CHAPTER 9THE ARROW OF TIME
第九章 時間箭頭
In previous chapters we have seen how our views of the nature of time have changed over the years. Up to thebeginning of this century people believed in an absolute time. That is, each event could be labeled by a numbercalled “time” in a unique way, and all good clocks would agree on the time interval between two events.However, the discovery that the speed of light appeared the same to every observer, no matter how he wasmoving, led to the theory of relativity – and in that one had to abandon the idea that there was a uniqueabsolute time. Instead, each observer would have his own measure of time as recorded by a clock that hecarried: clocks carried by different observers would not necessarily agree. Thus time became a more personalconcept, relative to the observer who measured it.
我們在前幾章中看到了， 長期以來人們關於時間性質的觀點是如何變化的。 直到本世紀初， 人們還相信絕對時間。 也就是說， 每一事件可由一個稱為“時間”的數以唯一的方式來標記， 所有好的鐘在測量兩個事件之間的時間間隔上都是一致的。 然而， 對於任何正在運動的觀察者光速總是一樣的這一發現， 導致了相對論；而在相對論中， 人們必須拋棄存在一個唯一的絕對時間的觀念。 代之以每個觀察者攜帶的鐘所記錄的他自己的時間測量——不同觀察者攜帶的鐘不必要讀數一樣。
When one tried to unify gravity with quantum mechanics, one had to introduce the idea of “imaginary” time.Imaginary time is indistinguishable from directions in space. If one can go north, one can turn around and headsouth; equally, if one can go forward in imaginary time, one ought to be able to turn round and go backward.This means that there can be no important difference between the forward and backward directions ofimaginary time. On the other hand, when one looks at “real” time, there’s a very big difference between theforward and backward directions, as we all know. Where does this difference between the past and the futurecome from? Why do we remember the past but not the future?
當人們試圖統一引力和量子力學時， 必須引入“虛”時間的概念。 虛時間是不能和空間方向區分的。 如果一個人能往北走， 他就能轉過頭並朝南走；同樣的， 如果一個人能在虛時間裡向前走， 他應該能夠轉過來並往後走。 這表明在虛時間裡， 往前和往後之間不可能有重要的差別。 另一方面， 當人們考察“實”時間時， 正如眾所周知的， 在前進和後退方向存在有非常巨大的差別。 這過去和將來之間的差別從何而來？為何我們記住過去而不是將來？
The laws of science do not distinguish between the past and the future. More precisely, as explained earlier,the laws of science are unchanged under the combination of operations (or symmetries) known as C, P, and T.(C means changing particles for antiparticles. P means taking the mirror image, so left and right areinterchanged. And T means reversing the direction of motion of all particles: in effect, running the motionbackward.) The laws of science that govern the behavior of matter under all normal situations are unchangedunder the combination of the two operations C and P on their own. In other words, life would be just the samefor the inhabitants of another planet who were both mirror images of us and who were made of antimatter,rather than matter.
科學定律並不區別過去和將來。 更精確地講， 正如前面所解釋的， 科學定律在稱作C、P和T的聯合作用（或對稱）下不變。
If the laws of science are unchanged by the combination of operations C and P, and also by the combination C,P, and T, they must also be unchanged under the operation T alone. Yet there is a big difference between theforward and backward directions of real time in ordinary life. Imagine a cup of water falling off a table andbreaking into pieces on the floor. If you take a film of this, you can easily tell whether it is being run forward orbackward. If you run it backward you will see the pieces suddenly gather themselves together off the floor andjump back to form a whole cup on the table. You can tell that the film is being run backward because this kindof behavior is never observed in ordinary life. If it were, crockery manufacturers would go out of business.
如果科學定律在CP聯合對稱以及CPT聯合對稱下都不變， 它們也必須在單獨的T對稱下不變。 然而， 在日常生活的即時間中， 前進和後退的方向之間還是有一個大的差異。 想像一杯水從桌子上滑落到地板上被打碎。 如果你將其錄影， 你可以容易地辨別出它是向前進還是向後退。 如果將其倒回來， 你會看到碎片忽然集中到一起離開地板，
The explanation that is usually given as to why we don’t see broken cups gathering themselves together off thefloor and jumping back onto the table is that it is forbidden by the second law of thermodynamics. This says thatin any closed system disorder, or entropy, always increases with time. In other words, it is a form of Murphy’slaw: things always tend to go wrong! An intact cup on the table is a state of high order, but a broken cup on thefloor is a disordered state. One can go readily from the cup on the table in the past to the broken cup on thefloor in the future, but not the other way round.
為何我們從未看到碎杯子集合起來， 離開地面並跳回到桌子上， 通常的解釋是這違背了熱力學第二定律所表述的在任何閉合系統中無序度或熵總是隨時間而增加。 換言之， 它是穆菲定律的一種形式：事情總是趨向於越變越糟：桌面上一個完整的杯子是一個高度有序的狀態， 而地板上破碎的杯子是一個無序的狀態。 人們很容易從早先桌子上的杯子變成後來地面上的碎杯子， 而不是相反。
The increase of disorder or entropy with time is one example of what is called an arrow of time, something thatdistinguishes the past from the future, giving a direction to time. There are at least three different arrows oftime. First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropyincreases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, thedirection in which we remember the past but not the future. Finally, there is the cosmological arrow of time. Thisis the direction of time in which the universe is expanding rather than contracting.
無序度或熵隨著時間增加是一個所謂的時間箭頭的例子。
In this chapter I shall argue that the no boundary condition for the universe, together with the weak anthropicprinciple, can explain why all three arrows point in the same direction – and moreover, why a well-defined arrowof time should exist at all. I shall argue that the psychological arrow is determined by the thermodynamic arrow,A Brief History of Time - Stephen Hawking... Chapter 9condition for the universe, we shall see that there must be well-defined thermodynamic and cosmologicalarrows of time, but they will not point in the same direction for the whole history of the universe. However, Ishall argue that it is only when they do point in the same direction that conditions are suitable for thedevelopment of intelligent beings who can ask the question: why does disorder increase in the same directionof time as that in which the universe expands?
我將在這一章論斷， 宇宙的無邊界條件和弱人擇原理一起能解釋為何所有的三個箭頭指向同一方向。 此外， 為何必須存在一個定義得很好的時間箭頭。 我將論證心理學箭頭是由熱力學箭頭所決定， 並且這兩種箭頭必須總是指向相同的方向。 如果人們假定宇宙的無邊界條件， 我們將看到必然會有定義得很好的熱力學和宇宙學時間箭頭。
I shall discuss first the thermodynamic arrow of time. The second law of thermodynamics results from the factthat there are always many more disordered states than there are ordered ones. For example, consider thepieces of a jigsaw in a box. There is one, and. only one, arrangement in which the pieces make a completepicture. On the other hand, there are a very large number of arrangements in which the pieces are disorderedand don’t make a picture.
首先， 我要討論熱力學時間箭頭。 總存在著比有序狀態更多得多的無序狀態的這一事實， 是使熱力學第二定律存在的原因。 譬如， 考慮一盒拼板玩具， 存在一個並且只有一個使這些小紙片拼成一幅完整圖畫的排列。 另一方面， 存在巨大數量的排列， 這時小紙片是無序的， 不能拼成一幅畫。
Suppose a system starts out in one of the small number of ordered states. As time goes by, the system willevolve according to the laws of science and its state will change. At a later time, it is more probable that thesystem will be in a disordered state than in an ordered one because there are more disordered states. Thusdisorder will tend to increase with time if the system obeys an initial condition of high order.
假設一個系統從這少數的有序狀態之中的一個出發。 隨著時間流逝， 這個系統將按照科學定律演化， 而且它的狀態將改變。到後來，因為存在著更多的無序狀態，它處於無序狀態的可能性比處於有序狀態的可能性更大。這樣，如果一個系統服從一個高度有序的初始條件，無序度會隨著時間的增加而增大。
Suppose the pieces of the jigsaw start off in a box in the ordered arrangement in which they form a picture. Ifyou shake the box, the pieces will take up another arrangement. This will probably be a disorderedarrangement in which the pieces don’t form a proper picture, simply because there are so many moredisordered arrangements. Some groups of pieces may still form parts of the picture, but the more you shakethe box, the more likely it is that these groups will get broken up and the pieces will be in a completely jumbledstate in which they don’t form any sort of picture. So the disorder of the pieces will probably increase with time ifthe pieces obey the initial condition that they start off in a condition of high order.
假定拼板玩具盒的紙片從能排成一幅圖畫的有序組合開始，如果你搖動這盒子，這些紙片將會採用其他組合，這可能是一個不能形成一幅合適圖畫的無序的組合，就是因為存在如此之多得多的無序的組合。有一些紙片團仍可能形成部份圖畫，但是你越搖動盒子，這些團就越可能被分開，這些紙片將處於完全混亂的狀態，在這種狀態下它們不能形成任何種類的圖畫。這樣，如果紙片從一個高度有序的狀態的初始條件出發，紙片的無序度將可能隨時間而增加。
Suppose, however, that God decided that the universe should finish up in a state of high order but that it didn’tmatter what state it started in. At early times the universe would probably be in a disordered state. This wouldmean that disorder would decrease with time. You would see broken cups gathering themselves together andjumping back onto the table. However, any human beings who were observing the cups would be living in auniverse in which disorder decreased with time. I shall argue that such beings would have a psychologicalarrow of time that was backward. That is, they would remember events in the future, and not remember eventsin their past. When the cup was broken, they would remember it being on the table, but when it was on thetable, they would not remember it being on the floor.
然而，假定上帝決定不管宇宙從何狀態開始，它都必須結束於一個高度有序的狀態，則在早期這宇宙有可能處於無序的狀態。這意味著無序度將隨時間而減小。你將會看到破碎的杯子集合起來並跳回到桌子上。然而，任何觀察杯子的人都生活在無序度隨時間減小的宇宙中，我將論斷這樣的人會有一個倒溯的心理學時間箭頭。這就是說，他們會記住將來的事件，而不是過去的事件。當杯子被打碎時，他們會記住它在桌子上的情形；但是當它是在桌子上時，他們不會記住它在地面上的情景。
It is rather difficult to talk about human memory because we don’t know how the brain works in detail. We do,however, know all about how computer memories work. I shall therefore discuss the psychological arrow oftime for computers. I think it is reasonable to assume that the arrow for computers is the same as that forhumans. If it were not, one could make a killing on the stock exchange by having a computer that wouldremember tomorrow’s prices!
由於我們不知道大腦工作的細節，所以討論人類的記憶是相當困難的。然而，我們確實知道電腦的記憶器是如何工作的。所以，我將討論電腦的心理學時間箭頭。我認為，假定電腦和人類有相同的箭頭是合理的。如果不是這樣，人們可能因為擁有一台記住明年價格的電腦而使股票交易所垮臺。
A computer memory is basically a device containing elements that can exist ineither of two states. A simple example is an abacus. In its simplest form, this consists of a number of wires; oneach wire there are a number of beads that can be put in one of two positions. Before an item is recorded in acomputer’s memory, the memory is in a disordered state, with equal probabilities for the two possible states.(The abacus beads are scattered randomly on the wires of the abacus.) After the memory interacts with thesystem to be remembered, it will definitely be in one state or the other, according to the state of the system.(Each abacus bead will be at either the left or the right of the abacus wire.) So the memory has passed from adisordered state to an ordered one. However, in order to make sure that the memory is in the right state, it isnecessary to use a certain amount of energy (to move the bead or to power the computer, for example). Thisenergy is dissipated as heat, and increases the amount of disorder in the universe. One can show that thisincrease in disorder is always greater than the increase in the order of the memory itself. Thus the heatexpelled by the computer’s cooling fan means that when a computer records an item in memory, the totalamount of disorder in the universe still goes up. The direction of time in which a computer remembers the pastis the same as that in which disorder increases.
大體來說，電腦的記憶器是一個包含可存在於兩種狀態中的任一種狀態的元件的設備，算盤是一個簡單的例子。其最簡單的形式是由許多鐵條組成；每一根鐵條上有一念珠，此念珠可呆在兩個位置之中的一個。|Qī-shu-ωang|在電腦記憶器進行存儲之前，其記憶器處於無序態，念珠等幾率地處於兩個可能的狀態中。（算盤珠雜亂無章地散佈在算盤的鐵條上）。在記憶器和所要記憶的系統相互作用後，根據系統的狀態，它肯定處於這種或那種狀態（每個算盤珠將位於鐵條的左邊或右邊。）這樣，記憶器就從無序態轉變成有序態。然而，為了保證記憶器處於正確的狀態，需要使用一定的能量（例如，移動算盤珠或給電腦接通電源）。這能量以熱的形式耗散了，從而增加了宇宙的無序度的量。人們可以證明，這個無序度增量總比記憶器本身有序度的增量大。這樣，由電腦冷卻風扇排出的熱量表明電腦將一個專案記錄在它的記憶器中時，宇宙的無序度的總量仍然增加。電腦記憶過去的時間方向和無序度增加的方向是一致的。
Our subjective sense of the direction of time, the psychological arrow of time, is therefore determined within ourbrain by the thermodynamic arrow of time. Just like a computer, we must remember things in the order in whichentropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with timebecause we measure time in the direction in which disorder increases You can’t have a safer bet than that!
所以，我們對時間方向的主觀感覺或心理學時間箭頭，是在我們頭腦中由熱力學時間箭頭所決定的。正像一個電腦，我們必須在熵增加的順序上將事物記住。這幾乎使熱力學定律變成為無聊的東西。無序度隨時間的增加乃是因為我們是在無序度增加的方向上測量時間。你不可能有比這個更具勝算的打賭了！
But why should the thermodynamic arrow of time exist at all? Or, in other words, why should the universe be ina state of high order at one end of time, the end that we call the past? Why is it not in a state of completedisorder at all times? After all, this might seem more probable. And why is the direction of time in whichdisorder increases the same as that in which the universe expands?
但是究竟為何必須存在熱力學時間箭頭？或換句話說，在我們稱之為過去時間的一端，為何宇宙處於高度有序的狀態？為何它不在所有時間裡處於完全無序的狀態？畢竟這似乎更為可能。並且為何無序度增加的時間方向和宇宙膨脹的方向相同？
In the classical theory of general relativity one cannot predict how the universe would have begun because allthe known laws of science would have broken down at the big bang singularity. The universe could havestarted out in a very smooth and ordered state. This would have led to well-defined thermodynamic andcosmological arrows of time, as we observe. But it could equally well have started out in a very lumpy anddisordered state. In that case, the universe would already be in a state of complete disorder, so disorder couldnot increase with time. It would either stay constant, in which case there would be no well-definedthermodynamic arrow of time, or it would decrease, in which case the thermodynamic arrow of time would pointin the opposite direction to the cosmological arrow. Neither of these possibilities agrees with what we observe.However, as we have seen, classical general relativity predicts its own downfall. When the curvature ofspace-time becomes large, quantum gravitational effects will become important and the classical theory willcease to be a good description of the universe. One has to use a quantum theory of gravity to understand howthe universe began.
在經典廣義相對論中，因為所有已知的科學定律在大爆炸奇點處失效，人們不能預言宇宙是如何開始的。宇宙可以從一個非常光滑和有序的狀態開始。這就會導致正如我們所觀察到的、定義很好的熱力學和宇宙學的時間箭頭。但是，它可以同樣合理地從一個非常波浪起伏的無序狀態開始。在那種情況下，宇宙已經處於一種完全無序的狀態，所以無序度不會隨時間而增加。或者它保持常數，這時就沒有定義很好的熱力學時間箭頭；或者它會減小，這時熱力學時間箭頭就會和宇宙學時間箭頭相反向。任何這些可能性都不符合我們所觀察到的情況。然而，正如我們看到的，經典廣義相對論預言了它自身的崩潰。當時空曲率變大，量子引力效應變得重要，並且經典理論不再能很好地描述宇宙時，人們必須用量子引力論去理解宇宙是如何開始的。
In a quantum theory of gravity, as we saw in the last chapter, in order to specify the state of the universe onewould still have to say how the possible histories of the universe would behave at the boundary of space-time inthe past. One could avoid this difficulty of having to describe what we do not and cannot know only if thehistories satisfy the no boundary condition: they are finite in extent but have no boundaries, edges, orsingularities. In that case, the beginning of time would be a regular, smooth point of space-time and theuniverse would have begun its expansion in a very smooth and ordered state. It could not have beencompletely uniform, because that would violate the uncertainty principle of quantum theory. There had to besmall fluctuations in the density and velocities of particles. The no boundary condition, however, implied thatthese fluctuations were as small as they could be, consistent with the uncertainty principle.
正如我們在上一章 看到的，在量子引力論中，為了指定宇宙的態，人們仍然必須說清在過去的空間-時間的邊界的宇宙的可能歷史是如何行為的。只有如果這些歷史滿足無邊界條件，人們才可能避免這個不得不描述我們不知道和無法知道的東西的困難：它們在尺度上有限，但是沒有邊界、邊緣或奇點。在這種情形下，時間的開端就會是規則的、光滑的空間-時間的點，並且宇宙在一個非常光滑和有序的狀態下開始它的膨脹。它不可能是完全均勻的，否則就違反了量子理論不確定性原理。必然存在密度和粒子速度的小起伏，然而無邊界條件意味著，這些起伏又是在與不確定性原理相一致的條件下盡可能的小。
The universe would have started off with a period of exponential or “inflationary” expansion in which it wouldhave increased its size by a very large factor. During this expansion, the density fluctuations would haveremained small at first, but later would have started to grow. Regions in which the density was slightly higherthan average would have had their expansion slowed down by the gravitational attraction of the extra mass.Eventually, such regions would stop expanding and collapse to form galaxies, stars, and beings like us. Theuniverse would have started in a smooth and ordered state, and would become lumpy and disordered as timewent on. This would explain the existence of the thermodynamic arrow of time.
宇宙剛開始時有一個指數或“暴漲”的時期，在這期間它的尺度增加了一個非常大的倍數。在膨脹時，密度起伏一開始一直很小，但是後來開始變大。在密度比平均值稍大的區域，額外品質的引力吸引使膨脹速度放慢。最終，這樣的區域停止膨脹，並坍縮形成星系、恒星以及我們這樣的人類。宇宙開始時處於一個光滑有序的狀態，隨時間演化成波浪起伏的無序的狀態。這就解釋了熱力學時間箭頭的存在。
But what would happen if and when the universe stopped expanding and began to contract? Would thethermodynamic arrow reverse and disorder begin to decrease with time? This would lead to all sorts ofscience-fiction-like possibilities for people who survived from the expanding to the contracting phase. Wouldthey see broken cups gathering themselves together off the floor and jumping back onto the table? Would theybe able to remember tomorrow’s prices and make a fortune on the stock market? It might seem a bit academicto worry about what will happen when the universe collapses again, as it will not start to contract for at leastanother ten thousand million years. But there is a quicker way to find out what will happen: jump into a blackhole. The collapse of a star to form a black hole is rather like the later stages of the collapse of the wholeuniverse. So if disorder were to decrease in the contracting phase of the universe, one might also expect it todecrease inside a black hole. So perhaps an astronaut who fell into a black hole would be able to make moneyat roulette by remembering where the ball went before he placed his bet. (Unfortunately, however, he would nothave long to play before he was turned to spaghetti. Nor would he be able to let us know about the reversal ofthe thermodynamic arrow, or even bank his winnings, because he would be trapped behind the event horizonof the black hole.)
如果宇宙停止膨脹並開始收縮將會發生什麼呢？熱力學箭頭會不會倒轉過來，而無序度開始隨時間減少呢？這為從膨脹相存活到收縮相的人們留下了五花八門的科學幻想的可能性。他們是否會看到杯子的碎片集合起來離開地板跳回到桌子上去？他們會不會記住明天的價格，並在股票市場上發財致富？由於宇宙至少要再等一百億年之後才開始收縮，憂慮那時會發生什麼似乎有點學究氣。但是有一種更快的辦法去查明將來會發生什麼，即跳到黑洞裡面去。恒星坍縮形成黑洞的過程和整個宇宙的坍縮的後期相當類似；這樣，如果在宇宙的收縮相無序度減小，可以預料它在黑洞裡面也會減小。所以，一個落到黑洞裡去的太空人能在投賭金之前，也許能依靠記住輪賭盤上球兒的走向而贏錢。（然而，不幸的是，玩不了多久，他就會變成義大利麵條。他也不能使我們知道熱力學箭頭的顛倒，或者甚至將他的贏錢存入銀行，因為他被困在黑洞的事件視界後面。）
At first, I believed that disorder would decrease when the universe recollapsed. This was because I thought thatthe universe had to return to a smooth and ordered state when it became small again. This would mean thatthe contracting phase would be like the time reverse of the expanding phase. People in the contracting phasewould live their lives backward: they would die before they were born and get younger as the universecontracted.
起初，我相信在宇宙坍縮時無序度會減小。這是因為，我認為宇宙再變小時，它必須回到光滑和有序的狀態。這表明，收縮相僅僅是膨脹相的時間反演。處在收縮相的人們將以倒退的方式生活：他們在出生之前即已死去，並且隨著宇宙收縮變得更年輕。
This idea is attractive because it would mean a nice symmetry between the expanding and contracting phases.However, one cannot adopt it on its own, independent of other ideas about the universe. The question is: is itimplied by the no boundary condition, or is it inconsistent with that condition? As I said, I thought at first that theno boundary condition did indeed imply that disorder would decrease in the contracting phase. I was misledpartly by the analogy with the surface of the earth. If one took the beginning of the universe to correspond tothe North Po le, then the end of the universe should be similar to the beginning, just as the South Pole is similarto the North. However, the North and South Poles correspond to the beginning and end of the universe inimaginary time. The beginning and end in real time can be very different from each other. I was also misled bywork I had done on a simple model of the universe in which the collapsing phase looked like the time reverse ofthe expanding phase. However, a colleague of mine, Don Page, of Penn State University, pointed out that theno boundary condition did not require the contracting phase necessarily to be the time reverse of the expandingphase. Further, one of my students, Raymond Laflamme, found that in a slightly more complicated model, thecollapse of the universe was very different from the expansion. I realized that I had made a mistake: the noboundary condition implied that disorder would in fact continue to increase during the contraction. Thethermodynamic and psychological arrows of time would not reverse when the universe begins to recontract, orinside black holes.
這個觀念是吸引人的，因為它表明在膨脹相和收縮相之間存在一個漂亮的對稱。然而，人們不能置其他有關宇宙的觀念於不顧，而只採用這個觀念。問題在於：它是否由無邊界條件所隱含或它是否與這個條件不相協調？正如我說過的，我起先以為無邊界條件確實意味著無序度會在收縮相中減小。我之所以被誤導，部分是由於與地球表面的類比引起的。如果人們將宇宙的開初對應於北極，那麼宇宙的終結就應該類似於它的開端，正如南極之與北極相似。然而，北南二極對應於虛時間中的宇宙的開端和終結。在即時間裡的開端和終結之間可有非常大的差異。我還被我作過的一項簡單的宇宙模型的研究所誤導，在此模型中坍縮相似乎是膨脹相的時間反演。然而，我的一位同事，賓夕凡尼亞州立大學的當·佩奇指出，無邊界條件沒有要求收縮相必須是膨脹相的時間反演。我的一個學生雷蒙·拉夫勒蒙進一步發現，在一個稍複雜的模型中，宇宙的坍縮和膨脹非常不同。我意識到自己犯了一個錯誤：無邊界條件意味著事實上在收縮相時無序度繼續增加。當宇宙開始收縮時或在黑洞中熱力學和心理學時間箭頭不會反向。
What should you do when you find you have made a mistake like that? Some people never admit that they arewrong and continue to find new, and often mutually inconsistent, arguments to support their case – asEddington did in opposing black hole theory. Others claim to have never really supported the incorrect view inthe first place or, if they did, it was only to show that it was inconsistent. It seems to me much better and lessconfusing if you admit in print that you were wrong. A good example of this was Einstein, who called thecosmological constant, which he introduced when he was trying to make a static model of the universe, thebiggest mistake of his life.
當你發現自己犯了這樣的錯誤後該如何辦？有些人從不承認他們是錯誤的，而繼續去找新的往往互相不協調的論據為自己辯解——正如愛丁頓在反對黑洞理論時之所為。另外一些人首先宣稱，從來沒有真正支援過不正確的觀點，如果他們支持了，也只是為了顯示它是不協調的。在我看來，如果你在出版物中承認自己錯了，那會好得多並少造成混亂。愛因斯坦即是一個好的榜樣，他在企圖建立一個靜態的宇宙模型時引入了宇宙常數，他稱此為一生中最大的錯誤。
To return to the arrow of time, there remains the question: why do we observe that the thermodynamic andcosmological arrows point in the same direction? Or in other words, why does disorder increase in the samedirection of time as that in which the universe expands? If one believes that the universe will expand and thencontract again, as the no boundary proposal seems to imply, this becomes a question of why we should be inthe expanding phase rather than the contracting phase.
回頭再說時間箭頭，餘下的問題是；為何我們觀察到熱力學和宇宙學箭頭指向同一方向？或換言之，為何無序度增加的時間方向正是宇宙膨脹的時間方向？如果人們相信，按照無邊界假設似乎所隱含的那樣，宇宙先膨脹然後重新收縮，那麼為何我們應在膨脹相中而不是在收縮相中，這就成為一個問題。
One can answer this on the basis of the weak anthropic principle. Conditions in the contracting phase would notbe suitable for the existence of intelligent beings who could ask the question: why is disorder increasing in thesame direction of time as that in which the universe is expanding? The inflation in the early stages of theuniverse, which the no boundary proposal predicts, means that the universe must be expanding at very close tothe critical rate at which it would just avoid recollapse, and so will not recollapse for a very long time. By then allthe stars will have burned out and the protons and neutrons in them will probably have decayed into lightparticles and radiation. The universe would be in a state of almost complete disorder. There would be no strongthermodynamic arrow of time. Disorder couldn’t increase much because the universe would be in a state ofalmost complete disorder already. However, a strong thermodynamic arrow is necessary for intelligent life tooperate. In order to survive, human beings have to consume food, which is an ordered form of energy, andconvert it into heat, which is a disordered form of energy. Thus intelligent life could not exist in the contractingphase of the universe. This is the explanation of why we observe that the thermodynamic and cosmologicalarrows of time point in the same direction. It is not that the expansion of the universe causes disorder toincrease. Rather, it is that the no boundary condition causes disorder to increase and the conditions to besuitable for intelligent life only in the expanding phase.
人們可以在弱人擇原理的基礎上回答這個問題。收縮相的條件不適合於智慧人類的存在，而正是他們能夠提出為何無序度增加的時間方向和宇宙膨脹的時間方向相同的問題。無邊界假設預言的宇宙在早期階段的暴漲意味著，宇宙必須以非常接近為避免坍縮所需要的臨界速率膨脹，這樣它在很長的時間內才不至坍縮。到那時候所有的恒星都會燒盡，而在其中的質子和中子可能會衰變成輕粒子和輻射。宇宙將處於幾乎完全無序的狀態，這時就不會有強的熱力學時間箭頭。由於宇宙已經處於幾乎完全無序的狀態，無序度不會增加很多。然而，對於智慧生命的行為來說，一個強的熱力學箭頭是必需的。為了生存下去，人類必須消耗能量的一種有序形式——食物，並將其轉化成能量的一種無序形式——熱量，所以智慧生命不能在宇宙的收縮相中存在。這就解釋了，為何我們觀察到熱力學和宇宙學的時間箭頭指向一致。並不是宇宙的膨脹導致無序度的增加，而是無邊界條件引起無序度的增加，並且只有在膨脹相中才有適合智慧生命的條件。
To summarize, the laws of science do not distinguish between the forward and backward directions of time.However, there are at least three arrows of time that do distinguish the past from the future. They are thethermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the directionof time in which we remember the past and not the future; and the cosmological arrow, the direction of time inwhich the universe expands rather than contracts. I have shown that the psychological arrow is essentially thesame as the thermodynamic arrow, so that the two would always point in the same direction. The no boundaryproposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because theuniverse must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow toagree with the cosmological arrow is that intelligent beings can exist only in the expanding phase. Thecontracting phase will be unsuitable because it has no strong thermodynamic arrow of time.
總之，科學定律並不能區分前進和後退的時間方向。然而，至少存在有三個時間箭頭將過去和將來區分開來。它們是熱力學箭頭，這就是無序度增加的時間方向；心理學箭頭，即是在這個時間方向上，我們能記住過去而不是將來；還有宇宙學箭頭，也即宇宙膨脹而不是收縮的方向。我指出了心理學箭頭本質上應和熱力學箭頭相同。宇宙的無邊界假設預言了定義得很好的熱力學時間箭頭，因為宇宙必須從光滑、有序的狀態開始。並且我們看到，熱力學箭頭和宇宙學箭頭的一致，乃是由於智慧生命只能在膨脹相中存在。收縮相是不適合於它的存在的，因為那兒沒有強的熱力學時間箭頭。
The progress of the human race in understanding the universe has established a small corner of order in anincreasingly disordered universe. If you remember every word in this book, your memory will have recordedabout two million pieces of information: the order in your brain will have increased by about two million units.However, while you have been reading the book, you will have converted at least a thousand calories ofordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air aroundyou by convection and sweat. This will increase the disorder of the universe by about twenty million millionmillion million units – or about ten million million million times the increase in order in your brain – and that’s ifyou remember everything in this book. In the next chapter but one I will try to increase the order in our neck ofthe woods a little further by explaining how people are trying to fit together the partial theories I have describedto form a complete unified theory that would cover everything in the universe.
人類理解宇宙的進步，是在一個無序度增加的宇宙中建立了一個很小的有序的角落。如果你記住了這本書中的每一個詞，你的記憶就記錄了大約200萬單位的資訊——你頭腦中的有序度就增加了大約200萬單位。然而，當你讀這本書時，你至少將以食物為形式的1千卡路里的有序能量，轉換成為以對流和汗釋放到你周圍空氣中的熱量的形式的無序能量。這就將宇宙的無序度增大了大約20億億億單位，或大約是你頭腦中有序度增量——那是如果你記住這本書的每一件事的話——的1000億億倍。我試圖在下一章更增加一些我們頭腦的有序度，解釋人們如何將我描述過的部分理論結合一起，形成一個完整的統一理論，這個理論將適用於宇宙中的任何東西。
Suppose the pieces of the jigsaw start off in a box in the ordered arrangement in which they form a picture. Ifyou shake the box, the pieces will take up another arrangement. This will probably be a disorderedarrangement in which the pieces don’t form a proper picture, simply because there are so many moredisordered arrangements. Some groups of pieces may still form parts of the picture, but the more you shakethe box, the more likely it is that these groups will get broken up and the pieces will be in a completely jumbledstate in which they don’t form any sort of picture. So the disorder of the pieces will probably increase with time ifthe pieces obey the initial condition that they start off in a condition of high order.
假定拼板玩具盒的紙片從能排成一幅圖畫的有序組合開始，如果你搖動這盒子，這些紙片將會採用其他組合，這可能是一個不能形成一幅合適圖畫的無序的組合，就是因為存在如此之多得多的無序的組合。有一些紙片團仍可能形成部份圖畫，但是你越搖動盒子，這些團就越可能被分開，這些紙片將處於完全混亂的狀態，在這種狀態下它們不能形成任何種類的圖畫。這樣，如果紙片從一個高度有序的狀態的初始條件出發，紙片的無序度將可能隨時間而增加。
Suppose, however, that God decided that the universe should finish up in a state of high order but that it didn’tmatter what state it started in. At early times the universe would probably be in a disordered state. This wouldmean that disorder would decrease with time. You would see broken cups gathering themselves together andjumping back onto the table. However, any human beings who were observing the cups would be living in auniverse in which disorder decreased with time. I shall argue that such beings would have a psychologicalarrow of time that was backward. That is, they would remember events in the future, and not remember eventsin their past. When the cup was broken, they would remember it being on the table, but when it was on thetable, they would not remember it being on the floor.
然而，假定上帝決定不管宇宙從何狀態開始，它都必須結束於一個高度有序的狀態，則在早期這宇宙有可能處於無序的狀態。這意味著無序度將隨時間而減小。你將會看到破碎的杯子集合起來並跳回到桌子上。然而，任何觀察杯子的人都生活在無序度隨時間減小的宇宙中，我將論斷這樣的人會有一個倒溯的心理學時間箭頭。這就是說，他們會記住將來的事件，而不是過去的事件。當杯子被打碎時，他們會記住它在桌子上的情形；但是當它是在桌子上時，他們不會記住它在地面上的情景。
It is rather difficult to talk about human memory because we don’t know how the brain works in detail. We do,however, know all about how computer memories work. I shall therefore discuss the psychological arrow oftime for computers. I think it is reasonable to assume that the arrow for computers is the same as that forhumans. If it were not, one could make a killing on the stock exchange by having a computer that wouldremember tomorrow’s prices!
由於我們不知道大腦工作的細節，所以討論人類的記憶是相當困難的。然而，我們確實知道電腦的記憶器是如何工作的。所以，我將討論電腦的心理學時間箭頭。我認為，假定電腦和人類有相同的箭頭是合理的。如果不是這樣，人們可能因為擁有一台記住明年價格的電腦而使股票交易所垮臺。
A computer memory is basically a device containing elements that can exist ineither of two states. A simple example is an abacus. In its simplest form, this consists of a number of wires; oneach wire there are a number of beads that can be put in one of two positions. Before an item is recorded in acomputer’s memory, the memory is in a disordered state, with equal probabilities for the two possible states.(The abacus beads are scattered randomly on the wires of the abacus.) After the memory interacts with thesystem to be remembered, it will definitely be in one state or the other, according to the state of the system.(Each abacus bead will be at either the left or the right of the abacus wire.) So the memory has passed from adisordered state to an ordered one. However, in order to make sure that the memory is in the right state, it isnecessary to use a certain amount of energy (to move the bead or to power the computer, for example). Thisenergy is dissipated as heat, and increases the amount of disorder in the universe. One can show that thisincrease in disorder is always greater than the increase in the order of the memory itself. Thus the heatexpelled by the computer’s cooling fan means that when a computer records an item in memory, the totalamount of disorder in the universe still goes up. The direction of time in which a computer remembers the pastis the same as that in which disorder increases.
大體來說，電腦的記憶器是一個包含可存在於兩種狀態中的任一種狀態的元件的設備，算盤是一個簡單的例子。其最簡單的形式是由許多鐵條組成；每一根鐵條上有一念珠，此念珠可呆在兩個位置之中的一個。|Qī-shu-ωang|在電腦記憶器進行存儲之前，其記憶器處於無序態，念珠等幾率地處於兩個可能的狀態中。（算盤珠雜亂無章地散佈在算盤的鐵條上）。在記憶器和所要記憶的系統相互作用後，根據系統的狀態，它肯定處於這種或那種狀態（每個算盤珠將位於鐵條的左邊或右邊。）這樣，記憶器就從無序態轉變成有序態。然而，為了保證記憶器處於正確的狀態，需要使用一定的能量（例如，移動算盤珠或給電腦接通電源）。這能量以熱的形式耗散了，從而增加了宇宙的無序度的量。人們可以證明，這個無序度增量總比記憶器本身有序度的增量大。這樣，由電腦冷卻風扇排出的熱量表明電腦將一個專案記錄在它的記憶器中時，宇宙的無序度的總量仍然增加。電腦記憶過去的時間方向和無序度增加的方向是一致的。
Our subjective sense of the direction of time, the psychological arrow of time, is therefore determined within ourbrain by the thermodynamic arrow of time. Just like a computer, we must remember things in the order in whichentropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with timebecause we measure time in the direction in which disorder increases You can’t have a safer bet than that!
所以，我們對時間方向的主觀感覺或心理學時間箭頭，是在我們頭腦中由熱力學時間箭頭所決定的。正像一個電腦，我們必須在熵增加的順序上將事物記住。這幾乎使熱力學定律變成為無聊的東西。無序度隨時間的增加乃是因為我們是在無序度增加的方向上測量時間。你不可能有比這個更具勝算的打賭了！
But why should the thermodynamic arrow of time exist at all? Or, in other words, why should the universe be ina state of high order at one end of time, the end that we call the past? Why is it not in a state of completedisorder at all times? After all, this might seem more probable. And why is the direction of time in whichdisorder increases the same as that in which the universe expands?
但是究竟為何必須存在熱力學時間箭頭？或換句話說，在我們稱之為過去時間的一端，為何宇宙處於高度有序的狀態？為何它不在所有時間裡處於完全無序的狀態？畢竟這似乎更為可能。並且為何無序度增加的時間方向和宇宙膨脹的方向相同？
In the classical theory of general relativity one cannot predict how the universe would have begun because allthe known laws of science would have broken down at the big bang singularity. The universe could havestarted out in a very smooth and ordered state. This would have led to well-defined thermodynamic andcosmological arrows of time, as we observe. But it could equally well have started out in a very lumpy anddisordered state. In that case, the universe would already be in a state of complete disorder, so disorder couldnot increase with time. It would either stay constant, in which case there would be no well-definedthermodynamic arrow of time, or it would decrease, in which case the thermodynamic arrow of time would pointin the opposite direction to the cosmological arrow. Neither of these possibilities agrees with what we observe.However, as we have seen, classical general relativity predicts its own downfall. When the curvature ofspace-time becomes large, quantum gravitational effects will become important and the classical theory willcease to be a good description of the universe. One has to use a quantum theory of gravity to understand howthe universe began.
在經典廣義相對論中，因為所有已知的科學定律在大爆炸奇點處失效，人們不能預言宇宙是如何開始的。宇宙可以從一個非常光滑和有序的狀態開始。這就會導致正如我們所觀察到的、定義很好的熱力學和宇宙學的時間箭頭。但是，它可以同樣合理地從一個非常波浪起伏的無序狀態開始。在那種情況下，宇宙已經處於一種完全無序的狀態，所以無序度不會隨時間而增加。或者它保持常數，這時就沒有定義很好的熱力學時間箭頭；或者它會減小，這時熱力學時間箭頭就會和宇宙學時間箭頭相反向。任何這些可能性都不符合我們所觀察到的情況。然而，正如我們看到的，經典廣義相對論預言了它自身的崩潰。當時空曲率變大，量子引力效應變得重要，並且經典理論不再能很好地描述宇宙時，人們必須用量子引力論去理解宇宙是如何開始的。
In a quantum theory of gravity, as we saw in the last chapter, in order to specify the state of the universe onewould still have to say how the possible histories of the universe would behave at the boundary of space-time inthe past. One could avoid this difficulty of having to describe what we do not and cannot know only if thehistories satisfy the no boundary condition: they are finite in extent but have no boundaries, edges, orsingularities. In that case, the beginning of time would be a regular, smooth point of space-time and theuniverse would have begun its expansion in a very smooth and ordered state. It could not have beencompletely uniform, because that would violate the uncertainty principle of quantum theory. There had to besmall fluctuations in the density and velocities of particles. The no boundary condition, however, implied thatthese fluctuations were as small as they could be, consistent with the uncertainty principle.
正如我們在上一章 看到的，在量子引力論中，為了指定宇宙的態，人們仍然必須說清在過去的空間-時間的邊界的宇宙的可能歷史是如何行為的。只有如果這些歷史滿足無邊界條件，人們才可能避免這個不得不描述我們不知道和無法知道的東西的困難：它們在尺度上有限，但是沒有邊界、邊緣或奇點。在這種情形下，時間的開端就會是規則的、光滑的空間-時間的點，並且宇宙在一個非常光滑和有序的狀態下開始它的膨脹。它不可能是完全均勻的，否則就違反了量子理論不確定性原理。必然存在密度和粒子速度的小起伏，然而無邊界條件意味著，這些起伏又是在與不確定性原理相一致的條件下盡可能的小。
The universe would have started off with a period of exponential or “inflationary” expansion in which it wouldhave increased its size by a very large factor. During this expansion, the density fluctuations would haveremained small at first, but later would have started to grow. Regions in which the density was slightly higherthan average would have had their expansion slowed down by the gravitational attraction of the extra mass.Eventually, such regions would stop expanding and collapse to form galaxies, stars, and beings like us. Theuniverse would have started in a smooth and ordered state, and would become lumpy and disordered as timewent on. This would explain the existence of the thermodynamic arrow of time.
宇宙剛開始時有一個指數或“暴漲”的時期，在這期間它的尺度增加了一個非常大的倍數。在膨脹時，密度起伏一開始一直很小，但是後來開始變大。在密度比平均值稍大的區域，額外品質的引力吸引使膨脹速度放慢。最終，這樣的區域停止膨脹，並坍縮形成星系、恒星以及我們這樣的人類。宇宙開始時處於一個光滑有序的狀態，隨時間演化成波浪起伏的無序的狀態。這就解釋了熱力學時間箭頭的存在。
But what would happen if and when the universe stopped expanding and began to contract? Would thethermodynamic arrow reverse and disorder begin to decrease with time? This would lead to all sorts ofscience-fiction-like possibilities for people who survived from the expanding to the contracting phase. Wouldthey see broken cups gathering themselves together off the floor and jumping back onto the table? Would theybe able to remember tomorrow’s prices and make a fortune on the stock market? It might seem a bit academicto worry about what will happen when the universe collapses again, as it will not start to contract for at leastanother ten thousand million years. But there is a quicker way to find out what will happen: jump into a blackhole. The collapse of a star to form a black hole is rather like the later stages of the collapse of the wholeuniverse. So if disorder were to decrease in the contracting phase of the universe, one might also expect it todecrease inside a black hole. So perhaps an astronaut who fell into a black hole would be able to make moneyat roulette by remembering where the ball went before he placed his bet. (Unfortunately, however, he would nothave long to play before he was turned to spaghetti. Nor would he be able to let us know about the reversal ofthe thermodynamic arrow, or even bank his winnings, because he would be trapped behind the event horizonof the black hole.)
如果宇宙停止膨脹並開始收縮將會發生什麼呢？熱力學箭頭會不會倒轉過來，而無序度開始隨時間減少呢？這為從膨脹相存活到收縮相的人們留下了五花八門的科學幻想的可能性。他們是否會看到杯子的碎片集合起來離開地板跳回到桌子上去？他們會不會記住明天的價格，並在股票市場上發財致富？由於宇宙至少要再等一百億年之後才開始收縮，憂慮那時會發生什麼似乎有點學究氣。但是有一種更快的辦法去查明將來會發生什麼，即跳到黑洞裡面去。恒星坍縮形成黑洞的過程和整個宇宙的坍縮的後期相當類似；這樣，如果在宇宙的收縮相無序度減小，可以預料它在黑洞裡面也會減小。所以，一個落到黑洞裡去的太空人能在投賭金之前，也許能依靠記住輪賭盤上球兒的走向而贏錢。（然而，不幸的是，玩不了多久，他就會變成義大利麵條。他也不能使我們知道熱力學箭頭的顛倒，或者甚至將他的贏錢存入銀行，因為他被困在黑洞的事件視界後面。）
At first, I believed that disorder would decrease when the universe recollapsed. This was because I thought thatthe universe had to return to a smooth and ordered state when it became small again. This would mean thatthe contracting phase would be like the time reverse of the expanding phase. People in the contracting phasewould live their lives backward: they would die before they were born and get younger as the universecontracted.
起初，我相信在宇宙坍縮時無序度會減小。這是因為，我認為宇宙再變小時，它必須回到光滑和有序的狀態。這表明，收縮相僅僅是膨脹相的時間反演。處在收縮相的人們將以倒退的方式生活：他們在出生之前即已死去，並且隨著宇宙收縮變得更年輕。
This idea is attractive because it would mean a nice symmetry between the expanding and contracting phases.However, one cannot adopt it on its own, independent of other ideas about the universe. The question is: is itimplied by the no boundary condition, or is it inconsistent with that condition? As I said, I thought at first that theno boundary condition did indeed imply that disorder would decrease in the contracting phase. I was misledpartly by the analogy with the surface of the earth. If one took the beginning of the universe to correspond tothe North Po le, then the end of the universe should be similar to the beginning, just as the South Pole is similarto the North. However, the North and South Poles correspond to the beginning and end of the universe inimaginary time. The beginning and end in real time can be very different from each other. I was also misled bywork I had done on a simple model of the universe in which the collapsing phase looked like the time reverse ofthe expanding phase. However, a colleague of mine, Don Page, of Penn State University, pointed out that theno boundary condition did not require the contracting phase necessarily to be the time reverse of the expandingphase. Further, one of my students, Raymond Laflamme, found that in a slightly more complicated model, thecollapse of the universe was very different from the expansion. I realized that I had made a mistake: the noboundary condition implied that disorder would in fact continue to increase during the contraction. Thethermodynamic and psychological arrows of time would not reverse when the universe begins to recontract, orinside black holes.
這個觀念是吸引人的，因為它表明在膨脹相和收縮相之間存在一個漂亮的對稱。然而，人們不能置其他有關宇宙的觀念於不顧，而只採用這個觀念。問題在於：它是否由無邊界條件所隱含或它是否與這個條件不相協調？正如我說過的，我起先以為無邊界條件確實意味著無序度會在收縮相中減小。我之所以被誤導，部分是由於與地球表面的類比引起的。如果人們將宇宙的開初對應於北極，那麼宇宙的終結就應該類似於它的開端，正如南極之與北極相似。然而，北南二極對應於虛時間中的宇宙的開端和終結。在即時間裡的開端和終結之間可有非常大的差異。我還被我作過的一項簡單的宇宙模型的研究所誤導，在此模型中坍縮相似乎是膨脹相的時間反演。然而，我的一位同事，賓夕凡尼亞州立大學的當·佩奇指出，無邊界條件沒有要求收縮相必須是膨脹相的時間反演。我的一個學生雷蒙·拉夫勒蒙進一步發現，在一個稍複雜的模型中，宇宙的坍縮和膨脹非常不同。我意識到自己犯了一個錯誤：無邊界條件意味著事實上在收縮相時無序度繼續增加。當宇宙開始收縮時或在黑洞中熱力學和心理學時間箭頭不會反向。
What should you do when you find you have made a mistake like that? Some people never admit that they arewrong and continue to find new, and often mutually inconsistent, arguments to support their case – asEddington did in opposing black hole theory. Others claim to have never really supported the incorrect view inthe first place or, if they did, it was only to show that it was inconsistent. It seems to me much better and lessconfusing if you admit in print that you were wrong. A good example of this was Einstein, who called thecosmological constant, which he introduced when he was trying to make a static model of the universe, thebiggest mistake of his life.
當你發現自己犯了這樣的錯誤後該如何辦？有些人從不承認他們是錯誤的，而繼續去找新的往往互相不協調的論據為自己辯解——正如愛丁頓在反對黑洞理論時之所為。另外一些人首先宣稱，從來沒有真正支援過不正確的觀點，如果他們支持了，也只是為了顯示它是不協調的。在我看來，如果你在出版物中承認自己錯了，那會好得多並少造成混亂。愛因斯坦即是一個好的榜樣，他在企圖建立一個靜態的宇宙模型時引入了宇宙常數，他稱此為一生中最大的錯誤。
To return to the arrow of time, there remains the question: why do we observe that the thermodynamic andcosmological arrows point in the same direction? Or in other words, why does disorder increase in the samedirection of time as that in which the universe expands? If one believes that the universe will expand and thencontract again, as the no boundary proposal seems to imply, this becomes a question of why we should be inthe expanding phase rather than the contracting phase.
回頭再說時間箭頭，餘下的問題是；為何我們觀察到熱力學和宇宙學箭頭指向同一方向？或換言之，為何無序度增加的時間方向正是宇宙膨脹的時間方向？如果人們相信，按照無邊界假設似乎所隱含的那樣，宇宙先膨脹然後重新收縮，那麼為何我們應在膨脹相中而不是在收縮相中，這就成為一個問題。
One can answer this on the basis of the weak anthropic principle. Conditions in the contracting phase would notbe suitable for the existence of intelligent beings who could ask the question: why is disorder increasing in thesame direction of time as that in which the universe is expanding? The inflation in the early stages of theuniverse, which the no boundary proposal predicts, means that the universe must be expanding at very close tothe critical rate at which it would just avoid recollapse, and so will not recollapse for a very long time. By then allthe stars will have burned out and the protons and neutrons in them will probably have decayed into lightparticles and radiation. The universe would be in a state of almost complete disorder. There would be no strongthermodynamic arrow of time. Disorder couldn’t increase much because the universe would be in a state ofalmost complete disorder already. However, a strong thermodynamic arrow is necessary for intelligent life tooperate. In order to survive, human beings have to consume food, which is an ordered form of energy, andconvert it into heat, which is a disordered form of energy. Thus intelligent life could not exist in the contractingphase of the universe. This is the explanation of why we observe that the thermodynamic and cosmologicalarrows of time point in the same direction. It is not that the expansion of the universe causes disorder toincrease. Rather, it is that the no boundary condition causes disorder to increase and the conditions to besuitable for intelligent life only in the expanding phase.
人們可以在弱人擇原理的基礎上回答這個問題。收縮相的條件不適合於智慧人類的存在，而正是他們能夠提出為何無序度增加的時間方向和宇宙膨脹的時間方向相同的問題。無邊界假設預言的宇宙在早期階段的暴漲意味著，宇宙必須以非常接近為避免坍縮所需要的臨界速率膨脹，這樣它在很長的時間內才不至坍縮。到那時候所有的恒星都會燒盡，而在其中的質子和中子可能會衰變成輕粒子和輻射。宇宙將處於幾乎完全無序的狀態，這時就不會有強的熱力學時間箭頭。由於宇宙已經處於幾乎完全無序的狀態，無序度不會增加很多。然而，對於智慧生命的行為來說，一個強的熱力學箭頭是必需的。為了生存下去，人類必須消耗能量的一種有序形式——食物，並將其轉化成能量的一種無序形式——熱量，所以智慧生命不能在宇宙的收縮相中存在。這就解釋了，為何我們觀察到熱力學和宇宙學的時間箭頭指向一致。並不是宇宙的膨脹導致無序度的增加，而是無邊界條件引起無序度的增加，並且只有在膨脹相中才有適合智慧生命的條件。
To summarize, the laws of science do not distinguish between the forward and backward directions of time.However, there are at least three arrows of time that do distinguish the past from the future. They are thethermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the directionof time in which we remember the past and not the future; and the cosmological arrow, the direction of time inwhich the universe expands rather than contracts. I have shown that the psychological arrow is essentially thesame as the thermodynamic arrow, so that the two would always point in the same direction. The no boundaryproposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because theuniverse must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow toagree with the cosmological arrow is that intelligent beings can exist only in the expanding phase. Thecontracting phase will be unsuitable because it has no strong thermodynamic arrow of time.
總之，科學定律並不能區分前進和後退的時間方向。然而，至少存在有三個時間箭頭將過去和將來區分開來。它們是熱力學箭頭，這就是無序度增加的時間方向；心理學箭頭，即是在這個時間方向上，我們能記住過去而不是將來；還有宇宙學箭頭，也即宇宙膨脹而不是收縮的方向。我指出了心理學箭頭本質上應和熱力學箭頭相同。宇宙的無邊界假設預言了定義得很好的熱力學時間箭頭，因為宇宙必須從光滑、有序的狀態開始。並且我們看到，熱力學箭頭和宇宙學箭頭的一致，乃是由於智慧生命只能在膨脹相中存在。收縮相是不適合於它的存在的，因為那兒沒有強的熱力學時間箭頭。
The progress of the human race in understanding the universe has established a small corner of order in anincreasingly disordered universe. If you remember every word in this book, your memory will have recordedabout two million pieces of information: the order in your brain will have increased by about two million units.However, while you have been reading the book, you will have converted at least a thousand calories ofordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air aroundyou by convection and sweat. This will increase the disorder of the universe by about twenty million millionmillion million units – or about ten million million million times the increase in order in your brain – and that’s ifyou remember everything in this book. In the next chapter but one I will try to increase the order in our neck ofthe woods a little further by explaining how people are trying to fit together the partial theories I have describedto form a complete unified theory that would cover everything in the universe.
人類理解宇宙的進步，是在一個無序度增加的宇宙中建立了一個很小的有序的角落。如果你記住了這本書中的每一個詞，你的記憶就記錄了大約200萬單位的資訊——你頭腦中的有序度就增加了大約200萬單位。然而，當你讀這本書時，你至少將以食物為形式的1千卡路里的有序能量，轉換成為以對流和汗釋放到你周圍空氣中的熱量的形式的無序能量。這就將宇宙的無序度增大了大約20億億億單位，或大約是你頭腦中有序度增量——那是如果你記住這本書的每一件事的話——的1000億億倍。我試圖在下一章更增加一些我們頭腦的有序度，解釋人們如何將我描述過的部分理論結合一起，形成一個完整的統一理論，這個理論將適用於宇宙中的任何東西。