愛因斯坦在1905年提出狹義相對論時，駁斥了一項19世紀的觀點：光波是由一種假想介質「乙 太」的振動而產生的。他主張，光波可以在真空中行進，並不需要任何物質來支撐，不像在介質中傳播的聲波，其實只是介質的振動而已。在近代物理的另外兩大支 柱（廣義相對論和量子力學）之中，這個狹義相對論的特性並沒有再修改。而到目前為止，小至次原子核，大至星系，所有的實驗數據，都能用這三大理論圓滿地解 釋。

　 　When Albert Einstein proposed his special theory of relativity in 1905, he rejected the 19th-century idea that light arises from vibrations of a hypothetical medium, the 「ether.」 Instead, he argued, light waves can travel in vacuo without being supported by any material—unlike sound waves, which are vibrations of the medium in which they propagate. This feature of special relativity is untouched in the two other pillars of modern physics, general relativity and quantum mechanics. Right up to the present day, all experimental data, on scales ranging from subnuclear to galactic, are successfully explained by these three theories.

　　儘管如此，物理學家卻得面對一個深刻的觀念問題。就現在的理解，廣義相對論和量子力學是不相容的。廣義相對論將重力歸因於時空連續體的曲 率，而這與量子理論的框架格格不入。在極短的距離之下，一般認為量子力學將會導致時空結構的高度彎曲，但理論學家對此的理解，進展卻極其微小。於是在挫折 之餘，有些人便轉向一條出人意表之路：凝態物理（也就是研究如晶體或流體這些一般物質的學問），以尋求指引。

　 　Nevertheless, physicists face a deep conceptual problem. As currently understood, general relativity and quantum mechanics are incompatible. Gravity, which general relativity attributes to the curvature of the spacetime continuum, stubbornly resists being incorporated into a quantum framework. Theorists have made only incremental progress toward understanding the highly curved structure of spacetime that quantum mechanics leads them to expect at extremely short distances. Frustrated, some have turned to an unexpected source for guidance: condensed-matter physics, the study of common substances such as crystals and fluids.

　　凝態物質在大尺度下，就和時空一 樣，看起來也是連續體，不同之處僅在於，它們的微觀結構，是由我們透徹瞭解的量子力學所支配。此外，由於聲波在不均勻流體中的傳播行為，和光波在彎曲時空 中傳播十分類似，因此我們和其他同行正在研究一種聲波的黑洞模型，企圖透過這項類比，獲得對於時空微觀行為的瞭解。這類的工作成果指出，時空也許正如流體 物質一樣，具有顆粒性，而且在微觀的尺度下，會有某個特別優越的參考座標──這和愛因斯坦的假設剛好相反。

　 　Like spacetime, condensed matter looks like a continuum when viewed at large scales, but unlike spacetime it has a well-understood microscopic structure governed by quantum mechanics. Moreover, the propagation of sound in an uneven fluid flow is closely analogous to the propagation of light in a curved spacetime. By studying a model of a black hole using sound waves, we and our colleagues are attempting to exploit this analogy to gain insight into the possible microscopic workings of spacetime. The work suggests that spacetime may, like a material fluid, be granular and possess a preferred frame of reference that manifests itself on fine scales—contrary to Einstein's assumptions.

黑洞其實並不黑
From Black Hole to Hot Coal

　　黑洞是測試量子重力論的最佳場所之一，因為不管是量子力學或廣義相對論，在黑洞附近都極為重要。1974年，英國劍橋大學的霍金（Stephen W. Hawking）將量子力學套用在黑洞的視界上，自此這兩大理論的融合向前邁進了一大步。

Black holes are a favorite testing ground for quantum gravity because they are among the few places where quantum mechanics and general relativity are both critically important. A major step toward a merger of the two theories came in 1974, when Stephen W. Hawking of the University of Cambridge applied quantum mechanics to the horizon of black holes.

　 　根據廣義相對論，所謂的視界就是將黑洞內部（這裡的重力強到沒有任何東西可以逃離）與外部分隔開來的曲面，它不是一種物質的界限。不幸掉進黑洞中的旅 人，在通過視界時，並不會有特別的感覺；可是一旦通過了視界，他們就再也無法將光波訊號傳送給黑洞外的人，更別說回到黑洞外頭去了。至於洞外的觀察者，只 會收到旅人在通過視界前所發送的訊號。當光波爬出黑洞的重力位井時，它們會被拉長，使得頻率向下偏移，訊號的持續時間也變長。結果對觀察者來說，旅人看起 來會像是用慢動作移動，而且會比平常的顏色要紅。

　 　According to general relativity, the horizon is the surface that separates the inside of a black hole (where gravity is so strong that nothing can escape) from the outside. It is not a material limit; unfortunate travelers falling into the hole would not sense anything special on crossing the horizon. But once having done so, they would no longer be able to send light signals to people outside, let alone return there. An outside observer would receive only the signals transmitted by the travelers before they crossed over. As light waves climb out of the gravitational well around a black hole, they get stretched out, shifting down in frequency and lengthening in duration. Consequently, to the observer, the travelers would appear to move in slow motion and to be redder than usual.

　　這種稱做重力紅移的效應，並不是黑洞所特有。舉例來說，當訊號在軌道衛星和地面基地之間傳遞 時，其頻率和時間也會因重力紅移而改變。GPS導航系統必須把這個變數考慮進來，才能準確運作。不過黑洞特殊的地方在於，隨著旅人向視界趨近，紅移會變成 無限大。從外部觀察者的角度來看，旅人墜入黑洞得花上無限久，儘管旅人自己會覺得只過了一段有限的時間而已。

　 　This effect, known as gravitational redshift, is not specific to black holes. It also alters the frequency and timing of signals between, say, orbiting satellites and ground stations. GPS navigation systems must take it into account to work accurately. What is specific to black holes, however, is that the redshift becomes infinite as the travelers approach the horizon. From the outside observer's point of view, the descent appears to take an infinite amount of time, even though only a finite time passes for the travelers themselves.

　　以上對於黑洞的描述，僅僅將光當 做是古典的電磁波。霍金所做的，是在把光的量子性考慮進來，重新思考無限紅移所衍生的結果。根據量子理論中的海森堡測不準原理，就算是完美的真空也不是空 無一物，而是充滿了量子漲落。量子漲落以虛光子對的形式出現。它們被叫做「虛」光子，是因為在遠離任何重力影響的非彎曲時空中，它們會不停的出現又消失， 若是沒有任何外力擾動，就無法觀測得到。

　 　So far this description of black holes has treated light as a classical electromagnetic wave. What Hawking did was to reconsider the implications of the infinite redshift when the quantum nature of light is taken into account. According to quantum theory, even a perfect vacuum is not truly empty; it is filled with fluctuations as a result of the Heisenberg uncertainty principle. The fluctuations take the form of pairs of virtual photons. These photons are called virtual because, in an uncurved spacetime, far from any gravitational influence, they appear and disappear restlessly, remaining unobservable in the absence of any disturbance.

　　可是在黑洞附近的彎曲時空中，虛光子對的其中一顆可能會陷進視界之內，而另一顆卻留在視界之外。於是 這對光子就會由虛轉實，形成一股可觀察到的向外光通量，而此時黑洞的質量也會相應下降。黑洞輻射整體的型態是熱輻射，就和灼熱木炭所發出來的類似，其溫度 和黑洞的質量成反比。這種現象就是所謂的霍金效應。除非黑洞吞噬新物質或新能量來彌補損失，要不然霍金輻射會把它所有的質量洩漏個精光。

　 　But in the curved spacetime around a black hole, one member of the pair can be trapped inside the horizon, while the other gets stranded outside. The pair can then pass from virtual to real, leading to an outward flux of observable light and a corresponding decrease in the mass of the hole. The overall pattern of radiation is thermal, like that from a hot coal, with a temperature inversely proportional to the mass of the black hole. This phenomenon is called the Hawking effect. Unless the hole swallows matter or energy to make up the loss, the Hawking radiation will drain it of all its mass.

　　有個 重點，在待會兒以流體來類比黑洞時，會變得非常重要，那就是在非常靠近黑洞視界的空間中，還會保持近乎完美的量子真空。事實上，這在霍金的論證中，是最根 本的條件。虛光子是最低能量子態（亦即「基態」）的一項特徵。只有在和同伴分離並爬出視界之外的過程之中，虛光子才會變成實光子。

　 　An important point—which will become critical later when considering fluid analogies to black holes—is that the space very near the black hole horizon remains a nearly perfect quantum vacuum. In fact, this condition is essential for Hawking's argument. The virtual photons are a feature of the lowest-energy quantum state, or 「ground state.」 It is only in the process of separating from their partners and climbing away from the horizon that the virtual photons become real.
 

終極顯微鏡
The Ultimate Microscope

　　在建構完整量子重力理論的各種嘗試中，霍金的分析扮演了重要的角色。想成為量子重力的候選理論（例如弦論），就必須先證明它能否重現與闡明這項效應（參見2005年12月號〈重力是一種幻覺嗎？〉）。 不過，雖然大多數的物理學家都接受霍金的論證，對它的實驗確認卻遲遲無法達成。原本預期會由星體或是星系黑洞所發出的輻射，因太過微弱而無法觀測。要觀測 霍金輻射唯一的希望，是找到早期宇宙殘存、或是在加速器裡製造出來的小型黑洞，但這些也許都是不可能的了（參見2005年6月號〈黑洞製造機〉）。

　 　Hawking's analysis has played a central role in the attempt to build a full quantum theory of gravity. The ability to reproduce and elucidate the effect is a crucial test for candidate quantum gravity theories, such as string theory [see 「The Illusion of Gravity,」 by Juan Maldacena; Scientific American, November]. Yet although most physicists accept Hawking's argument, they have never been able to confirm it experimentally. The predicted emission from stellar and galactic black holes is far too feeble to see. The only hope for observing Hawking radiation is to find miniature holes left over from the early universe or created in particle accelerators, which may well prove impossible [see 「Quantum Black Holes,」 by Bernard Carr and Steven Giddings; Scientific American, May].

　 　缺乏經驗實證的霍金效應，有一個惱人的陰影，特別教人心煩：其實，這個理論中有個潛在的瑕疵，就是光子會有無限大的紅移。想一想，要是把時間倒轉來看， 發射光子的過程會變成什麼樣子呢？隨著霍金光子越來越靠近黑洞，它會藍移到一個較高的頻率與相對較短的波長。它的時間回溯得越早，就越靠近視界，而波長也 就變得越短。一旦波長變得比黑洞還短得多的時候，這個粒子就和它的夥伴結合起來，而變成了之前所討論的虛光子對。

　 　The lack of empirical confirmation of the Hawking effect is particularly vexing in view of the disturbing fact that the theory has potential flaws, stemming from the infinite redshift that it predicts a photon will undergo. Consider what the emission process looks like when viewed reversed in time. As the Hawking photon gets nearer to the hole, it blueshifts to a higher frequency and correspondingly shorter wavelength. The further back in time it is followed, the closer it approaches the horizon and the shorter its wavelength becomes. Once the wavelength becomes much smaller than the black hole, the particle joins its partner and becomes the virtual pair discussed earlier.

　　藍移會持續下去到任意短的距離。可是到了比10^-35公 尺（即所謂的普朗克長度）還小時，不管是相對論還是標準的量子理論，就都沒辦法預測粒子會有什麼行為了。這時候你需要量子重力理論才行。因此黑洞的視界就 好像是一個神奇的顯微鏡，可帶領觀察者去接觸未知的物理。然而對理論學家而言，這种放大功能卻讓人憂慮。假如霍金的預測是建立在未知的物理上，我們難道不 該懷疑它的效力嗎？就像物質的熱容量和聲速，會和它的微觀結構與動力學有關一樣，霍金輻射的性質、甚至是否存在，會不會和時空的微觀性質有關？還是說，情 況就和霍金原始的論證一樣，這個效應完全是由黑洞的巨觀性質（它的質量和自轉角動量）來決定的呢？

　　The blueshifting continues without abatement, down to arbitrarily short distances. Smaller than a distance of about 10^-35 meter, known as the Planck length, neither relativity nor standard quantum theory can predict what the particle will do. A quantum theory of gravity is needed. A black hole horizon thus acts as a fantastic microscope that brings the observer into contact with unknown physics. For a theorist, this magnification is worrisome. If Hawking's prediction relies on unknown physics, should we not be suspicious of its validity? Might the properties, even the existence, of Hawking radiation depend on the microscopic properties of spacetime—much as, for example, the heat capacity or speed of sound of a substance depends on its microscopic structure and dynamics? Or is the effect, as Hawking originally argued, entirely determined just by the macroscopic properties of the black hole, namely, its mass and spin?

小溪裡的漣漪，有著和時空中的光波十分類似的行為。在岩石附近的水流不均勻，因此漣漪的行進方向會彎曲，其波長也會改變。同樣的事情也會發生在光波行經行星或恆星重力場的時候。在某些情況下，水流的速度太快，以至於漣漪不能向上游傳播，正如同光不能從黑洞中向外傳播一樣。

響聲與亮光
Sound Bites

　　為了回答這些令人坐立難安的問題，加拿大卑詩大學的安魯（William Unruh）開啟了一門新的研究。1981年，他證明了聲波在流體中的傳播，和光在彎曲空間中的傳播有極為接近的類比。他提出，在評估微觀物理對霍金輻射 起源上的影響時，這種類比也許會很有用。而且，它說不定可讓類霍金現象的實驗觀測成真。

　　On effort to answer these embarrassing questions began with the work of William Unruh of the University of British Columbia. In 1981 he showed that there is a close analogy between the propagation of sound in a moving fluid and that of light in a curved spacetime. He suggested that this analogy might be useful in assessing the impact of microscopic physics on the origin of Hawking radiation. Moreover, it might even allow for experimental observation of a Hawking-like phenomenon.

　　聲波就和光波一樣，是以頻率、波長和傳播速度為其特 徵。我們對聲波的觀念，只適用於波長比流體分子間距大得多的時候；在更小的尺度下，聲波就不存在了。而正是這個限制，讓這項類比這麼有趣，因為它可以讓物 理學家研究微觀結構對巨觀現象的影響。然而，真要讓這項類比派上用場，它必須要能延伸到量子的層次。通常，分子的隨機熱運動，會讓聲波的行為和光量子有 別。不過當溫度接近絕對零度的時候，聲波就會表現得和量子一樣了，物理學家稱之為「聲子」（phonon），來強調它和「光子」（光的粒子）的類比。實驗 家對於聲子在晶體以及低溫下仍保持流體狀態的物質（如液態氦）之中的行為，早就在進行例行的觀測了。

　　Like light waves, acoustic (sound) waves are characterized by a frequency, wavelength and propagation speed. The very concept of a sound wave is valid only when the wavelength is much longer than the distance between molecules of the fluid; on smaller scales, acoustic waves cease to exist. It is precisely this limitation that makes the analogy so interesting, because it can allow physicists to study the macroscopic consequences of microscopic structure. To be truly useful, however, this analogy must extend to the quantum level. Ordinarily, random thermal jigging of the molecules prevents sound waves from behaving analogously to light quanta. But when the temperature approaches absolute zero, sound can behave like quantum particles, which physicists call 「phonons」 to underline the analogy with the particles of light, photons. Experimenters routinely observe phonons in crystals and in substances that remain fluid at sufficiently low temperatures, such as liquid helium.

　　聲子在靜止與均勻流動的流體中的行為，就和光子在沒有重力的平坦空間中一樣。這類聲子以固定波長、頻率與速度沿直線傳播，像聲音在游泳池或是平順流動的河流中，就是從音源一直線傳遞到我們耳朵。

　　The behavior of phonons in a fluid at rest or moving uniformly is like that of photons in flat spacetime, where gravity is absent. Such phonons propagate in straight lines with unchanging wavelength, frequency and velocity. Sound in, say, a swimming pool or a smoothly flowing river travels straight from its source to the ear.

　 　然而，在流動不均勻的流體中，聲子的速度會改變，而且它們的波長也會拉長，正如同彎曲空間中的光子一般。在流入峽谷的河流中，或是在旋進排水孔的渦流 中，聲波會變形扭曲，並且沿著彎曲的路徑行進，就像是星體附近的光一樣。事實上，這類情況可以用廣義相對論的數學幾何工具來描述。

　　In a fluid moving nonuniformly, however, the phonons' velocity is altered and their wavelength can become stretched, just like photons in a curved spacetime. Sound in a river entering a narrow canyon or water swirling down the drain becomes distorted and follows a bent path, like light around a star. In fact, the situation can be described using the geometrical tools of general relativity.

　　流體對聲音 的作用方式，甚至可以像黑洞對光的作用方式一樣。創造這種聲學黑洞的方法之一，是利用一種流體力學家稱為「拉瓦爾噴嘴」（Laval nozzle）的裝置。這種噴嘴的設計，會讓流體在最狹窄處，達到並且超過聲速，而不會產生衝擊波（一種流體性質上的突然變化）。其等效的聲學幾何，與黑 洞的時空幾何非常類似。超音速的區域與黑洞的內部相對應：相反於流動方向傳播的聲波，只能被衝往下游，就像被黑洞中心拉住的光一樣。次音速的區域則對應到 黑洞之外的時空：聲波能夠往上游傳播，而唯一的代價是波長被拉長，就像光會被紅移一樣。在這兩個區域的交界，行為上和黑洞的視界是一模一樣的。

　　A fluid flow can even act on sound as a black hole acts on light. One way to create such an acoustic black hole is to use a device that hydrodynamicists call a Laval nozzle. The nozzle is designed so that the fluid reaches and exceeds the speed of sound at the narrowest point without producing a shock wave (an abrupt change in fluid properties). The effective acoustic geometry is very similar to the spacetime geometry of a black hole. The supersonic region corresponds to the hole's interior: sound waves propagating against the direction of the flow are swept downstream, like light pulled toward the center of a hole. The subsonic region is the exterior of the hole: Sound waves can propagate upstream but only at the expense of being stretched, like light being redshifted. The boundary between the two regions behaves exactly like a black hole horizon.

原子論
Atomism

　　假如流體夠冷，這個類比還可以延伸到量子的層次。安魯論證，聲音的「視界」也會發出和霍金輻射類 似的熱聲子。視界附近的量子漲落導致聲子對的出現；其中一個聲子被衝到超音速的區域，再也回不來了，而另一個同伴則向上游波動，並被流體拉長。擺在上游的 麥克風會收到模糊的嘶聲，而嘶聲的能量則是從流體的動能中抽取出來的。

　　If the fluid is cold enough, the analogy extends to the quantum level. Unruh argued that the sonic horizon emits thermal phonons analogous to Hawking radiation. Quantum fluctuations near the horizon cause pairs of phonons to appear; one partner gets swept into the supersonic region, never to return, while the other ripples upstream, getting stretched out by the fluid flow. A microphone placed upstream picks up a faint hiss. The sound energy of the hiss is drawn from the kinetic energy of the fluid flow.

　　雜音中的主要音調取決於幾何；觀測到聲子的典型波長，和流速隨空間變化 率的倒數相當。這種波長遠大於分子間的距離，因此安魯在他的原始分析中，假設流體是平滑而且連續的。可是源自視界附近的聲子，它們的波長應該會短到可以感 覺到流體顆粒性的程度。這對最後的結果會有影響嗎？實際的流體真的會發出類霍金聲子嗎？還是說，安魯的預測只是在連續流體這種理想條件下的人工產物呢？假 如這個問題可以在聲學黑洞上找到答案，或許利用類比的方式，也可以指點物理學家，該如何處理重力黑洞的問題。

　　The dominant tone of the noise depends on the geometry; the typical wavelength of the observed phonons is comparable to the distance over which the flow velocity changes appreciably. This distance is much larger than the distance between molecules, so Unruh did his original analysis assuming that the fluid is smooth and continuous. Yet the phonons originate near the horizon with wavelengths so short that they should be sensitive to the granularity of the fluid. Does that affect the end result? Does a real fluid emit Hawking-like phonons, or is Unruh's prediction an artifact of the idealization of a continuous fluid? If that question can be answered for acoustic black holes, it may by analogy guide physicists in the case of gravitational black holes.

　　除了超音速流體以外，物理學家還 提出了好幾個黑洞的類比模型。其中一種牽涉到的並非聲波，而是液體表面或是沿著兩層超流氦之間介面傳播的漣漪（超流氦冷到在運動時完全沒有摩擦阻力）。最 近安魯和德國德勒斯登科技大學的許茨侯（Ralf Schützhold）提議，研究在一個微小、精巧的電子管路中通行的電磁波。將雷射沿著管路掃過，可以改變局部的波速，運用這種方式，物理學家也許可以 創造出視界來。而另一個主意，是模仿宇宙的加速膨脹，來產生類似霍金輻射的東西。一團玻色–愛因斯坦凝聚（一種冷到原子會喪失其個體性的氣體），可以像膨 脹的宇宙對光的作用一樣，來對聲音作用，不管是令其飛散，或是用磁場來操縱，都可以得到同樣的效應。

　　Physicists have proposed a number of black hole analogues besides the transsonic fluid flow. One involves not sound waves but ripples on the surface of a liquid or along the interface between layers of superfluid helium, which is so cold that it has lost all frictional resistance to motion. Recently Unruh and Ralf Schützhold of the Technical University of Dresden in Germany proposed to study electromagnetic waves passing through a tiny, carefully engineered electronic pipe. By sweeping a laser along the pipe to change the local wave speed, physicists might be able to create a horizon. Yet another idea is to model the accelerating expansion of the universe, which generates a Hawking-like radiation. A Bose-Einstein condensate—a gas so cold that the atoms have lost their individual identity—can act on sound like an expanding universe does on light, either by literally flying apart or by being manipulated using a magnetic field to give the same effect.

　　由於程序繁複，而且實驗學家還有一大堆其他的低溫現象要忙，到目前為止，還沒有人在實驗室裡造出任何一種上述的裝置。因此理論學家只好著手探討，是否在這個問題上，可以藉由數學先有所進展。

　　As yet, experimenters have not created any of these devices in the laboratory. The procedures are complicated, and experimenters have plenty of other low-temperature phenomena to keep them busy. So theorists have been working to see whether they can make headway on the problem mathematically.

　 　流體的分子結構如何影響聲子，要瞭解起來是極度複雜的。幸好，在安魯提出他的聲學類比的後10年，賈可布森（本文作者之一）想出一個非常有用的簡化方 式。分子結構實質上的細節，可以化約在聲波的頻率和波長之間的相依關係中。這個相依關係，稱為「色散關係」（dispersion relation），決定了波的傳播速度。對於長波長的波，傳播速度是常數。而對於波長短到接近分子間距離的波，其速度則會隨頻率而改變。

　　 Understanding how the molecular structure of the fluid affects phonons is extremely complicated. Fortunately, 10 years after Unruh proposed his sonic analogy, one of us (Jacobson) came up with a very useful simplification. The essential details of the molecular structure are encapsulated in the way that the frequency of a sound wave depends on its wavelength. This dependence, called the dispersion relation, determines the velocity of propagation. For large wavelengths, the velocity is constant. For short wavelengths, approaching the intermolecular distance, the velocity can vary with wavelength.

　　有 三種不同的行為可能會出現。第一型是沒有色散：短波長和長波長的行為無異；第二型的速度隨波長變短而下降；而第三型則是波長越短速度越快。第一型可以描述 相對論中的光子，第二型則可以描述如超流氦中的聲子，而第三型所描述的則是稀薄的玻色–愛因斯坦凝聚中的聲子。這三型的分類，為理解分子結構在巨觀層次上 如何對聲波造成影響，提供了一套有條理的原則。從1995年開始，安魯與之後的其他學者，已經檢驗了霍金效應在第二和第三型色散模型中的表現。

　　 Three different behaviors can arise. Type I is no dispersion—the wave behaves the same at short wavelengths as it does at long ones. For type II, the velocity decreases as the wavelength decreases, and for type III, velocity increases. Type I describes photons in relativity. Type II describes phonons in, for example, superfluid helium, and type III describes phonons in dilute Bose-Einstein condensates. This division into three types provides an organizing principle for figuring out how molecular structure affects sound on a macroscopic level. Beginning in 1995, Unruh and then other researchers have examined the Hawking effect in the presence of type II and type III dispersion.

　 　考慮時間軸倒轉的情況下，類霍金聲子看起來會怎樣。剛開始，不同類型的色散並無影響。聲子往下游的視界游去，而它們的波長則一直變短。一旦波長接近分子 間的距離時，各自特定的色散關係就變得重要了。第二型的聲子會慢下來，倒轉方向，然後又開始回頭朝上遊走。至於第三型的聲子則會加速，超過長波的聲速，然 後穿越視界。

　　Consider how the Hawking-like phonons look when viewed backward in time. Initially the dispersion type does not matter. The phonons swim downstream toward the horizon, their wavelengths decreasing all the while. Once the wavelength approaches the intermolecular distance, the specific dispersion relation becomes important. For type II, the phonons slow down, then reverse direction and start heading upstream again. For type III, they accelerate, break the long-wavelength speed of sound, then cross the horizon.

乙太的復出
Ether Redux

　　真正霍金效應的類比，必須要符合一個重要的條件：虛聲子對必須從它們的基態中誕生，就像是黑洞附 近的虛光子對一樣。在實際的流體中，這個條件可以輕易達成。只要巨觀的流體隨時間與空間的變化率不大（和分子層次事件的速度相比），分子的狀態就有時間持 續地調整，使整個系統的能量達到最小。至於流體由哪一種分子組成，並沒有關係。

　　A true analogy to the Hawking effect must meet an important condition: the virtual phonon pairs must begin life in their ground state, as do the virtual photon pairs around the black hole. In a real fluid, this condition would be easily met. As long as the macroscopic fluid flow changes slowly in time and space (compared with the pace of events at the molecular level), the molecular state continuously adjusts to minimize the energy of the system as a whole. It does not matter which molecules the fluid is made of.

　　只要符合這個條件，那麼無論該流體屬於哪一型色散關係，都會發 出類霍金輻射，流體的微觀細節並不會有任何影響。這些細節會在聲子離開視界的過程中清洗得一乾二淨。而且，原來霍金在分析時所藉助的任意短波長，不管在考 慮第二型還是第三型色散的模型中，都沒有出現。取而代之的現象是，波長還不到分子間的距離就已達到下限。無限紅移只是無限小的原子這個非物理假設的化身。

　　With this condition met, it turns out that the fluid emits Hawking-like radiation no matter which of the three types of dispersion relations applies. The microscopic details of the fluid do not have any effect. They get washed out as the phonons travel away from the horizon. In addition, the arbitrarily short wavelengths invoked by original Hawking analysis do not arise when either type II or III dispersion is included. Instead the wavelengths bottom out at the intermolecular distance. The infinite redshift is an avatar of the unphysical assumption of infinitely small atoms.

　 　應用在真正的黑洞上，流體類比為霍金所得結果的正確性，增添了信心，儘管霍金做了不少簡化。而且，對某些學者而言，這表示重力場中黑洞附近的無限紅移， 或許可以運用短波長光波的色散，以類似的方法來加以迴避。不過此處有個陷阱。相對論斷言，光在真空中不會有色散。光子的波長對不同的觀察者來說並不相同； 由一個幾乎以光速在運動的參考座標來看，波長可以是任意長的。因此，物理定律不可以指定一個固定的截止長度（波長比這個長度為短的色散關係從第一型行為變 成第二型或第三型），否則每個觀察者會認知到不同的截止長度。

　　Applied to real black holes, the fluid analogy lends confidence that Hawking's result is correct despite the simplifications he made. Moreover, it suggests to some researchers that the infinite redshift at a gravitational black hole horizon may be similarly avoided by dispersion of short wavelength light. But there is a catch. Relativity theory flatly asserts that light does not undergo dispersion in a vacuum. The wavelength of a photon appears different to different observers; it is arbitrarily long when viewed from a reference frame that is moving sufficiently close to the speed of light. Hence, the laws of physics cannot mandate a fixed short-wavelength cutoff, at which the dispersion relation changes from type I to type II or III. Each observer would perceive a different cutoff.

　　於是物理學家陷入一個兩難的困境。他們要不就保留愛因斯坦的戒律，反對任何所謂 特別優越的座標，並把無限紅移硬吞下去；要不就假設光子不會發生無限紅移，這樣就得引進一個較適合的特定參考座標。這種座標一定會破壞相對論嗎？沒有人知 道。也許這特定的座標僅僅是出現在黑洞視界附近的局部效應；在這種情況下，一般而言相對論還是繼續適用的。另一方面，也許特定的座標隨處都在，而不只在黑 洞附近；這種情況下，相對論就只是自然界更深層理論的一個近似而已了。實驗學家目前還沒看到這樣的座標，不過看不出跡象並不代表沒有，也許只是缺乏足夠的 精確度使然。

　　Physicists thus face a dilemma. Either they retain Einstein's injunction against a preferred frame and they swallow the infinite redshifting, or they assume that photons do not undergo an infinite redshift and they have to introduce a preferred reference frame. Would this frame necessarily violate relativity? No one yet knows. Perhaps the preferred frame is a local effect that arises only near black hole horizons—in which case relativity continues to apply in general. On the other hand, perhaps the preferred frame exists everywhere, not just near black holes—in which case relativity is merely an approximation to a deeper theory of nature. Experimenters have yet to see such a frame, but the null result may simply be for want of sufficient precision.

　　物理學家老早就懷疑，要讓廣義相對論和量子力學相調和，會牽涉到一個短距離的截止長度，也許和普朗克尺度有關。聲學類比更坐實了這種疑慮。時空必須要有某種顆粒性來馴服曖昧的無限紅移。

　　Physicists have long suspected that reconciling general relativity with quantum mechanics would involve a short-distance cutoff, probably related to the Planck scale. The acoustic analogy bolsters this suspicion. Spacetime must be somehow granular to tame the dubious infinite redshift.

　 　假如真的是這樣，聲與光之間的類比，就比安魯原始的想法要接近多了。廣義相對論和量子力學的統一，也許會讓我們放棄連續時空這個理想條件，而發現時空的 「原子」。愛因斯坦可能早就有過類似的想法。1954年，也就是愛因斯坦過世的前一年，他在寫給好友貝索（Michele Besso）的信中提到：「我認為，物理很可能不是以場的概念為基礎，也就是說，物理不是奠基在連續的結構之上。」可是這會完全摧毀物理的根本基礎，而目 前科學家也不清楚有什麼候補的理論可以替代。的確，愛因斯坦下一句話接著說：「然後我整座懸空的城堡就會完全崩毀，不只重力理論，就連近代物理的其他部份 也不會留下片瓦。」50年後，城堡依舊完好如初，雖然它的未來有點模糊。而黑洞和它的聲學類比，也許正要開始照亮前路。 （本文出自SA 200512）

　　If so, the analogy between sound and light propagation would be even better than Unruh originally thought. The unification of general relativity and quantum mechanics may lead us to abandon the idealization of continuous space and time and to discover the 「atoms」 of spacetime. Einstein may have had similar thoughts when he wrote to his close friend Michele Besso in 1954, the year before his death: 「I consider it quite possible that physics cannot be based on the field concept, that is, on continuous structures.」 But this would knock out the very foundation from under physics, and at present scientists have no clear candidate for a substitute. Indeed, Einstein went on to say in his next sentence, 「Then nothing remains of my entire castle in the air, including the theory of gravitation, but also nothing of the rest of modern physics.」 Fifty years later the castle remains intact, although its future is unclear. Black holes and their acoustic analogues have perhaps begun to light the path and sound out the way.