DENNIS OVERBYE November 25, 2015

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.”

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.

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.

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.

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.

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.

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.”

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.

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.

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.

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.

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.

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.

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

“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).”

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.

A Breakthrough Moment

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.

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.

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.

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.

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

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.

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.

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

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.

“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.”

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

Designing a Universe

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?

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.

“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.

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.

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.

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.

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.

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

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

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.

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.

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.

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.

Nobody said this was easy, even for Einstein.

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.

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.”

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.

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.”

And still the champ.