藍色情懷

天天遇見愛因斯坦
EVERYDAY EINSTEIN

  - 愛因斯坦並非只是抽象理論的化身，生活裡，我們常常與他的發明擦身而過。商店自動門使用的偵測器、隨身攜帶的數位相機，甚至是家用娛樂的DVD播放機都是他的功勞。

  - Finding your way out of the woods with GPS? Hanging a picture frame with a laser level? Making photocopies? Better thank Einstein

作者╱任文駒 ( Philip Yam )
譯者╱張明哲

　　對紐約客而言，皇后郡只不過是紐約市的機場以及大都會隊打棒球的地方。某個週六下午，沒有要趕飛機，大 都會隊也不在城內，我跑到皇后區的東北邊探險；更準確地說，是到學院角（College Point）附近。沿著擁擠的第20街而建的帶狀購物中心裡，我尋覓著愛因斯坦。

　　To provincial Manhattanites, Queens County is known only as the place where New York City keeps its airports and where the Mets play baseball. One Saturday afternoon, when I didn't have a flight to catch and the Mets were out of town, I ventured to the northeast part of Queens—specifically, to the College Point neighborhood. There, in a strip mall stretching along a congested 20th Avenue, I went to look for Albert Einstein.

　　愛因斯坦的想法在許多科學研究裡都很關鍵，這不令人意外，這些想法讓物理學家得以加速粒子到接近光速， 也讓天文學家得以測量星空中的現象並給出模型。不過，愛因斯坦一生的貢獻也涵蓋並深入日常科技中。他對光為何像粒子、原子如何放出輻射，以及速度與重力如 何影響時鐘的解釋，對於現今常見裝置的運作都很重要。

　　Not surprisingly, Einstein's ideas are essential in many kinds of scientific research, enabling physicists to accelerate particles to near light speed and permitting astronomers to measure and model celestial phenomena. But Einstein's contributions over his life also extend deeply into our everyday encounters with technology. His descriptions of how light can act as particles, how atoms can emit radiation, and how velocity and gravity affect clocks are all important to making common devices work today.

　　在學院角的購物中心裡，我第一次接觸愛因斯坦，是在進入大型折扣商店「標靶」（Target）時。一顆 光電池（「電子」眼）偵測到我的靠近後敞開大門。這個偵測器長得很像三明治，是在兩片電極間夾著半導體，可以用來感應光線。光線強度的變化（例如光束被遮 斷或是一般照明的降低），會造成偵測器裡產生的電流隨著改變。搭配適當的電路後，就可以啟動開門。

　　At the College Point mall, my first interaction with Einstein happened as I entered the giant discount store Target. The doors swung open after a photocell—an “electric eye”—spied my approach. The sensor, made from a semiconductor sandwiched between two electrodes, responds to light. As the intensity of light varies—by the breaking of a light beam, say, or a decrease in general illumination—the amount of current generated by the sensor changes. Coupled to appropriate circuitry, it can trigger the doors to open.

　　這種偵測器是光電效應的一種應用，照在金屬上的光線造成電子飛離金屬。這個現象並不是愛因斯坦發現的， 它最初是1839年時在法國發現的。不過，他在思索德國物理學家普朗克（Max Planck）的計算時，為其找出正確的解釋。1900年，普朗克根據實驗的觀察推論出，一個受熱的物體在放出某種頻率（或顏色）的光時，是以稱為量子的 不連續量放射。普朗克推算出現在很有名的常數h，以寫下可用以描述這種稱為黑體輻射現象的方程式。

　　Such sensors represent an application of the photoelectric effect, in which light falling on metal sends electrons flying off it. Einstein did not discover the phenomenon, which was first noticed in France in 1839. He did, however, correctly explain it while puzzling out the calculations of German physicist Max Planck. Based on observations, Planck in 1900 figured that a heated body releases light of a given frequency, or color, in discrete amounts called quanta. Planck derived his now famous constant, h, to make the equations describing this so-called blackbody radiation work out.

　　不過愛因斯坦推測，h不僅是數學上的一種修正。他假設，光不是以連續的能量波，而是以波包的方式移動。在他1905年的分析及隨後的論文裡，愛因斯坦說明了光可以像是一束粒子流；如果這樣，它會像撞球時母球撞開排好的球一樣，將電子打離金屬。

　　But Einstein theorized that h was more than a mathematical patch. He postulated that light, rather than flowing as a continuous wave of energy, travels in packets. With his 1905 analysis, along with subsequent papers, Einstein showed that light can behave as a stream of particles; when it does, it knocks electrons out of the metal in the way a cue ball breaks a billiard rack.

　　愛因斯坦也解釋了光電效應裡一個令人困擾的現象。雖然較強的光能從金屬裡打出較多的電子，但是不管光多 亮或多暗，這些電子的速度始終一樣。要改變電子速度的唯一方法，是用不同顏色的光。為了解釋這個現象，愛因斯坦推算出，每個光粒子（或光子）的能量取決於 其頻率乘以h。隨後的實驗證實了愛因斯坦的預測，由於他對光電效應的解釋，愛因斯坦得到1921年的諾貝爾物理獎。

　　Einstein also explained a baffling feature of the photoelectric effect. Although the intensity of light sent more electrons shooting off the metal, the velocity of the liberated electrons remained the same no matter how dim or bright the light was. The only way to change the velocity of the electrons was to use a different color of light. To account for the observation, Einstein figured that the energy of each light particle, or photon, depends on its frequency multiplied by h. Subsequent experiments confirmed Einstein's predictions, and for his explanation of the photoelectric effect, Einstein won the 1921 Nobel Prize in Physics.

　　現在光電效應是許多儀器的基礎：在薄暮時打開街燈、調節影印機碳粉的濃度、控制相機的曝光時間等。事實 上，幾乎在任何控制或感應光線的電子裝置裡都會用到。連在呼氣酒測器裡都有光電裝置，裡面的光電池可以偵測試驗氣體與酒精反應後顏色的變化。這個效應也導 致光電倍增管的發明，它由內含一連串金屬台階的玻璃真空管組成。當光子撞及起始的金屬靶之後，這些台階會依序噴出越來越多的電子。以這種方式可以將微弱的 光訊號放大。光電倍增管在天文偵測器及電視攝影機裡都會用到。


 　The photoelectric effect today underlies instruments that turn on the streetlights at dusk, regulate the density of toner in photocopy machines and govern the exposure times of cameras—in fact, it is involved in just about any electronic device that controls or responds to lighting. Photoelectric devices are even used in Breathalyzers—the photocell picks up a color change appearing after a test gas has reacted with alcohol. The effect also led to the invention of photomultipliers, which consist of evacuated glass tubes containing a series of metal steps. The steps cough up successively more electrons after an initial metal target is struck by photons. In this way, a weak light signal is amplified. Photomultipliers channel light in astronomical detectors and television cameras.

　　光電效應最明顯的應用是在太陽能電池（或光電電池）裡。從1950年開始發展，現在太陽能電池能將15~30%的入射光轉換為電能，用來驅動計算機、手錶、環保住屋、繞地衛星，以及火星探測車等。

　　The most visible application of the photoelectric effect is in solar, or photovoltaic, cells. Pioneered in the 1950s, solar cells convert 15 to 30 percent of the incident light into electricity and power calculators, watches, environmentally conscious homes, orbiting satellites and Martian rovers.


激發思考
Stimulated Thinking

　　回到購物中心裡，我看到靠牆的是「標靶」的電子產品部，就在30個結帳櫃檯後不遠的，是許多排的DVD 及可攜式CD隨身聽，有些售價低到12.99美元（約440台幣）。結帳櫃檯及隨身聽都用到某種型式的光電池，但是從愛因斯坦的觀點來看，更有趣的是它們 所射出來的紅色同調光束。現在到處都是雷射，其存在得歸功於愛因斯坦在1917年所提出來的理論架構。

　　BACK AT THE MALL, I see that against the walls lining Target's electronics section, just beyond the 30 checkout registers, are stacks of DVD and portable CD players, some costing as little as $12.99. The registers and players all use some kind of photocell, but what is more interesting from an Einsteinian perspective is the red beam of coherent light they shoot. The now ubiquitous laser owes its existence to a theoretical framework erected by Einstein in 1917.

　　在〈論輻射的量子理論〉這篇論文裡，愛因斯坦繼續探索光與物質。特別是他了解到原子在吸收光之後可以變成激發狀態（也就是跳到較高的能階）。接著它們會自發性地放光而回到較低的能階。

　　With his paper “On the Quantum Theory of Radiation,” Einstein continued to explore light and matter. In particular, he realized that atoms can become excited—that is, jump to a higher energy level—if they absorb light. They spontaneously emit light to return to a lower level.

　　除了吸收與自發放射之外，愛因斯坦推論出必須存在第三種交互作用，也就是光子會誘使受激發的原子放射出另一個光子。這兩個光子接著會激發另兩個原子放出光子而產生四個光子。這四個光子接著產生八個光子，依此類推。

　　In addition to absorption and spontaneous emission, Einstein deduced that a third kind of interaction must exist, one in which a photon could induce an excited atom to emit another photon. These two photons in turn could stimulate two other atoms to emit photons, yielding four photons. Those four photons could lead to eight more, and so on.

　　產生同調光束的技巧是先做出「粒子數反轉」（population inversion），讓被激發的原子比未被激發的多，然後想辦法讓射出的光子累積成強力的光束。這直到1954才做出來，當時美國哥倫比亞大學的湯斯 （Charles H. Townes）及其同事設計出雷射的前身，稱為「邁射」（maser，經由受激輻射產生的微波放大）。

　　The trick to creating a coherent beam would be establishing a “population inversion”—having more atoms excited than not excited—and finding a way to allow the photons emitted to accumulate into an intense beam. That wouldn't happen until 1954, when Charles H. Townes of Columbia University and his colleagues devised the laser's predecessor, the “maser” (microwave amplification through stimulated emission of radiation).

　　事後，湯斯在他1999年出版的《雷射怎麼出現的》這本回憶錄裡寫道：「花了那麼久的時間才發明出雷 射，實在令人不可思議。雷射可以早個30年出現的。」有一個可能的原因是：雖然愛因斯坦的方程式說受激輻射可以產生更多的光子，但是並沒有明說它會產生完 全一樣的光子：不只是頻率，連相位也一模一樣的光子。太陽或者鎢絲之類的光源可以產生大量頻率相同的光子，但是這些光子並不同步，他們產生的是光學上的雜 訊。讓所有的光子同調（同一時間奏同一個「音」），結果會是尖銳的巨響而非單調的嘶嘶聲。

　　In retrospect, “it is a wonder that invention of the laser took so long,” Townes wrote in his 1999 memoir, How the Laser Happened. “[The] laser could have happened 30 years earlier than it did.” One possible reason: although Einstein's equations state that stimulated emission produces additional photons, they do not explicitly indicate that it produces exact copies, identical not just in frequency but also in phase. Light sources such as the sun and tungsten filaments produce plenty of photons of the same frequency, but they are out of step—they produce the optical version of random noise. Get all the photons to be coherent—to play the same note at the same time—and the result will be a singular roar rather than a dull hiss.

　　現在在加州大學柏克萊分校的湯斯推測，愛因斯坦「從沒考慮過同調性」。不過，「我很確定如果我問愛因斯坦，他會很快地斷定一定會有同調性，而且，如果有人能使夠多的原子處於適當的高能態，他就會得到淨放大的效果。」

　　Einstein “never considered coherence,” surmised Townes, now at the University of California at Berkeley. But “I feel sure that if asked, Einstein would have quickly concluded there must be coherence and that if one had enough atoms in an appropriate upper state, one would get net amplification.”

　　即使有些物理學家了解到光子會同調，愛因斯坦的計算仍顯示，受激輻射極難發生。羅徹斯特大學研究量子光 學的物理學家斯特勞德（Carlos R. Stroud）說：「愛因斯坦所預測的是一個其小無比的效應，所以我不認為人們了解其重要性。」或者，如斯特勞德的同事渥爾夫（Emil Wolf）所說的：「愛因斯坦比所有人超前了許多年。」

　　Even if some physicists recognized that the photons would be coherent, Einstein's calculations showed that stimulated emission would rarely occur. “It's an incredibly small effect that Einstein predicted, so I don't think people appreciated the significance,” says Carlos R. Stroud, a quantum optics physicist at the University of Rochester. Or, as Stroud's colleague Emil Wolf puts it: “Einstein was years and years ahead of everyone else.”

　　在1917年論文發表後的幾十年內，有些文獻曾零零星星地提到產生受激輻射，但這些想法都沒有被進一步 研究。湯斯在1950年代早期理解到，產生輻射放大的關鍵在於共振腔。在邁射出現幾年之後發明出來的雷射，其所用的共振腔，不過就是兩片鏡子所夾的空間， 光在裡面可以來回反射使強度逐漸增強，直到光束從其中的一面（可以部份透射的）鏡子穿透射出。

　　In the decades after the 1917 paper, sporadic references to creating stimulated emission appeared, but none of the ideas were pursued. The key ingredient to making amplified radiation, Townes realized in the early 1950s, was a resonant cavity. In lasers—invented a few years after the maser—the cavity is simply the space contained by two mirrors, so that the light bounces back and forth, building up in intensity until a beam emerges from one of the mirrors (which is partially transmitting).

　　有了這些基本知識後，工程師發現可以從許多材料做出雷射──包括摻有螢光染料的果凍，甚至是奎寧水 （tonic water）。雷射的廣泛使用得歸功於半導體工業以及發光二極體的設計。的確，使用受激輻射的產品多得嚇人。除了DVD播放機、雷射平準儀與指示筆之外， 飛機裡的環狀陀螺儀、供商業用途的切割工具、醫療儀器，與光纖的傳播訊號裡都有雷射。雷射在科學是不可或缺的工具，就舉兩個例子，幾位研究者使用它來研究 化學反應及操縱微觀物體，因而獲得諾貝爾獎。在美國海軍天文台裡，邁射可做為準確的時鐘，也可以放大天文研究裡微弱的無線電訊號。

　　Armed with the basics, engineers found they could make lasers from many substances—including Jell-O infused with fluorescent dye and even tonic water. Widespread use of lasers came about thanks to the semiconductor industry and to the design of light-emitting diodes. Indeed, stimulated emission occurs in an astonishing array of products. Besides DVD players, levels and pointers, lasers are behind ring gyroscopes in aircraft, commercial cutting tools, medical instruments and communications signals through fiber optics. Lasers have become indispensable in science, earning Nobel prizes for several investigators who used them to study chemical reactions and to manipulate microscopic objects, to name two. Masers act as accurate clocks for the U.S. Naval Observatory and amplify faint radio signals in astronomy studies.


GPS的滴答聲
GPS Ticks

　　我逛「標靶」的下一站是戶外運動部，不過沒找到想找的東西，我逛回電子產品部。詢問櫃檯人員：「你們有賣GPS裝置嗎？」得到的回答是：「已經不再賣了。」

　　MY NEXT STOP inside Target was the outdoor sports section, but unable to find my quarry, I backtracked to the electronics department. “Do you have GPS devices?” I asked at the counter. “Not no more,” came the reply.

　　不過隔壁的「電器城」（Circuit City）有好幾種款式，少數幾款價格不到200美元。這些手持式裝置藉著接收全球定位系統的衛星時間信號，可以提供經度、緯度以及海拔高度。要準確的測 量距離得有準確的計時器，所以24個GPS衛星都各自攜有原子鐘（參見2004年6月號〈GPS：讓路痴不再迷路〉）。

　　 The Circuit City next door, however, offered several models, a few less than $200. These handheld instruments provide latitude, longitude and altitude by picking up timing signals from Global Positioning System satellites. Accurate distance measurements require accurate timepieces, which is why each of the 24 GPS satellites carries an atomic clock [see “Retooling the Global Positioning System,” by Per Enge; Scientific American, May].

　　現在大多數購自商店的GPS接收器可以定出你的位置，誤差範圍約15公尺。科羅拉多大學波爾德分校的物 理學家阿什比（Neil Ashby）說，誤差小於30公尺的話，表示GPS接收器一定有考慮到相對論。華盛頓大學的物理學家威爾（Clifford M. Will）進一步解釋：「如果沒有考慮相對論的話，天上的時鐘跟地上的就不會同步。」相對論說，快速移動的物體會比靜止不動的老化得慢。威爾計算了一下， 每個GPS衛星每小時約飛行1萬4000公里，這表示它上頭的原子鐘比地上的每天要慢上約7微秒。

　　Today most store-bought GPS receivers can pin down your position to within about 15 meters. Accuracy of less than 30 meters, notes physicist Neil Ashby of the University of Colorado at Boulder, assuredly means that a GPS receiver incorporates relativity. “If you didn't take relativity into account, then the clocks up there would not be in sync with the clocks down here,” elaborates Clifford M. Will, a physicist at Washington University. Relativity states that fast-moving objects age more slowly than stationary ones. Each GPS satellite zips along at about 14,000 kilometers per hour, meaning that its onboard atomic clock lags the pace of clocks on the earth by about seven microseconds per day, Will calculates.

　　不過，重力的相對論效應對時間的影響更大。平均說來，GPS衛星位於地面上空兩萬公里，它們所感受的重 力只是地面上的1/4。因此，衛星上的時鐘每天要快上45微秒。因此GPS裡得考慮這38微秒的總偏差。阿什比解釋說：「如果衛星不做頻率修正，每天就會 增加11公里的誤差。」（實際效應更複雜些，因為衛星軌道有離心率，所以離地球有時近有時遠。）

　　Gravity, however, exerts a greater relativistic effect on timing. At an average of 20,000 kilometers up, the GPS satellites experience one fourth of the gravitational pull they would on the ground. As a result, onboard clocks run faster by 45 microseconds per day. An overall offset of 38 microseconds thus has to be figured into GPS. “If you didn't have frequency offset in satellites, then an 11-kilometer-per-day error would build up,” Ashby explains. (The effects are actually more complicated because the satellites follow an eccentric orbit, traveling closer to the earth in some instances and farther away at others.)

　　對那些在1970年代最早設計GPS的人來說（大多是軍方工程師），並沒特別想到要考慮相對論修正。當 時任顧問的阿什比回憶：「這有爭議性，有些人認為必須考慮；有些認為不必。」設計師的意見分歧到在第一次發射GPS衛星時並沒做頻率修正，但是必要時可以 打開一個開關做修正。阿什比說，很快就清楚了，開關必須打開。

　　The idea of correcting for relativity was not obvious to the original GPS designers, mostly military engineers, back in the 1970s. “It was controversial,” recalls Ashby, who served as a consultant. “Some people believed you had to account for it; some didn't.” So divided were the designers that the first GPS satellite was launched without the frequency offset but had a switch to turn on the offset just in case. It quickly became apparent that the switch had to be on, Ashby says.

　　較新的GPS方法較不需要做相對論效應修正，至少對地面資料來說是如此。差分GPS技術除了用到掌上裝 置之外，還需要在地面上一些已知地點放置接收器，這樣可以有效消除偏差。（這種方法稱為廣域擴增系統，簡寫為WAAS。）不過對那些用GPS計時的人來說 （例如無線電天文學家），還是得有愛因斯坦在旁邊。

　　Newer GPS methods are less dependent on correcting for relativistic effects, at least for positional data. In differential GPS, which requires receivers at known ground locations in addition to the handheld unit, the offset errors effectively cancel out. (The approach is called the wide-area augmentation system, or WAAS.) But those who use GPS to keep track of time, such as radio astronomers, still need Einstein by their side.


發明家愛因斯坦
Einstein as Inventor

　　唉，愛因斯坦還是有一個發明，是在我逛的（或其他的）購物中心裡都找不到的。他對製造器具的消遣性研 究，應該沒做出歷久彌新的消費性產品，不過與他專利相關的機制在其他地方有用到。愛因斯坦與物理同夥西拉德（Leo Szilard）在1920年代設計出一種冰箱。這個機器用的是不會漏的電磁幫浦（那時的冷卻氣體仍有毒）。在較安全的冷煤發明後，這種不會漏的幫浦就過 時了，因此愛因斯坦的電冰箱從未在家電展示區出現。不過，他的幫浦現在被用來傳送液態鈉，以冷卻一種稱為快速滋生的核子反應爐。當然，愛因斯坦的動機並非 在於鈔票，主要是想要了解自然界的渴望。他的推理所帶來的技術成果則留給其他人去做。E＝mc²，一個在他1905年的相對論論文裡所出現的關係式就是如此。斯特勞德評論：「在那之前，沒人想到物質能以任何方式轉變為能量。」由於它簡單得誘人，只是一小塊質量乘以光速平方以獲得大量的能量，所以應該能用各種方式實現它。威爾猜想：「我猜它讓很多人思索這件事。」

　　EINSTEIN DID HAVE one type of invention that, alas, can't be found at the mall I visited—or at any mall, for that matter. His dabbling in appliance making may not have produced any durable consumer goods, but the related mechanisms that he patented are in use elsewhere. With fellow physicist Leo Szilard, Einstein came up with refrigerator designs in the 1920s. The machines relied on electromagnetic pumps that did not leak (cooling gases back then were toxic). The invention of safer refrigerants quickly rendered the leakless pump obsolete, and Einstein's fridge never appeared in appliance showrooms. The pump, however, survives as a means to move sodium to cool a type of nuclear reactor called a fast breeder [see “The Einstein-Szilard Refrigerators,” by Gene Dannen; Scientific American, January 1997]. Of course, the inventor's yen did not propel Einstein, who was primarily driven by the desire to understand nature. He left the technological consequences of his reasoning to others. The same could be said of E = mc², a relation that emerged from his 1905 relativity paper. “Before that, people had not considered that matter was in any way convertible to energy,” Stroud remarks. Given its seductive simplicity—multiply a tiny bit of mass with the speed of light squared to get a lot of energy—there had to be ways to see it in action. “I suspect it got a lot of people thinking about it,” Will surmises.

　　當然，在做核分裂彈時，驅動曼哈坦計畫科學家的，是比證實E真的等於mc²來得急迫的命令。這是愛因斯坦的技術遺產裡仍可能劇烈改變世界的一項，也是賣場裡保證不會賣的。

　　Certainly, in making the fission bomb, the Manhattan Project scientists were motivated by imperatives more pressing than confirming that E really does equal mc². It is one of Einstein's technological legacies that still might radically change the world—and assuredly one never to be sold at a shopping mall.

1.How the Laser Happened: Adventures of a Scientist. Charles H. Townes. Oxford University Press, 1999. 

2.Relativity and the Global Positioning System. Neil Ashby in Physics Today, Vol. 55, No. 5, pages 41-47; May 2002. 

3.Einstein on the Photoelectric Effect. David Cassidy. www.aip.org/history/einstein/essay-photoelectric.htm

4.The Einstein-Szilard Refrigerators. Gene Dannen in Scientific American; January 1997.