CHAPTER 10WORMHOLES AND TIME TRAVEL

第十章 蟲洞和時間旅行

The last chapter discussed why we see time go forward: why disorder increases and why we remember thepast but not the future. Time was treated as if it were a straight railway line on which one could only go one wayor the other.

我們在上一章討論了，爲什麼我們看到時間向前進；爲什麼無序度增加並且我們記住過去而不是將來。時間好像是一條筆直的鐵軌，人們只能往一個方向前進。

But what if the railway line had loops and branches so that a train could keep going forward but come back to astation it had already passed? In other words, might it be possible for someone to travel into the future or thepast?

如果該鐵軌有環圈以及分叉，使得一直往前開動的火車卻返回原先通過的車站，這是怎麼回事呢？換言之，人們可能旅行到未來或過去嗎？，

H. G. Wells in The Time Machine explored these possibilities as have countless other writers of science fiction.Yet many of the ideas of science fiction, like submarines and travel to the moon, have become matters ofscience fact. So what are the prospects for time travel?

H·G·韋爾斯在《時間機器》中探討了這些可能性，正好像其他無數的科學幻想作家那樣。科學幻想的許多觀念，如潛水艇以及飛往月亮等等都被科學實現了。那麼，時間旅行的前景如何呢？

The first indication that the laws of physics might really allow people to travel in time came in 1949 when KurtGodel discovered a new space-time allowed by general relativity. Godel was a mathematician who was famousfor proving that it is impossible to prove all true statements, even if you limit yourself to trying to prove all thetrue statements in a subject as apparently cut and dried as arithmetic. Like the uncertainty principle, Godel’sincompleteness theorem may be a fundamental limitation on our ability to understand and predict the universe,but so far at least it hasn’t seemed to be an obstacle in our search for a complete unified theory.

1949年庫爾特·哥德爾發現了廣義相對論允許的新的時空。這首次表明物理學定律的確允許人們在時間裏旅行。哥德爾是一名數學家，他因證明了不完備性定理而名震天下。該定理是說，不可能證明所有真的陳述，哪怕你把自己限制去證明在像算術這麼一目瞭然而且枯燥的學科中所有真的陳述。這個定理也許是我們理解和預言宇宙能力的基本極限，然而迄今它還未成爲我們尋求完整統一理論的障礙。

Godel got to know about general relativity when he and Einstein spent their later years at the Institute forAdvanced Study in Princeton. His space-time had the curious property that the whole universe was rotating.One might ask: “Rotating with respect to what?” The answer is that distant matter would be rotating withrespect to directions that little tops or gyroscopes point in.

哥德爾在和愛因斯坦於普林斯頓高級學術研究所度過他們晚年時通曉了廣義相對論。他的時空具有一個古怪的性質：整個宇宙都在旋轉。人們也許會問：“它相對於何物而旋轉？”其答案是遠處的物體繞着小陀螺或者陀螺儀的指向旋轉。

This had the side effect that it would be possible for someone to go off in a rocket ship and return to earthbefore he set out. This property really upset Einstein, who had thought that general relativity wouldn’t allow timetravel. However, given Einstein’s record of ill-founded opposition to gravitational collapse and the uncertaintyprinciple, maybe this was an encouraging sign. The solution Godel found doesn’t correspond to the universewe live in because we can show that the universe is not rotating. It also had a non-zero value of thecosmological constant that Einstein introduced when he thought the universe was unchanging. After Hubblediscovered the expansion of the universe, there was no need for a cosmological constant and it is nowgenerally believed to be zero. However, other more reasonable space-times that are allowed by generalrelativity and which permit travel into the past have since been found. One is in the interior of a rotating blackhole. Another is a space-time that contains two cosmic strings moving past each other at high speed. As theirname suggests, cosmic strings are objects that are like string in that they have length but a tiny cross section.Actually, they are more like rubber bands because they are under enormous tension, something like a millionmillion million million tons. A cosmic string attached to the earth could accelerate it from 0 to 60 mph in 1/30thof a second. Cosmic strings may sound like pure science fiction but there are reasons to believe they couldhave formed in the early universe as a result of symmetry-breaking of the kind discussed in Chapter 5.Because they would be under enormous tension and could start in any configuration, they might accelerate tovery high speeds when they straighten out.

這導致了一個附加的效應，一位航天員可以在他出發之前即回到地球。這個性質使愛因斯坦非常沮喪，他曾經以爲廣義相對論不允許時間旅行。然而，鑑於愛因斯坦對引力坍縮和不確定原理的無端反對，這也許反而是一個令人鼓舞的跡象。因爲我們可以證明，我們生存其中的宇宙是不旋轉的，所以哥德爾找到的解並不對應於它。它還有一個非零的宇宙常數。宇宙常數是當愛因斯坦以爲宇宙是不變時引進的。在哈勃發現了宇宙的膨脹後，就不再需要宇宙常數，而現在普遍認爲它應爲零。然而，之後從廣義相對論又找到其他一些更合理的時空，它們允許旅行到過去。其中之一即是旋轉黑洞的內部。另外一種是包含兩根快速穿越的宇宙弦的時空。顧名思義，宇宙弦是弦狀的物體，它具有長度，但是截面很微小。實際上，它們更像在巨大張力下的橡皮筋，其張力大約爲1億億億噸。把一根宇宙弦繫到地球上，就會把地球在1/3O秒的時間裏從每小時零英里（1英里= 1.609公里）加速到每小時60英里（1英里=1.609公里）。宇宙弦初聽起來像是科學幻想物，但有理由相信，它在早期宇宙中可由在第五章討論過的那種對稱破缺機制而產生。因爲宇宙弦具有巨大的張力，而且可以從任何形態起始，所以它們一旦伸展開來，就會加速到非常高的速度。

The Godel solution and the cosmic string space-time start out so distorted that travel into the past was alwayspossible. God might have created such a warped universe but we have no reason to believe he did.Observations of the microwave background and of the abundances of the light elements indicate that the earlyuniverse did not have the kind of curvature required to allow time travel. The same conclusion follows ontheoretical grounds if the no boundary proposal is correct. So the question is: if the universe starts out withoutthe kind of curvature required for time travel, can we subsequently warp local regions of space-time sufficientlyto allow it?

哥德爾解和宇宙弦時空一開始就扭曲，使得總能旅行到過去。上帝也許會創生了一個如此捲曲的宇宙，但是我們沒有理由相信他上帝會這樣做。微波背景和輕元素丰度的觀測表明，早期宇宙並沒有允許時間旅行的曲率。如果無邊界設想是正確的，從理論的基礎上也能導出這個結論。這樣問題就變成：如果宇宙初始就沒有時間旅行所必須的曲率，我們能否隨後把時空的局部區域捲曲到這種程度，以至於允許時間旅行？

A closely related problem that is also of concern to writers of science fiction is rapid interstellar or intergalactictravel. According to relativity, nothing can travel faster than light. If we therefore sent a spaceship to our nearestneighboring star, Alpha Centauri, which is about four light-years away, it would take at least eight years beforewe could expect the travelers to return and tell us what they had found. If the expedition were to the center ofour galaxy, it would be at least a hundred thousand years before it came back. The theory of relativity doesallow one consolation. This is the so-called twins paradox mentioned in Chapter 2.

快速恆星際或星系際旅行是一個密切相關的問題，也是科學幻想作家所關心的。根據相對論，沒有東西比光運動得更快。因此，如果我們向我們最近鄰的恆星α-半人馬座——發送空間飛船，由於它大約在4光年那麼遠，所以我們預料至少要8年才能等到旅行者們回來報告他們的發現。如果要去銀河系中心探險，至少要10萬年才能返回。相對論確實給了我們一些寬慰。這就是在第二章提及的雙生子佯謬。

Because there is no unique standard of time, but rather observers each have their own time as measured byclocks that they carry with them, it is possible for the journey to seem to be much shorter for the space travelersthan for those who remain on earth. But there would not be much joy in returning from a space voyage a fewyears older to find that everyone you had left behind was dead and gone thousands of years ago. So in order tohave any human interest in their stories, science fiction writers had to suppose that we would one day discoverhow to travel faster than light. What most of thee authors don’t seem to have realized is that if you can travelfaster than light, the theory of relativity implies you can also travel back in the, as the following limerick says:

因爲時間不存在惟一的標準，而每一位觀察者都擁有他自己的時間。這種時間是用他攜帶的時鐘來測量的，這樣航程對於空間旅行者比對於留在地球上的人顯得更短暫是可能的。但是，這對於那些只老了幾歲的回程的空間旅行者，並沒有什麼值得高興的，因爲他發現留在地球上的親友們已經死去幾千年了。這樣，科學幻想作家爲了使人們對他們的故事有興趣，必須設想有朝一日我們能運動得比光還快。大部分這些作家似乎未意識到的是，如果你能運動得比光還快，則相對論意味着，你能向時間的過去運動，正如以下五行打油詩所描寫的那樣：

There was a young lady of Wight

Who traveled much faster than light.

She departed one day,

In a relative way,

And arrived on the previous night

有位年輕小姐名懷特，

她能行走得比光還快。

她以相對性的方式，

在當天剛剛出發，

卻已在前晚到達。

The point is that the theory of relativity says hat there is no unique measure of time that all observers will agreeon Rather, each observer has his or her own measure of time. If it is possible for a rocket traveling below thespeed of light to get from event A (say, the final of the 100-meter race of the Olympic Games in 202) to event B(say, the opening of the 100,004th meeting of the Congress of Alpha Centauri), then all observers will agreethat event A happened before event B according to their times. Suppose, however, that the spaceship wouldhave to travel faster than light to carry the news of the race to the Congress. Then observers moving atdifferent speeds can disagree about whether event A occurred before B or vice versa. According to the time ofan observer who is at rest with respect to the earth, it may be that the Congress opened after the race. Thusthis observer would think that a spaceship could get from A to B in time if only it could ignore the speed-of-lightspeed limit. However, to an observer at Alpha Centauri moving away from the earth at nearly the speed of light,it would appear that event B, the opening of the Congress, would occur before event A, the 100-meter race.The theory of relativity says that the laws of physics appear the same to observers moving at different speeds.

關鍵在於相對論認爲不存在讓所有觀察者同意的惟一的時間測量。相反地，每位觀察者各有自己的時間測量。如果一枚火箭能以低於光的速度從事件A（譬如 2012年奧林匹克競賽的100米決賽）至事件B（譬如α-半人馬座議會第 100，004屆會議的開幕式），那麼根據所有觀察者的時間，他們都同意事件A發生於事件B之先。然而，假定飛船必須以超過光的速度才能把競賽的消息送到議會，那麼以不同速度運動的觀察者關於事件A和事件B何爲前何爲後就衆說紛紜。按照一位相對於地球靜止的觀察者，議會開幕也許是在競賽之後。這樣，這位觀察者會認爲，如果他不理光速限制的話，該飛船能及時地從A趕到B。然而，在α-半人馬座上以接近光速在離開地球方向飛行的觀察者就會覺得事件B，也就是議會開幕，先於事件A，也就是百米決賽發生。相對論告訴我們。對於以不同速度運動的觀察者，物理定律是完全相同的。

This has been well tested by experiment and is likely to remain a feature even if we find a more advancedtheory to replace relativity Thus the moving observer would say that if faster-than-light travel is possible, itshould be possible to get from event B, the opening of the Congress, to event A, the 100-meter race. If onewent slightly faster, one could even get back before the race and place a bet on it in the sure knowledge thatone would win.

這已被實驗很好地檢驗過。人們認爲，即使用更高級的理論去取代相對論，它仍然會被作爲一個特性而保留下來。這樣，如果超光速旅行是可能的，運動的觀察者會說，就有可能從事件B，也就是議會開幕式，趕到事件A，也就是百米競賽。如果他運動得更快一些，他甚至還來得及在賽事之前趕回，並在得知誰是贏家的情形下放下賭金。

There is a problem with breaking the speed-of-light barrier. The theory of relativity says that the rocket powerneeded to accelerate a spaceship gets greater and greater the nearer it gets to the speed of light. We haveexperimental evidence for this, not with spaceships but with elementary particles in particle accelerators likethose at Fermilab or CERN (European Centre for Nuclear Research). We can accelerate particles to 99.99percent of the speed of light, but however much power we feed in, we can’t get them beyond the speed-of-lightbarrier. Similarly with spaceships: no matter how much rocket power they have, they can’t accelerate beyondthe speed of light.

要打破光速壁壘存在一些問題。相對論告訴我們，飛船的速度越接近光速，用以對它加速的火箭功率就必須越來越大。對此我們已有實驗的證據，但不是空間飛船的經驗，而是在諸如費米實驗室或者歐洲核子研究中心的粒子加速器中的基本粒子的經驗。我們可以把粒子加速到光速的99．99％，但是不管我們注入多少功率，也不能把它們加速到超過光速壁壘。空間飛船的情形也是類似的：不管火箭有多大功率，也不可能加速到光速以上。

That might seem to rule out both rapid space travel and travel back in time. However, there is a possible wayout. It might be that one could warp space-time so that there was a shortcut between A and B One way of doingthis would be to create a wormhole between A and B. As its name suggests, a wormhole is a thin tube ofspace-time which can connect two nearly flat regions far apart.

這樣看來，快速空間旅行和往時間過去旅行似乎都不可行了。然而，還可能有辦法。人們也許可以把時空捲曲起來，使得A和B之間有一近路。在A和B之間創造一個蟲洞就是一個法子。顧名思義，蟲洞就是一個時空細管，它能把兩個幾乎平坦的相隔遙遠的區域連接起來。

There need be no relation between the distance through the wormhole and the separation of its ends in thenearly Hat background. Thus one could imagine that one could create or find a wormhole that world lead fromthe vicinity of the Solar System to Alpha Centauri. The distance through the wormhole might be only a fewmillion miles even though earth and Alpha Centauri are twenty million million miles apart in ordinary space. Thiswould allow news of the 100-meter race to reach the opening of the Congress. But then an observer movingtoward 6e earth should also be able to find another wormhole that would enable him to get from the opening ofthe Congress on Alpha Centauri back to earth before the start of the race. So wormholes, like any otherpossible form of travel faster than light, would allow one to travel into the past.

蟲洞兩個端點之間在幾乎平坦的背景裏的分離和通過蟲洞本身的距離之間沒必要有什麼關係。這樣，人們可以想像，他可以創造或者找到一個從太陽系附近通到。半人馬座的蟲洞。雖然在通常的空間中地球和α-半人馬座相隔20萬億英里（1英里=1.609公里），而通過蟲洞的距離卻只有幾百萬英里（1英里=1.6O9公里）。這樣百米決賽的消息就能趕在議會開幕式前到達。然後一位往地球飛去的觀察者也應該能找到另一個蟲洞，使他從α-半人馬座議會開幕在賽事之前回到地球。因此，蟲洞正和其他可能的超光速旅行方式一樣，允許人們往過去旅行。

The idea of wormholes between different regions of space-time was not an invention of science fiction writersbut came from a very respectable source.

時空不同區域之間的蟲洞的思想並非科學幻想作家的發明，它的起源是非常令人尊敬的。

In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed whatthey called “bridges,” but which are now known as wormholes. The Einstein-Rosen bridges didn’t last longenough for a spaceship to get through: the ship would run into a singularity as the wormhole pinched off.However, it has been suggested that it might be possible for an advanced civilization to keep a wormhole open.To do this, or to warp space-time in any other way so as to permit time travel, one can show that one needs aregion of space-time with negative curvature, like the surface of a saddle. Ordi-nary matter, which has apositive energy density, gives space-time a positive curvature, like the surface of a sphere. So what one needs,in order to warp space-time in a way that will allow travel into the past, is matter with negative energy density.

1935年愛因斯坦和納珍·羅森寫了一篇論文。在該論文中他們指出廣義相對論允許他們稱爲“橋”，而現在稱爲蟲洞的東西。愛因斯坦——羅森橋不能維持得足夠久，使得空間飛船來得及穿越：蟲洞會縮緊，而飛船撞到奇點上去。然而，有人提出，一個先進的文明可能使蟲洞維持開放。人們可以把時空以其他方式捲曲，使它允許時間旅行。可以證明這需要一個負曲率的時空區域，如同一個馬鞍面。通常的物質具有正能量密度，賦予時空以正曲率，如同一個球面。所以爲了使時空捲曲成允許旅行到過去的樣子，人們需要負能量密度的物質。

Energy is a bit like money: if you have a positive balance, you can distribute it in various ways, but according tothe classical laws that were believed at the beginning of the century, you weren’t allowed to be overdrawn. Sothese classical laws would have ruled out any possibility of time travel. However, as has been described inearlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle. Thequantum laws are more liberal and allow you to be overdrawn on one or two accounts provided the totalbalance is positive. In other words, quantum theory allows the energy density to be negative in some places,provided that this is made up for by positive energy densities in other places, so that the total energy re-mainspositive. An example of how quantum theory can allow negative energy densities is provided by what is calledthe Casimir effect. As we saw in Chapter 7, even what we think of as “empty” space is filled with pairs of virtualparticles and antiparticles that appear together, move apart, and come back together and annihilate each other.Now, suppose one has two parallel metal plates a short distance apart. The plates will act like mirrors for thevirtual photons or particles of light. In fact they will form a cavity between them, a bit like an organ pipe that willresonate only at certain notes. This means that virtual photons can occur in the space between the plates onlyif their wavelengths (the distance between the crest of one wave and the next) fit a whole number of times intothe gap between the plates. If the width of a cavity is a whole number of wavelengths plus a fraction of awave-length, then after some reflections backward and forward between the plates, the crests of one wave willcoincide with the troughs of another and the waves will cancel out.

能量有點像金錢：如果你有正的能量，就可以用不同方法分配，但是根據本世紀初相信的經典定律，你不允許透支。這樣，這些經典定律排除了時間旅行的任何可能性。然而，正如在前面幾章所描述的，量子定律已經超越了經典定律。量子定律是以不確定性原理爲基礎的。量子定律更慷慨些，只要你總的能量是正的，你就允許從一個或兩個賬號透支。換言之，量子理論允許在一些地方的能量密度爲負，只要它可由在其他地方的正的能量密度所補償，使得總能量保持爲正的。量子理論允許負能量密度的一個例子是所謂的卡西米爾效應。正如我們在第七章看到的，甚至我們認爲是“空”的空間也充滿了虛粒子和虛反粒子對，它們一起出現分離開，再返回一起並且相互湮滅。現在，假定人們有兩片距離很近的平行金屬板。金屬板對於虛光子起着類似鏡子的作用。事實上，在它們之間形成了一個空腔。它有點像風琴管，只對指定的音階共鳴。這意味着，只有當平板間的距離是虛光子波長（相鄰波峯之間的距離）的整數倍時，這些虛光子纔會在平板之中的空間出現。如果空腔的寬度是波長的整數倍再加上部分波長，那麼在前後反射多次後，一個波的波峯就會和另一個波谷相重合，這樣波動就被抵消了。

Because the virtual photons between the plates can have only the resonant wavelengths, there will be slightlyfewer of them than in the region outside the plates where virtual photons can have any wavelength. Thus therewill be slightly fewer virtual photons hitting the inside surfaces of the plates than the outside surfaces. Onewould therefore expect a force on the plates, pushing them toward each other. This force has actually beendetected and has the predicted value. Thus we have experimental evidence that virtual particles exist and havereal effects.

因爲平板之間的虛光子只能具有共振的波長，所以虛光子的數目比在平板之外的區域要略少些，在平板之外的虛光子可以具有任意波長。所以人們可以預料到這兩片平板遭受到把它們往裏擠的力。實際上已經測量到這種力。並且和預言的值相符。這樣，我們得到了虛粒子存在並具有實在效應的實驗證據。

The fact that there are fewer virtual photons between the plates means that their energy density will be lessthan elsewhere. But the total energy density in “empty” space far away from the plates must be zero, becauseotherwise the energy density would warp the space and it would not be almost flat. So, if the energy densitybetween the plates is less than the energy density far away, it must be negative.

在平板之間存在更少虛光子的事實意味着它們的能量密度比它處更小。但是在遠離平板的“空的”空間的總能量密度必須爲零，因爲否則的話，能量密度會把空間捲曲起來，而不能保持幾乎平坦。這樣，如果平板間的能量密度比遠處的能量密度更小，它就必須爲負的。

We thus have experimental evidence both that space-time can be warped (from the bending of light duringeclipses) and that it can be curved in the way necessary to allow time travel (from the Casimir effect). Onemight hope therefore that as we advance in science and technology, we would eventually manage to build atime machine. But if so, why hasn’t anyone come back from the future and told us how to do it? There might begood reasons why it would be unwise to give us the secret of time travel at our present primitive state ofdevelopment, but unless human nature changes radically, it is difficult to believe that some visitor from thefuture wouldn’t spill the beans. Of course, some people would claim that sightings of UFOs are evidence thatwe are being visited either by aliens or by people from the future. (If the aliens were to get here in reasonabletime, they would need faster-than-light travel, so the two possibilities may be equivalent.)

這樣，我們對以下兩種現象都獲得了實驗的證據。第一，從日食時的光線彎折得知時空可以被捲曲。第二，從卡西米爾效應得知時空可被彎曲成允許時間旅行的樣子。所以，人們希望隨着科學技術的推進，我們最終能夠造出時間機器。但是，如果這樣的話，爲什麼從來沒有一個來自未來的人回來告訴我們如何實現呢？鑑於我們現在處於初級發展階段，也許有充分理由認爲，讓我們分享時間旅行的祕密是不智的。除非人類本性得到徹底改變，非常難以相信，某位從未來飄然而至的訪客會貿然泄漏天機。當然，有些人會宣稱，觀察到幽浮就是外星人或者來自未來的人們來訪的證據（如果外星人在合理的時間內到達此地，他們則需要超光速旅行，這樣兩種可能性其實是等同的）。

However, I think that any visit by aliens or people from the future would be much more obvious and, probably,much more unpleasant. If they are going to reveal themselves at all, why do so only to those who are notregarded as reliable witnesses? If they are trying to warn us of some great danger, they are not being veryeffective.

然而，我認爲，任何外星來的或者來自未來的人的造訪應該是更加明顯，或許更加令人不悅。如果他們有意顯靈的話，爲何只對那些被認爲不太可靠的證人進行？如果他們試圖警告我們大難臨頭，這樣做也不是非常有效的。

A possible way to explain the absence of visitors from the future would be to say that the past is fixed becausewe have observed it and seen that it does not have the kind of warping needed to allow travel back from thefuture. On the other hand, the future is unknown and open, so it might well have the curvature required. Thiswould mean that any time travel would be confined to the future. There would be no chance of Captain Kirk andthe Starship Enterprise turning up at the present time.

一種對來自未來的訪客缺席的可能解釋方法是，因爲我們觀察了過去並且發現它並沒有允許從未來旅行返回所需的那類捲曲，所以過去是固定的。另一方面，未來是未知的開放的，所以也可能有所需的曲率。這意味着，任何時間旅行都被侷限於未來。此時此刻，柯克船長和星際航船沒有機會出現。

This might explain why we have not yet been overrun by tourists from the future, but it would not avoid theproblems that would arise if one were able to go back and change history. Suppose, for example, you wentback and killed your great-great-grandfather while he was still a child. There are many versions of this paradoxbut they are essentially equivalent: one would get contradictions if one were free to change the past.

這也許可以解釋，當今世界爲何還沒被來自未來的遊客所充斥。但是如果人們能夠回到以前並改變歷史，則問題就不能迴避。例如，假定你回到過去並且將你的祖先在他仍爲孩童時殺死。這類佯謬有許多版本，但是它們根本上是等效的：如果一個人可以自由地改變過去，則他就會遇到矛盾。

There seem to be two possible resolutions to the paradoxes posed by time travel. One I shall call the consistenthistories approach. It says that even if space-time is warped so that it would be possible to travel into the past,what happens in space-time must be a consistent solution of the laws of physics. According to this viewpoint,you could not go back in time unless history showed that you had already arrived in the past and, while there,had not killed your great-great-grandfather or committed any other acts that would conflict with your currentsituation in the present. Moreover, when you did go back, you wouldn’t be able to change recorded history.That means you wouldn’t have free will to do what you wanted. Of course, one could say that free will is anillusion anyway. If there really is a complete unified theory that governs everything, it presumably alsodetermines your actions. But it does so in a way that is impossible to calculate for an organism that is ascomplicated as a human being. The reason we say that humans have free will is because we can’t predict whatthey will do. However, if the human then goes off in a rocket ship and comes back before he or she set off, wewill be able to predict what he or she will do because it will be part of recorded history. Thus, in that situation,the time traveler would have no free will.

看來有兩種方法解決由時間旅行導致的佯謬。我把一種稱爲協調歷史方法。它是講，甚至當時空被捲曲得可能旅行到過去時，在時空中所發生的必須是物理定律的協調的解。根據這一觀點，除非歷史表明，你曾經到達過去，並且當時並沒有殺死你的祖先或者沒有任何行爲和你的現狀相沖突，你才能回到過去。況且，當你回到過去，你不能改變歷史記載。那表明你並沒有自由意志爲所欲爲。當然，人們可以說，自由意志反正是虛幻的。如果確實存在一套制約萬物的完整的統一理論，它也應該決定你的行動。但是對於像人類這麼複雜的機體，其制約和決定方式是不可能計算出來的。我們之所以說人們具有意志，乃在於我們不能預言他們未來的行動。然而，如果一個人乘火箭飛船出發並在這之前已經回返，我們就將能預言其未來行爲，因爲那將是歷史記載的一部分。這樣，在這種情形下，時間旅行者沒有自由意志。

The other possible way to resolve the paradoxes of time travel might be called the alternative historieshypothesis. The idea here is that when time travelers go back to the past, they enter alternative histories whichdiffer from recorded history. Thus they can act freely, without the constraint of consistency with their previoushistory. Steven Spiel-berg had fun with this notion in the Back to the Future films: Marty McFly was able to goback and change his parents’ courtship to a more satisfactory history.

解決時間旅行的其他可能的方法是稱爲選擇歷史假想。其思想是，當時間旅行者回到過去，他就進入和歷史記載不同的另外的歷史中去。這樣，他們可以自由地行動，不受和原先的歷史相一致的約束。史蒂芬·斯匹柏十分喜愛影片《迴歸未來》中的創意：瑪提·馬克弗萊能夠返回而且把他雙親戀愛的歷史改得更令人滿意。

The alternative histories hypothesis sounds rather like Richard Feynman’s way of expressing quantum theoryas a sum over histories, which was described in Chapters 4 and 8. This said that the universe didn’t just have asingle history: rather it had every possible history, each with its own probability. However, there seems to be animportant difference between Feynman’s proposal and alternative histories. In Feynman’s sum, each historycomprises a complete space-time and everything in it. The space-time may be so warped that it is possible totravel in a rocket into the past. But the rocket would remain in the same space-time and therefore the samehistory, which would have to be consistent. Thus Feynman’s sum over histories proposal seems to support theconsistent histories hypothesis rather than the alternative histories.

選擇歷史假想聽起來，和理查德·費因曼把量子理論表達成歷史求和的方法相類似，這已在第四章和第八章描述過。它是說宇宙不僅僅有一個單獨歷史，它有所有可能的歷史，每一個歷史都有自己的概率。然而，在費因曼的設想和選擇歷史之間似乎存在一個重要的差別。在費因曼求和中，每一個歷史都是由完整的時空和其中的每一件東西組成的。時空可以被捲曲成可能乘火箭旅行到過去。但是火箭要留在同一時空即同一歷史中，因而歷史必須是協調的。這樣，費因曼的歷史求和設想似乎支持協調歷史假想，而不支持選擇歷史假想。

The Feynman sum over histories does allow travel into the past on a microscopic scale. In Chapter 9 we sawthat the laws of science are unchanged by combinations of the operations C, P, and T. This means that anantiparticle spinning in the anticlockwise direction and moving from A to B can also be viewed as an ordinaryparticle spinning clockwise and moving backward in time from B to A. Similarly, an ordinary particle movingforward in time is equivalent to an antiparticle moving backward in time. As has been discussed in this chapterand Chapter 7, “empty” space is filled with pairs of virtual particles and antiparticles that appear together, moveapart, and then come back together and annihilate each other.

費因曼歷史求和允許在微觀的尺度下旅行到過去。我們在第九章看到，科學定律在CPT聯合對稱下不變。這表明，一個在反時鐘方向自旋並從A運動到B的反粒子還可以被認爲是在時鐘方向自旋並從B運動回A的通常粒子。類似地，一個在時間中向前運動的通常粒子等價於在時間中往後運動的反粒子。正如在本章以及第七章討論過的，“空” 的空間充滿了虛的粒子和反粒子對，它們一道出現、分離，然後回到一塊並且相互湮滅。

So, one can regard the pair of particles as a single particle moving on a closed loop in space-time. When thepair is moving forward in time (from the event at which it appears to that at which it annihilates), it is called aparticle. But when the particle is traveling back in time (from the event at which the pair annihilates to that atwhich it appears), it is said to be an antiparticle traveling forward in time.

這樣，人們可以把這對粒子認爲是在時空中沿着一個閉合圖運動的單獨粒子。當對子在時間中向前運動時（從它出現的事件出發到達它湮滅的事件），它被稱爲粒子。但是，當粒子在時間中往回運動時（從對湮滅的事件出發到達它出現的事件），可以說成反粒子在時間中向前運動。

The explanation of how black holes can emit particles and radiation (given in Chapter 7) was that one memberof a virtual particle/ antiparticle pair (say, the antiparticle) might fall into the black hole, leaving the othermember without a partner with which to annihilate. The forsaken particle might fall into the hole as well, but itmight also escape from the vicinity of the black hole. If so, to an observer at a distance it would appear to be aparticle emitted by the black hole.

在解釋黑洞何以發射粒子並輻射（見第七章）時認爲，虛的粒子/反粒子對中的一個成員（譬如反粒子）會落到黑洞中去，另一個成員留下來，失去和它湮滅的夥伴。這個被拋棄的粒子也可以落入黑洞，但是它也可以從黑洞的鄰近掙脫。如果這樣的話，對於一位遠處的觀察者，它就作爲從黑洞發射出的粒子而出現。

One can, however, have a different but equivalent intuitive picture of the mechanism for emission from blackholes. One can regard the member of the virtual pair that fell into the black hole (say, the antiparticle) as aparticle traveling backward in time out of the hole. When it gets to the point at which the virtualparticle/antiparticle pair appeared together, it is scattered by the gravitational field into a particle travelingforward in time and escaping from the black hole. If, instead, it were the particle member of the virtual pair thatfell into the hole, one could regard it as an antiparticle traveling back in time and coming out of the black hole.Thus the radiation by black holes shows that quantum theory allows travel back in time on a microscopic scaleand that such time travel can produce observable effects.

然而，人們對於黑洞輻射的機制可有不同的卻是等價的圖像。人們可以把虛對中的那個落入黑洞的成員（譬如反粒子）看成從黑洞出來的在時間中往回運動的粒子。當它到達虛粒子反粒子對一道出現的那一點，它被引力場散射成從黑洞逃脫的在時間中向前運動的粒子。相反地，如果是虛對中的粒子成員落入黑洞，人們可以把它認爲是從黑洞出來的在時間中往回運動的反粒子。這樣，黑洞輻射表明，量子理論在微觀尺度上允許在時間中的往回運動，而且這種時間旅行能產生可觀測的效應。

One can therefore ask: does quantum theory allow time travel on a macroscopic scale, which people coulduse? At first sight, it seems it should. The Feynman sum over histories proposal is supposed to be over allhistories. Thus it should include histories in which space-time is so warped that it is possible to travel into thepast. Why then aren’t we in trouble with history? Suppose, for example, someone had gone back and given theNazis the secret of the atom bomb?

因此產生這樣的問題：量子理論在宏觀尺度上允許人們可以利用的時間旅行嗎？初看起來應該是可以的。費因曼歷史求和的設想是指對所有的歷史進行的。這樣，它應包括被捲曲成允許旅行到過去的時空。那麼，爲什麼我們並沒有受到歷史的騷擾？例如，假定有人回到過去，並把原子彈祕密提供給納粹？

One would avoid these problems if what I call the chronology protection conjecture holds. This says that thelaws of physics conspire to prevent macroscopic bodies from carrying information into the past. Like the cosmiccensorship conjecture, it has not been proved but there are reasons to believe it is true.

如果我稱作時序防衛猜測成立的話，這些問題便可以避免。它是講，物理學定律防止宏觀物體將信息傳遞到過去。它正如宇宙監督猜測一樣，還未被證明，但是有理由相信它是成立的。

The reason to believe that chronology protection operates is that when space-time is warped enough to maketravel into the past possible, virtual particles moving on closed loops in space-time can become real particlestraveling forward in time at or below the speed of light. As these particles can go round the loop any number oftimes, they pass each point on their route many times. Thus their energy is counted over and over again andthe energy density will become very large. This could give space-time a positive curvature that would not allowtravel into the past. It is not yet clear whether these particles would cause positive or negative curvature orwhether the curvature produced by some kinds of virtual particles might cancel that produced by other kinds.Thus the possibility of time travel remains open. But I’m not going to bet on it. My opponent might have theunfair advantage of knowing the future.

相信時序防衛有效的原因是，當時空被捲曲得可以旅行到過去時，在時空中的閉圈上運動的虛粒子，在時間前進的方向以等於或者低於光速的速度運動時，就會變成實粒子。由於這些粒子可以任意多次地繞着圈子運動，它們通過路途中的每一點許多次。這樣，它們的能量被一次又一次地計算，使能量密度變得非常大。這也許賦予時空以正的曲率，因而不允許旅行到過去。這些粒子引起正的還是負的曲率，或者由某種虛粒子產生的曲率是否被別種粒子產生的抵消，仍然不清楚。這樣，時間旅行的可能性仍然未決。但是我不準備爲之打賭，我的對手或許具有通曉未來的不公平的優勢。

彎曲的時空和蟲洞↑