Thank you for putting up these pictures of my colleagues over here. (Laughter) We'll be talking about them. Now, I'm going try an experiment. I don't do experiments, normally. I'm a theorist. But I'm going see what happens if I press this button. Sure enough. OK. I used to work in this field of elementary particles. What happens to matter if you chop it up very fine? What is it made of? And the laws of these particles are valid throughout the universe, and they're very much connected with the history of the universe.
謝謝你在旁邊掛上我"同事"的相片. (笑聲). 等一下會談到他們. 現在, 我想作個實驗. 但我平時不作實驗的, 我是搞理論的. 來看看按下這個按鈕會發生什麼現象. 果然如此. 好的. 我曾研究過基本粒子. 若你將它切成很小塊會發生什麼事呢? 它是由什麼組成的? 這些粒子的物理定律放諸宇宙各處都是正確的, 且它們與宇宙的歷史是息息相關的.
We know a lot about four forces. There must be a lot more, but those are at very, very small distances, and we haven't really interacted with them very much yet. The main thing I want to talk about is this: that we have this remarkable experience in this field of fundamental physics that beauty is a very successful criterion for choosing the right theory. And why on earth could that be so?
我們雖了解四種基本力(強,弱作用,電磁,重力). 但一定還有更多種未知力, 只是其作用距離非常, 非常小, 我們還未真的接觸過它們. 我主要想談的是: 對於探究基本的物理定律, 我們有一個神奇的經驗法則, 就是若方程式越"簡潔優美", 往往越有希望是正確的理論. 但這未免也太扯了吧?
Well, here's an example from my own experience. It's fairly dramatic, actually, to have this happen. Three or four of us, in 1957, put forward a partially complete theory of one of these forces, this weak force. And it was in disagreement with seven -- seven, count them, seven experiments. Experiments were all wrong.
好吧, 舉一個我個人的經驗為例. 其實還蠻 戲劇化的. 1957年時, 包括我共三或四位 對四種力之一的弱作用力, 提出了一個半完成的理論. 但是當時與七個實驗結果不相符. (七, 沒錯, 竟有七個) 那些實驗結果全錯了.
And we published before knowing that, because we figured it was so beautiful, it's gotta be right! The experiments had to be wrong, and they were. Now our friend over there, Albert Einstein, used to pay very little attention when people said, "You know, there's a man with an experiment that seems to disagree with special relativity. DC Miller. What about that?" And he would say, "Aw, that'll go away." (Laughter)
但我們早在被證實前, 照樣敢發表那理論 因為我們覺得那理論太美了, 它非得要對才行! 所以那些實驗非得是錯的, 果不其然. 現在來談談我們的一位老友, 愛因斯坦, 他總是毫不在意當有人對他說: "你聽說了嗎, DC Miller作出一項實驗似乎與相對論矛盾, 你有什麼看法?" 他總是答: "喔, 那會過去的." (笑聲)
Now, why does stuff like that work? That's the question. Now, yeah, what do we mean by beautiful? That's one thing. I'll try to make that clear -- partially clear. Why should it work, and is this something to do with human beings? I'll let you in on the answer to the last one that I offer, and that is, it has nothing to do with human beings. Somewhere in some other planet, orbiting some very distant star, maybe in a another galaxy, there could well be entities that are at least as intelligent as we are, and are interested in science. It's not impossible; I think there probably are lots.
所以, 到底為什麼簡潔優美如此成功? 這是關鍵問題. 現在, 對, 至於我所指的"美"是什麼意思? 這是另一個問題, 我會試著解釋清楚, 大致上清楚. 為何美如此成功, 這跟人類的心靈有關嗎? 這答案我就直接講了, 答案就是, 它跟人類心靈一點關係都沒有. 假設有另一個繞著某個太陽的地球, 或許在另一個銀河系裡, 在那星球上的某處, 住著與我們至少並論的智慧生物, 且它們對科學也有興趣. 這非不可能, 我覺得還蠻有機會的.
Very likely, none is close enough to interact with us. But they could be out there, very easily. And suppose they have, you know, very different sensory apparatus, and so on. They have seven tentacles, and they have 14 little funny-looking compound eyes, and a brain shaped like a pretzel. Would they really have different laws? There are lots of people who believe that, and I think it is utter baloney. I think there are laws out there, and we of course don't understand them at any given time very well -- but we try. And we try to get closer and closer.
顯而易見的, 我們相隔過遠無法互動. 但是它們現在可能就在外面, 輕而易舉地. 假設它們存在, 你也知道, 有著奇特的感覺器官等. 可能有七肢觸手, 14個可笑的複眼, 及 一個長得像中國繩結的腦. 那它們會有不同的物理定律嗎? 有許多人是這樣認為的, 但我認為那是一派胡言. 我認為世上存在著終極正確的物理定律組, 當然人類至今從未真正的掌握它們, 但我們不斷嘗試. 試著去揭開它層層面紗.
And someday, we may actually figure out the fundamental unified theory of the particles and forces, what I call the "fundamental law." We may not even be terribly far from it. But even if we don't run across it in our lifetimes, we can still think there is one out there, and we're just trying to get closer and closer to it. I think that's the main point to be made. We express these things mathematically. And when the mathematics is very simple -- when in terms of some mathematical notation, you can write the theory in a very brief space, without a lot of complication -- that's essentially what we mean by beauty or elegance.
或許有那麼一天, 我們真的解出有關粒子與其作用力 的 終極 統一 基本物理理論, 我稱之為"基本定律". 我們離此目標也許已非遙不可及. 但就算在我們有生之年還未能達成, 我們可以相信那是存在的, 並朝此目標慢慢靠近. 我覺得這就是我想傳達的. 我們用數學去描述定律. 當我指數學型式很簡潔時, 只要利用一些已知數學符號, 就可以將整個理論寫下來, 且用很小的空間, 也不會很複雜. 這就是我所指的美或優雅.
Here's what I was saying about the laws. They're really there. Newton certainly believed that. And he said, here, "It is the business of natural philosophy to find out those laws." The basic law, let's say -- here's an assumption. The assumption is that the basic law really takes the form of a unified theory of all the particles. Now, some people call that a theory of everything. That's wrong because the theory is quantum mechanical. And I won't go into a lot of stuff about quantum mechanics and what it's like, and so on. You've heard a lot of wrong things about it anyway. (Laughter) There are even movies about it with a lot of wrong stuff.
這裡是我剛才對於物理定律所談的. 它們真的存在. 牛頓也深信不疑. 他說過, 在這, "找出那些定律是科學的主要工作." 讓我們對"基本定律"作個假設: "假定基本定律真的將 所有基本力與粒子的量子理論 統一了." 現在, 有些人稱它為 無所不知理論(上帝不擲骰子). 那是錯的, 因為這理論與量子力學有關. 我不會講一堆量子力學的東西, 或試著去解釋它之類的. 反正你們早就聽過許多, 但錯誤, 的訊息了. (笑聲) 甚至連許多相關的電影也充斥著錯誤.
But the main thing here is that it predicts probabilities. Now, sometimes those probabilities are near certainties. And in a lot of familiar cases, they of course are. But other times they're not, and you have only probabilities for different outcomes. So what that means is that the history of the universe is not determined just by the fundamental law. It's the fundamental law and this incredibly long series of accidents, or chance outcomes, that are there in addition.
但量子力學最主要一點就是: 它與機率有關,(測不準, 上帝擲骰子) 好 ,有時候測不準的範圍非常小, 接近準確. 對許多日常熟悉的現象, 一像也都是如此準確. 但其他時候可不是, 你只能知道各種可能發生的結果的機率而已. 所以這表示, 宇宙至今天的歷史不全由單單基本定律所決定的, 是由基本定律, "和"無時無刻不斷的意外, 或說"機率下的結果", 兩者交互參雜所致.
And the fundamental theory doesn't include those chance outcomes; they are in addition. So it's not a theory of everything. And in fact, a huge amount of the information in the universe around us comes from those accidents, and not just from the fundamental laws. Now, it's often said that getting closer and closer to the fundamental laws by examining phenomena at low energies, and then higher energies, and then higher energies, or short distances, and then shorter distances, and then still shorter distances, and so on, is like peeling the skin of an onion. And we keep doing that, and build more powerful machines, accelerators for particles. We look deeper and deeper into the structure of particles, and in that way we get probably closer and closer to this fundamental law.
基本定律並"不能算出"隨機下的結果, 所以它不是"無所不知理論". 事實上, 在宇宙中 有非常大量的資訊都是因種種意外產生 而不僅僅基本定律在作用而已. 現在, 常有人提到, 為了要越來越接近基本定律, 需要研究低能量物理, 而後是高能量, 接著再更高, 或是縮小量測尺度, 然後再小一點, 接著再更小, 等等. 類似剝洋蔥皮. 我們奉行不渝, 建造更強大的機器, 例粒子加速器. 我們越來越深入研究粒子的內在結構. 如此這般, 我們或許越來越接近所謂基本定律.
Now, what happens is that as we do that, as we peel these skins of the onion, and we get closer and closer to the underlying law, we see that each skin has something in common with the previous one, and with the next one. We write them out mathematically, and we see they use very similar mathematics. They require very similar mathematics. That is absolutely remarkable, and that is a central feature of what I'm trying to say today. Newton called it -- that's Newton, by the way -- that one.
現在, 當我們實行這些事, 或剝掉層層洋蔥皮時, 也越來越靠近其蘊藏的定律, 我們發現每一層皮與前一層有某些相似之處, 對下一層也是. 當用數學表示時, 發現它們使用的數學很類似. 所需的數學工具很類似. 這是絕對值得關注的, 這也是我今天 試著想表達的重點. 牛頓稱其為, (順便說一下, 他是牛頓, 那一位.
This one is Albert Einstein. Hi, Al! And anyway, he said, "nature conformable to herself" -- personifying nature as a female. And so what happens is that the new phenomena, the new skins, the inner skins of the slightly smaller skins of the onion that we get to, resemble the slightly larger ones. And the kind of mathematics that we had for the previous skin is almost the same as what we need for the next skin. And that's why the equations look so simple. Because they use mathematics we already have.
這位是愛因斯坦. 嗨, 小愛! 言歸正傳), 他說:"大自然遵循她自己". (將大自然擬人化為女性) 所以當我們探究新的現象時, 也就是洋蔥新的一層皮 (稍小且位於內層的皮, 相較於稍大的舊皮). 我們研究舊皮所得的數學知識, 與瞭解新皮所需的數學知識大致相等. 由於所需的數學已被研究過了, 這也是為什麼物理定理方程式看起來非常簡潔.
A trivial example is this: Newton found the law of gravity, which goes like one over the square of the distance between the things gravitated. Coulomb, in France, found the same law for electric charges. Here's an example of this similarity. You look at gravity, you see a certain law. Then you look at electricity. Sure enough. The same rule. It's a very simple example. There are lots of more sophisticated examples. Symmetry is very important in this discussion. You know what it means. A circle, for example, is symmetric under rotations about the center of the circle. You rotate around the center of the circle, the circle remains unchanged. You take a sphere, in three dimensions, you rotate around the center of the sphere, and all those rotations leave the sphere alone. They are symmetries of the sphere. So we say, in general, that there's a symmetry under certain operations if those operations leave the phenomenon, or its description, unchanged.
舉個平凡的例子: 牛頓發現了重力, 其力的強弱隨兩物體間距的平方衰減. 庫倫, 法國人, 發現電荷間的作用力 也是依間距平方衰減. 這就是一個數學相似例子. 當你看重力時, 你得到一個定律. 當你看電力時. 當然, 也是同樣一個定律. 這是一個簡單的例子. 還有許多複雜的例子, 其中, "對稱性"非常重要. 你也知道的. 比如說, 一個圓 就轉動而言, 是對稱於其圓心. 當你將它繞著其圓心旋轉, 其外形不會改變. 或是有一個三維立體的球殼, 將之繞其球心旋轉, 不管怎麼轉, 它的外形還是不變. 這就是球殼的對稱性. 所以我們可將之推廣: "若某物在一特定的操作下, 其本身持有的現象或特徵沒有改變, 我們就說它, 在那操作之下是對稱的."
Maxwell's equations are of course symmetrical under rotations of all of space. Doesn't matter if we turn the whole of space around by some angle, it doesn't leave the -- doesn't change the phenomenon of electricity or magnetism. There's a new notation in the 19th century that expressed this, and if you use that notation, the equations get a lot simpler. Then Einstein, with his special theory of relativity, looked at a whole set of symmetries of Maxwell's equations, which are called special relativity. And those symmetries, then, make the equations even shorter, and even prettier, therefore.
麥克斯威(Maxwell)方程組, 當然, 在空間中的旋轉下是對稱的. 也就是說, 我們可以任意改變觀察的角度, 但不會讓...不會改變電磁效應的實驗結果. 19世紀時, 對於這種 旋轉對稱 有新的數學符號, 若你使用了這種符號, 麥克斯威方程組 可被大大的簡化. 接著, 愛因斯坦 透過特殊的座標轉換理論, 更看到了 麥克斯威方程組 裡新的對稱性, 也就是狹義相對論. 這些對稱性, 使得此方程組更簡短, 更美, 因此....
Let's look. You don't have to know what these things mean, doesn't make any difference. But you can just look at the form. (Laughter) You can look at the form. You see above, at the top, a long list of equations with three components for the three directions of space: x, y and z. Then, using vector analysis, you use rotational symmetry, and you get this next set. Then you use the symmetry of special relativity and you get an even simpler set down here, showing that symmetry exhibits better and better. The more and more symmetry you have, the better you exhibit the simplicity and elegance of the theory.
你來看. 你不須要瞭解這些東西的意義, 沒什麼差. 你只須看它的外形. (笑聲) 你可以看它的外形. 看上面, 在頂端, 有一長列清單 表示麥克斯威方程式, 在三維空間中的不同方向, 可寫成不同的式子. 接著, 利用向量分析, 旋轉的對稱性 來簡化, 你可得到到第二組. 若再運用 狹義相對論 裡的對稱性, 甚至能更加精簡至 在下面這, 其對稱性已展露無遺. 若方程式有越多種類的對稱性, 你越能展現出那個理論的精簡與優美.
The last two, the first equation says that electric charges and currents give rise to all the electric and magnetic fields. The next -- second -- equation says that there is no magnetism other than that. The only magnetism comes from electric charges and currents. Someday we may find some slight hole in that argument. But for the moment, that's the case.
最後兩行, 第一個方程式表示電荷與電流會 產生電場及磁場. 下一個...第二個方程式表示, 沒有其它辦法可以生成磁場. 磁場產生唯一的來源, 就只能是電流. 或許有天我們能找出此論點的小漏洞, 但目前為止, 就是這樣.
Now, here is a very exciting development that many people have not heard of. They should have heard of it, but it's a little tricky to explain in technical detail, so I won't do it. I'll just mention it. (Laughter) But Chen Ning Yang, called by us "Frank" Yang -- (Laughter) -- and Bob Mills put forward, 50 years ago, this generalization of Maxwell's equations, with a new symmetry. A whole new symmetry. Mathematics very similar, but there was a whole new symmetry. They hoped that this would contribute somehow to particle physics -- didn't. It didn't, by itself, contribute to particle physics.
好, 物理有一個非常另人興奮的突破, 許多人可能沒聽過. 但都應該要知道. 只不過若要解釋其中技術上的細節, 有一點微妙, 所以我不幹. 我只會帶過. (笑聲) 楊振寧(英名: 富蘭克林), 我們稱他"阿富", (笑聲) 與 米爾斯(Bob Mills) 50年前提出 更廣義的 麥克斯威方程式 與其蘊涵的新的對稱性質. 前所未見的對稱性. 數學上很類似, 不過是全新的對稱性. 他們希望這能對 粒子物理 多少有些貢獻, 可惜. 光靠那還不足以幫助到 粒子物理理論.
But then some of us generalized it further. And then it did! And it gave a very beautiful description of the strong force and of the weak force. So here we say, again, what we said before: that each skin of the onion shows a similarity to the adjoining skins. So the mathematics for the adjoining skins is very similar to what we need for the new one. And therefore it looks beautiful because we already know how to write it in a lovely, concise way.
後來有些粒子物理學家將之更進一步推廣, 終於成功了! 對於強, 弱作用力 給出了非常漂亮的解釋. 所以我們可以說, 老話一句: 相鄰的洋蔥皮保有許多相似處. 所以探究新的皮所需俱備的數學工具, 與舊皮非常相似. 理論看起來很美, 是因為我們早知道如何將其數學化簡, 美化.
So here are the themes. We believe there is a unified theory underlying all the regularities. Steps toward unification exhibit the simplicity. Symmetry exhibits the simplicity. And then there is self-similarity across the scales -- in other words, from one skin of the onion to another one. Proximate self-similarity. And that accounts for this phenomenon. That will account for why beauty is a successful criterion for selecting the right theory.
總而言之, 我們相信, 在所有這些規律性之下, 存在一個大統一的理論. 理論相互不斷地統合導致簡化. 對稱性也使之趨向簡化. 且物理在不同的尺度下, 都有許多相似處. 換句話說, 對不同層的洋蔥皮, 彼此類似. 這解釋了一個現象, 解釋了為什麼"美"對於正確的理論這麼重要.
Here's what Newton himself said: "Nature is very consonant and conformable to her self." One thing he was thinking of is something that most of us take for granted today, but in his day it wasn't taken for granted. There's the story, which is not absolutely certain to be right, but a lot of people told it. Four sources told it. That when they had the plague in Cambridge, and he went down to his mother's farm -- because the university was closed -- he saw an apple fall from a tree, or on his head or something. And he realized suddenly that the force that drew the apple down to the earth could be the same as the force regulating the motions of the planets and the moon.
這裡是牛頓他説曾說的: "大自然始終如一的遵循她自己." 他當初提出了一個東西, 如今大部分人覺得理所當然, 但在當時可不一樣. 這個故事就是, (可能不全然事實, 但流傳很廣, 故事來源有四處.) 當時劍橋瘟疫流行, 牛頓就回到他母親的農場. (因為大學暫時停課) 他看到一顆蘋果從樹上落下, 不知道有沒有砸到他的頭或什麼. 他突然頓悟, 將蘋果從樹上拉下來的力與 控制行星及月亮移動的力是相同的.
That was a big unification for those days, although today we take it for granted. It's the same theory of gravity. So he said that this principle of nature, consonance: "This principle of nature being very remote from the conceptions of philosophers, I forbore to describe it in that book, lest I should be accounted an extravagant freak ... " That's what we all have to watch out for, (Laughter) especially at this meeting. " ... and so prejudice my readers against all those things which were the main design of the book."
這在當時可是個大膽的統合, 雖然如今看似理所當然. 那些力都可以用重力來解釋. 所以他覺得大自然的原理, 始終如一, 他說: "大自然的原理與哲學家所想的差很多, 我克制自己不將之公布在那本書裡, 以免我被形容成狂妄的怪胎..." ( 這也是我們所要提防的.(笑聲) 特別是在這個聚會. ) "...或令讀者對書中主要想傳達的理念有偏見."
Now, who today would claim that as a mere conceit of the human mind? That the force that causes the apple to fall to the ground is the same force that causes the planets and the moon to move around, and so on? Everybody knows that. It's a property of gravitation. It's not something in the human mind. The human mind can, of course, appreciate it and enjoy it, use it, but it's not -- it doesn't stem from the human mind. It stems from the character of gravity. And that's true of all the things we're talking about. They are properties of the fundamental law. The fundamental law is such that the different skins of the onion resemble one another, and therefore the math for one skin allows you to express beautifully and simply the phenomenon of the next skin.
好, 如今有誰會認為這些僅是人類心靈下的產物? 例如"讓蘋果落下的力與 控制行星及月亮移動的力是相同的." 之類的. 這是常識了. 這就是重力的性質. 這與人類心靈無關. 人類心靈可以, 當然, 理解它 欣賞它, 應用它. 但它不是... 它不源自於人類的心靈. 它就是重力的性質. 我們剛在談論的其它物理也一樣適用. 它們都是"基本定律"的性質. 基本定律使得不同層的洋蔥皮彼此相似, 因而前一層皮所運用到的數學工具可以用在下一層皮, 以致描述的美而簡潔.
I say here that Newton did a lot of things that year: gravity, the laws of motion, the calculus, white light composed of all the colors of the rainbow. And he could have written quite an essay on "What I Did Over My Summer Vacation." (Laughter) So we don't have to assume these principles as separate metaphysical postulates. They follow from the fundamental theory. They are what we call emergent properties. You don't need -- you don't need something more to get something more. That's what emergence means.
1665年夏天, 所謂牛頓的不可思義年: 萬有引力定律, 三大運動定律, 微積分, 白光是由彩虹色的光組成的. 他應該有許多事情可以寫進 "我的暑假活動" . (笑聲) 所以我們不必妄言 大自然, 美,與數學 皆各行其是, 或僅是純哲學下的公理. 它們可能都源自於同一個基本理論. 這就是我們稱的"衍生"性質. 你不需要...你不需要再多, 以得到更多. 這就是"衍生"的含意.
Life can emerge from physics and chemistry, plus a lot of accidents. The human mind can arise from neurobiology and a lot of accidents, the way the chemical bond arises from physics and certain accidents. It doesn't diminish the importance of these subjects to know that they follow from more fundamental things, plus accidents. That's a general rule, and it's critically important to realize that. You don't need something more in order to get something more. People keep asking that when they read my book, "The Quark and the Jaguar," and they say, "Isn't there something more beyond what you have there?" Presumably, they mean something supernatural. Anyway, there isn't. (Laughter) You don't need something more to explain something more. Thank you very much. (Applause)
生命是由物理及化學伴隨著許多隨機的意外衍生出來. 人類的心靈是由神經生物學及許多意外所產生的. 化學鍵是由物理及某些意外所產生的. 知道這些事物是由許多更基本的事物及 意外所衍生的, 並不會削弱它們的重要性. 這只是個通則, 但領悟這點是極其重要的. 你不需要再多, 以得到更多. 當人們在讀我的書"夸克與美洲豹"時,總會問: "有沒有某些東西是遠超出存在的事物?" 想必, 他們指的是某種超自然現象. 嗯, 無論如何, 沒有. (笑聲) 你不需再多, 以解釋更多. 非常謝謝大家. (鼓掌)