如何建造時光機？－藍色情懷

如何建造時光機？
HOW TO BUILD A TIME MACHINE

回到未來，到底可不可能？
- It wouldn't be easy, but it might be possible

- 想不想乘坐電影「回到未來」的極速飛車，到未來看看汽車能否在空中穿梭飛馳？有人會說，那不過是科幻電影創造的奇想世界罷了，可是竟有物理學家想使夢想成真，一步步教你製造神奇時光機！

撰文╱戴維斯（Paul Davis），雪梨麥覺理大學澳洲天文生物學中心的理論物理學家。他寫了很多關於物理的科普讀物，研究興趣包括黑洞、量子場論、宇宙起源、意識的本質與生命的起源。
翻譯／陳義裕，美國加州理工學院物理博士，台灣大學物理系教授，主要研究非線性物理，餘暇並從事科普工作。

時光旅行，可能嗎？

自從威爾斯在1895年寫下《時光機器》這部膾炙人口的小說後，時光旅行就一直是科幻小說的流行主題。可是這真的造得出來嗎？我們真能造部機器把人傳送到過去或未來嗎？

　　Time travel has been a popular science-fiction theme since H. G. Wells wrote his celebrated novel The Time Machine in 1895. But can it really be done? Is it possible to build a machine that would transport a human being into the past or future?

在過去數十年中，時光旅行一直是和科學殿堂沾不上邊的，但近年來，這個話題已經開始在理論物理學家間發酵，其動機一部分是好玩，想一想時光旅行其實是蠻有趣的，但此研究也有它嚴肅的一面。瞭解因果關係，對於創製一統的物理理論是個關鍵。如果不受限的時光旅行竟成可能，甚或只是原理上行得通，則此一統理論的本質也會受到徹底的影響。

　　For decades, time travel lay beyond the fringe of respectable science. In recent years, however, the topic has become something of a cottage industry among theoretical physicists. The motivation has been partly recreational—time travel is fun to think about. But this research has a serious side, too. Understanding the relation between cause and effect is a key part of attempts to construct a unified theory of physics. If unrestricted time travel were possible, even in principle, the nature of such a unified theory could be drastically affected.

我們對時間的最佳認識是從愛因斯坦的相對論而來。在相對論問世前，一般認為時間是既絕對又普適，不論所處物理環境為何，它對每個人都一樣。在其狹義相對論中，愛因斯坦倡議，我們測到的兩個事件的時間間隔，會取決於觀察者如何運動。重要的一點是，做不同運動的兩位觀察者感受同樣兩個事件，這兩事件間流逝的時間並不相同。

　　Our best understanding of time comes from Einstein's theories of relativity. Prior to these theories, time was widely regarded as absolute and universal, the same for everyone no matter what their physical circumstances were. In his special theory of relativity, Einstein proposed that the measured interval between two events depends on how the observer is moving. Crucially, two observers who move differently will experience different durations between the same two events.

相對論中的「時差」
Jet Lag

這個效應通常是利用「孿生子佯謬」（twin paradox）來敘述。假設莎莉和山姆是孿生子。莎莉登上一艘火箭船以高速駛往鄰近的恆星，調個頭，然後飛回地球，而山姆則始終留守家園。就莎莉而言，這趟旅程也許耗時一年，可是當她回來踏出太空船時，會發現地球上已歷經10年了。她的兄弟已經比她老了九歲。莎莉和山姆這下就不再同歲數，雖然他們是同一天生的。這例子可說明其中一類有限制的時光旅行，實際上，莎莉已躍入九年後地球的未來。

　　The effect is often described using the 「twin paradox.」 Suppose that Sally and Sam are twins. Sally boards a rocket ship and travels at high speed to a nearby star, turns around and flies back to Earth, while Sam stays at home. For Sally the duration of the journey might be, say, one year, but when she returns and steps out of the spaceship, she finds that 10 years have elapsed on Earth. Her brother is now nine years older than she is. Sally and Sam are no longer the same age, despite the fact that they were born on the same day. This example illustrates a limited type of time travel. In effect, Sally has leaped nine years into Earth's future.

每當兩個觀察者之間有相對運動時，這個叫作「時間膨脹」（time dilation）的效應就會發生。但在日常生活中，我們不會感受到這種奇異的時間扭曲，這是因為此效應只在運動接近光速時才顯著。就以飛機的速度來算，時間膨脹在一般的飛航旅程中也只有數奈秒而已，比起威爾斯那類的歷險來，根本是小巫見大巫了。然而，原子鐘的精準度確實能記錄這個時間差，並驗證時間真的會因運動而拉長。所以，到未來旅行是個已經證實的事情，雖然到目前為止，這麼小的量實在沒什麼好令人興奮的。

　　THE EFFECT, KNOWN AS time dilation, occurs whenever two observers move relative to each other. In daily life we don't notice weird time warps, because the effect becomes dramatic only when the motion occurs at close to the speed of light. Even at aircraft speeds, the time dilation in a typical journey amounts to just a few nanoseconds—hardly an adventure of Wellsian proportions. Nevertheless, atomic clocks are accurate enough to record the shift and confirm that time really is stretched by motion. So travel into the future is a proved fact, even if it has so far been in rather unexciting amounts.

想看到真正顯著的時間扭曲，我們就必須突破日常經驗的藩籬。次原子粒子在大型加速器中便可推進到幾近光速，而當中的一部分粒子就有內在的鍾，例如緲子，因為它們有固定的半衰期。我們發現，加速器內快速運動的緲子的確是以慢動作在衰變，就如愛因斯坦理論所預言。某些宇宙射線也會經歷到很驚人的時間扭曲，這些粒子的運動速度太接近光速，以致從它們的觀點來看時，穿過宇宙只花了數分鐘，但是從地球的參考坐標系來看，它們似乎花了數萬年才辦到。如果時間扭曲沒發生，這些粒子早就會因衰變而永無到達之日。

　　To observe really dramatic time warps, one has to look beyond the realm of ordinary experience. Subatomic particles can be propelled at nearly the speed of light in large accelerator machines. Some of these particles, such as muons, have a built-in clock because they decay with a definite half-life; in accordance with Einstein's theory, fast-moving muons inside accelerators are observed to decay in slow motion. Some cosmic rays also experience spectacular time warps. These particles move so close to the speed of light that, from their point of view, they cross the galaxy in minutes, even though in Earth's frame of reference they seem to take tens of thousands of years. If time dilation did not occur, those particles would never make it here.

建造蠹孔時光機器的三個步驟（不怎麼容易喔）

1.尋找或製造一個蠹孔︰這是連接空間中兩地點的一種隧道。大的蠹孔也許自然存在於太空深處，是大霹靂的遺蹟。要不然我們就只好拿次原子蠹孔來充數。它們可能自然存在（有人說它們就在你我週遭不斷冒出又消失），或是人造的（譬如此處所想像，由粒子加速器製造）。這些小蠹孔必須放大到有用的大小，譬如用上類似大霹靂後讓空間膨脹的能量場。

2.使蠹孔穩定︰注入負能量，譬如利用開斯米效應（Casimir effect）等量子方式，使訊號或物體得以安全穿越蠹孔。蠹孔傾向於擠壓成一個密度無窮大或近乎無窮大的點，而負能量可對抗這個趨勢；換言之，它會避免蠹孔變成黑洞。

3.拖曳蠹孔︰假設有一艘具有高度先進科技的太空船，會將蠹孔的兩個口分開。其中一個開口或許可置放於中子星表面附近。中子星是極度緻密、有強大重力場的星球，此強重力場會使時間過得慢多了。由於時間在蠹孔的另一開口處過得較快，此兩開口便在空間及時間上都被分開來了。

速度是讓時間往前跳的一個辦法，而重力是另一個辦法。在愛因斯坦的廣義相對論中，他預言了重力會讓時間變慢。時鐘在閣樓上會比在地下室中走得稍快些，因為地下室較接近地心，所以是在比較強的重力場中。同理，時鐘在太空中跑得比在地面上快。再一次地，該效應是極其微小的，但我們已運用準確的時鐘直接測量到了。事實上，這些時間扭曲效應在全球定位系統中都必須計入，否則水手、計程車司機及巡弋飛彈會發現自己竟偏離路線許多公里。

　　Speed is one way to jump ahead in time. Gravity is another. In his general theory of relativity, Einstein predicted that gravity slows time. Clocks run a bit faster in the attic than in the basement, which is closer to the center of Earth and therefore deeper down in a gravitational field. Similarly, clocks run faster in space than on the ground. Once again the effect is minuscule, but it has been directly measured using accurate clocks. Indeed, these time-warping effects have to be taken into account in the Global Positioning System. If they weren't, sailors, taxi drivers and cruise missiles could find themselves many kilometers off course.

在中子星表面，重力場強到會讓時間比地球時間延遲了30%。從這種星球看到我們這裡發生的事件，就像把錄影帶往前快轉一樣。黑洞更是時間扭曲的極端範例：在它的表面上，時間相對於地球而言是靜止不動的，這表示如果你從黑洞旁邊掉進去的話，則在你到達表面的那一小段時間內，外面的宇宙就已經歷了滄海桑田的永恆。所以自外界看來，黑洞附近的區域簡直是時間的化外之地，因此，如果有位太空人可以貼近黑洞再折回而毫髮無傷的話（我得說，這是很唐吉訶德式的英勇舉動），那他應可躍入遠遠的未來。

　　At the surface of a neutron star, gravity is so strong that time is slowed by about 30 percent relative to Earth time. Viewed from such a star, events here would resemble a fast-forwarded video. A black hole represents the ultimate time warp; at the surface of the hole, time stands still relative to Earth. This means that if you fell into a black hole from nearby, in the brief interval it took you to reach the surface, all of eternity would pass by in the wider universe. The region within the black hole is therefore beyond the end of time, as far as the outside universe is concerned. If an astronaut could zoom very close to a black hole and return unscathed—admittedly a fanciful, not to mention foolhardy, prospect—he could leap far into the future.

旋得暈頭轉向
My Head Is Spinning

截至目前，我只談論了往未來旅行。那往過去又如何？這問題就大了。1948年，美國新澤西州普林斯頓高等研究院的哥德爾（Kurt Godel），造出了一個愛因斯坦重力場方程式的解，用來描述旋轉的宇宙。在這個宇宙裡，太空人可經由在空間中旅行而回到他自己的過去，此乃肇因於重力對於光的影響。宇宙的轉動會拖著光線（也就包括了物體彼此之間的因果關係）一起走，使得物質實體可以在空間及時間中都循著一條封閉曲線運動，而且在這粒子附近，全程都不會超過光速。哥德爾的解在當時只被視為好玩的數學遊戲，沒有人認真看待，畢竟經由觀測顯示，宇宙並無半點整體在旋轉的跡象。不過他的結果仍然證明，時光倒流並非為相對論所禁止的。事實上呢，愛因斯坦還承認，他曾被自己的理論在特定情況下可能允許時光倒流這想法所苦哩！

　　SO FAR I HAVE DISCUSSED travel forward in time. What about going backward? This is much more problematic. In 1948 Kurt Gödel of the Institute for Advanced Study in Princeton, N.J., produced a solution of Einstein's gravitational field equations that described a rotating universe. In this universe, an astronaut could travel through space so as to reach his own past. This comes about because of the way gravity affects light. The rotation of the universe would drag light (and thus the causal relations between objects) around with it, enabling a material object to travel in a closed loop in space that is also a closed loop in time, without at any stage exceeding the speed of light in the immediate neighborhood of the particle. Gödel's solution was shrugged aside as a mathematical curiosity—after all, observations show no sign that the universe as a whole is spinning. His result served nonetheless to demonstrate that going back in time was not forbidden by the theory of relativity. Indeed, Einstein confessed that he was troubled by the thought that his theory might permit travel into the past under some circumstances.

接著也發現別種「旅行到過去」的方式，例如1974年在美國杜蘭大學的提普勒（Frank J. Tipler）就曾做過計算，一個質量很大、無限長的圓柱體，若沿著軸心以接近光速自轉，便可讓太空人造訪他自己的過去；同樣的，這也是拖著光線繞著軸，以封閉曲線運動。1991年，美國普林斯頓大學的戈特（Richard Gott）則預測，宇宙弦（宇宙學家認為這種結構是在大霹靂初期形成）可以造成相似的結果。但是在1980年代中期，製造時光機器最實際的方法業已出現，那就是利用蠹孔（wormhole）這個概念。

　　Other scenarios have been found to permit travel into the past. For example, in 1974 Frank J. Tipler of Tulane University calculated that a massive, infinitely long cylinder spinning on its axis at near the speed of light could let astronauts visit their own past, again by dragging light around the cylinder into a loop. In 1991 J. Richard Gott of Princeton University predicted that cosmic strings—structures that cosmologists think were created in the early stages of the big bang—could produce similar results. But in the mid-1980s the most realistic scenario for a time machine emerged, based on the concept of a wormhole.

在科幻小說裡，蠹孔有時候也叫「星際閘門」，因為它們為空間中相距甚遠的兩點之間提供了一條捷徑。跳進這麼一個假設中的蠹孔，你也許能在瞬間後從星系的另一頭出現。蠹孔可以很自然地符合廣義相對論，正由於重力既會扭曲時間，對空間亦然。這個理論就好像我們可以在兩點間另闢蹊徑，或是挖鑿隧道使之相連一樣；數學家把這種情形稱作「多連通空間」（multiply connected space）。正如貫穿山丘的隧道會比繞山而行的道路要短，一個蠹孔也可能會比平常空間中的一般路徑短。

　　In science fiction, wormholes are sometimes called star-gates; they offer a shortcut between two widely separated points in space. Jump through a hypothetical wormhole, and you might come out moments later on the other side of the galaxy. Wormholes naturally fit into the general theory of relativity, whereby gravity warps not only time but also space. The theory allows the analogue of alternative road and tunnel routes connecting two points in space. Mathematicians refer to such a space as multiply connected. Just as a tunnel passing under a hill can be shorter than the surface street, a wormhole may be shorter than the usual route through ordinary space.

在1985年薩根（Carl Sagan）所寫的小說《接觸未來》之中，蠹孔也擔綱一種假想裝置的角色。受到薩根的激勵，美國加州理工學院的索恩（Kip S. Thorne）與他的夥伴，決定要找出蠹孔是否和已知的物理學相符。他們的出發點是，蠹孔應與黑洞相似，都是有著駭人重力的物體，但與只提供單行道卻到不了任何地方的黑洞不一樣的是，蠹孔除了有個入口之外，還會有個出口。

　　The wormhole was used as a fictional device by Carl Sagan in his 1985 novel Contact. Prompted by Sagan, Kip S. Thorne and his co-workers at the California Institute of Technology set out to find whether wormholes were consistent with known physics. Their starting point was that a wormhole would resemble a black hole in being an object with fearsome gravity. But unlike a black hole, which offers a one-way journey to nowhere, a wormhole would have an exit as well as an entrance.

置身於迴圈之內
In the Loop

要使蠹孔可以通行，它就得包含索恩稱之為「奇異物質」的東西。簡單說，這是一種能產生反重力的東西，從而能抗衡巨大質量系統會因自身重量而內爆成黑洞的自然趨勢。反重力（或稱重力排斥）可藉由負能量或負壓力而產生，我們已知負能量狀態可在若干量子系統內存在，這表示索恩的奇異物質並未被物理定律所排除，雖然我們也不清楚是否可以集結夠多的反重力物質來保持蠹孔的穩定。

　　FOR THE WORMHOLE to be traversable, it must contain what Thorne termed exotic matter. In effect, this is something that will generate antigravity to combat the natural tendency of a massive system to implode into a black hole under its intense weight. Antigravity, or gravitational repulsion, can be generated by negative energy or pressure. Negative-energy states are known to exist in certain quantum systems, which suggests that Thorne's exotic matter is not ruled out by the laws of physics, although it is unclear whether enough anti-gravitating stuff can be assembled to stabilize a wormhole [see 「Negative Energy, Wormholes and Warp Drive,」 by Lawrence H. Ford and Thomas A. Roman; Scientific American, January 2000].

很快地，索恩與他的同事便體認到：一旦可以製造出穩定的蠹孔，那它就可以很容易轉變成一部時光機器。一位穿越蠹孔的太空人，也許不只是在宇宙的某個地方出現，他還可以在某個時刻出現，而這「某時」可以是未來，或是過去。

　　Soon Thorne and his colleagues realized that if a stable wormhole could be created, then it could readily be turned into a time machine. An astronaut who passed through one might come out not only somewhere else in the universe but somewhen else, too—in either the future or the past.

要改造蠹孔以進行時光之旅，可以把它的一個開口拖往中子星，並安放在其表面附近。中子星的重力會使蠹孔開口處的時間減慢，這樣就會使蠹孔兩端的時間差逐漸累加。如果我們接著把兩個開口安置在適宜的空間位置上，這個時間差就會凍結住。

　　To adapt the wormhole for time travel, one of its mouths could be towed to a neutron star and placed close to its surface. The gravity of the star would slow time near that wormhole mouth, so that a time difference between the ends of the wormhole would gradually accumulate. If both mouths were then parked at a convenient place in space, this time difference would remain frozen in.

假設此時間差是10年，一位單向穿越此蠹孔的太空人就會躍入10年後的未來，而逆向穿越的太空人就會躍入10年前的過去。只要這第二位太空人以高速經由平常的空間返回出發點，則他的確有可能於尚未出發前便返回家園。換句話說，空間中的一條迴圈也有可能成為時間的迴圈。唯一的限制是：太空人不可能回到蠹孔首度製造出來之前的時間點。

　　Suppose the difference were 10 years. An astronaut passing through the wormhole in one direction would jump 10 years into the future, whereas an astronaut passing in the other direction would jump 10 years into the past. By returning to his starting point at high speed across ordinary space, the second astronaut might get back home before he left. In other words, a closed loop in space could become a loop in time as well. The one restriction is that the astronaut could not return to a time before the wormhole was first built.

要製造一台蠹孔時光機器所面臨的最大難題，就是要先製造一個蠹孔。也許空間早就自然地為這些結構所纏繞，因為它們是大霹靂的遺蹟；果真如此，或許已經有某個超文明可以駕馭它。另一種可能性則是，蠹孔可能在普朗克長度（約10^-33公分）這種極微的尺度下自然存在，這可是只有原子核的1/1020那麼小。理論上，這麼小的蠹孔，只需要一束能量脈衝便可將之穩住，接著便可將它膨脹到可資使用的大小。

　　A formidable problem that stands in the way of making a wormhole time machine is the creation of the wormhole in the first place. Possibly space is threaded with such structures naturally—relics of the big bang. If so, a supercivilization might commandeer one. Alternatively, wormholes might naturally come into existence on tiny scales, the so-called Planck length, about 20 factors of 10 as small as an atomic nucleus. In principle, such a minute wormhole could be stabilized by a pulse of energy and then somehow inflated to usable dimensions.

未來需要時間警察！
Censored!

　　假設我們已可克服技術上的問題，一旦時光機器被造出來，也等於打開了裝有因果佯謬的潘朵拉盒子。舉個例說吧，一個時間旅者回到過去，把他那仍在少女時代的母親給謀殺了。這下我們要怎麼釐清整件事呢？如果女孩死了，那她怎可能成為時間旅者的母親？而如果這個時間旅者從未出生，他哪能回到過去並謀殺其母？

　　ASSUMING THAT the engineering problems could be overcome, the production of a time machine could open up a Pandora's box of causal paradoxes. Consider, for example, the time traveler who visits the past and murders his mother when she was a young girl. How do we make sense of this? If the girl dies, she cannot become the time traveler's mother. But if the time traveler was never born, he could not go back and murder his mother.

　　這類佯謬之所以發生，是因為時間旅者企圖改變過去，而這顯然是不可能的，可是這並不表示某人就不可以參與過去。假設此時間旅者回到過去，並在謀殺案中拯救了一位年輕女孩，該女孩長大後變成了他的母親。這個因果迴圈現在就是前後一致而不再矛盾了。因果的一致性也許會對時間旅者只能做什麼事設限，但它並未排除時光旅行本身。

　　Paradoxes of this kind arise when the time traveler tries to change the past, which is obviously impossible. But that does not prevent someone from being a part of the past. Suppose the time traveler goes back and rescues a young girl from murder, and this girl grows up to become his mother. The causal loop is now self-consistent and no longer paradoxical. Causal consistency might impose restrictions on what a time traveler is able to do, but it does not rule out time travel per se.

　　不過，就算嚴格說來時光旅行不再矛盾好了，它肯定是很怪異的。試想一位時間旅者往前跳一年，在未來的《科學人》中讀到一個新的數學定理。他記下了細節，回到他自己的時代，並且把該定理教給一位學生，而這學生為《科學人》撰寫了這個定理；當然，該篇文章正是此時間旅者讀過的。這時，問題就來了：有關此定理的資訊究竟從何而來？不會是來自時間旅者，因為他是讀來的，可是也不會來自於學生，因為他是從時間旅者那裡學來的。這個資訊似乎莫名其妙地無中生有。

　　Even if time travel isn't strictly paradoxical, it is certainly weird. Consider the time traveler who leaps ahead a year and reads about a new mathematical theorem in a future edition of Scientific American. He notes the details, returns to his own time and teaches the theorem to a student, who then writes it up for Scientific American. The article is, of course, the very one that the time traveler read. The question then arises: Where did the information about the theorem come from? Not from the time traveler, because he read it, but not from the student either, who learned it from the time traveler. The information seemingly came into existence from nowhere, reasonlessly.

　　時光旅行這種怪異的結果，使部分科學家斷然排拒了此一概念。英國劍橋大學的霍金（Stephen W. Hawking）便提出了「時序保護臆測」，直接斬斷因果迴圈。由於已知相對論是允許因果迴圈的，所以時序的保護就得動用到別的干預因素，以免回到過去。這因素會是什麼呢？有一種說法是：量子作用便可伸出援手。時光機器的存在，會允許粒子輪迴至它自己的過去。某些計算暗示，接續發生的擾動會自我放大，形成一股失去控制的超大能量，終至毀了蠹孔。

　　The bizarre consequences of time travel have led some scientists to reject the notion outright. Stephen W. Hawking of the University of Cambridge has proposed a 「chronology protection conjecture,」 which would outlaw causal loops. Because the theory of relativity is known to permit causal loops, chronology protection would require some other factor to intercede to prevent travel into the past. What might this factor be? One suggestion is that quantum processes will come to the rescue. The existence of a time machine would allow particles to loop into their own past. Calculations hint that the ensuing disturbance would become self-reinforcing, creating a runaway surge of energy that would wreck the wormhole.

　　時序保護還只是個臆測而已，所以時光旅行仍是可能的。這件事最終的解決之道，恐怕得等到量子力學與重力的成功結合，或許經由像弦論或其延伸的M理論之類。我們甚至可以想見，下一代的粒子加速器或許能造出存活夠久的次原子蠹孔來，這樣一來，鄰近的粒子就可跑出短暫的因果迴圈。這和威爾斯所想像的時光機器自是大異其趣，但它將永遠改變我們對「物理事實」的看法。

　　Chronology protection is still just a conjecture, so time travel remains a possibility. A final resolution of the matter may have to await the successful union of quantum mechanics and gravitation, perhaps through a theory such as string theory or its extension, so-called M-theory. It is even conceivable that the next generation of particle accelerators will be able to create subatomic wormholes that survive long enough for nearby particles to execute fleeting causal loops. This would be a far cry from Wells's vision of a time machine, but it would forever change our picture of physical reality.

本文全文請見本期《科學人》中〈如何建造時光機？〉，文末提及英國劍橋大學著名宇宙學家霍金反駁時光旅行可能性的「時序保護臆測」理論，讀者可以在霍金的新作《胡桃裡的宇宙》（大塊出版）找到相關內容。
有幾本談及時光旅行、時光機器、蠹孔的中文書可供參考︰《時間機器》，CG威爾斯著、《踏入宇宙的一小步：黑洞、蟲孔與時光機》（究竟出版）、《光錐．蛀孔．宇宙弦》（天下出版）。

2002年11月號《科學人》特別邀請中研院天文所博士後研究員蔡駿導讀〈如何建造時光機？〉，內有詳細的時光旅行圖解，不可錯過！

Paul J. Nahin於1993年所寫的"Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction."、J. Richard Gott III.於2001年所寫的" Time Travel in Einstein's Universe: The Physical Possibilities of Travel through Time."以及本文作者戴維斯於2002年最新出版的" How to Build a Time Machine."，都是想要瞭解時光旅行不可不讀的重要參考書籍。