(Laughter) We'll be talking about them.

(笑聲). 等一下會談到他們.

Now, I'm going try an experiment. I don't do experiments, normally. I'm a theorist.

現在, 我想作個實驗. 但我平時不作實驗的, 我是搞理論的.

But I'm going see what happens if I press this button.

來看看按下這個按鈕會發生什麼現象.

Sure enough. OK. I used to work in this field of elementary particles.

果然如此. 好的. 我曾研究過基本粒子.

What happens to matter if you chop it up very fine?

若你將它切成很小塊會發生什麼事呢?

What is it made of?

它是由什麼組成的?

And the laws of these particles are valid throughout the universe,

這些粒子的物理定律放諸宇宙各處都是正確的,

and they're very much connected with the history of the universe.

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,

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,

but those are at very, very small distances,

只是其作用距離非常, 非常小,

and we haven't really interacted with them very much yet.

我們還未真的接觸過它們.

The main thing I want to talk about is this:

我主要想談的是:

that we have this remarkable experience in this field of fundamental physics

對於探究基本的物理定律, 我們有一個神奇的經驗法則,

that beauty is a very successful criterion for choosing the right theory.

就是若方程式越"簡潔優美", 往往越有希望是正確的理論.

And why on earth could that be so?

但這未免也太扯了吧?

Well, here's an example from my own experience.

好吧, 舉一個我個人的經驗為例.

It's fairly dramatic, actually, to have this happen.

其實還蠻 戲劇化的.

Three or four of us, in 1957,

1957年時, 包括我共三或四位

put forward a partially complete theory of one of these forces, this weak force.

對四種力之一的弱作用力, 提出了一個半完成的理論.

And it was in disagreement with seven -- seven, count them, seven experiments.

但是當時與七個實驗結果不相符. (七, 沒錯, 竟有七個)

Experiments were all wrong.

那些實驗結果全錯了.

And we published before knowing that,

但我們早在被證實前, 照樣敢發表那理論

because we figured it was so beautiful, it's gotta be right!

因為我們覺得那理論太美了, 它非得要對才行!

The experiments had to be wrong, and they were.

所以那些實驗非得是錯的, 果不其然.

Now our friend over there, Albert Einstein,

現在來談談我們的一位老友, 愛因斯坦,

used to pay very little attention when people said,

他總是毫不在意當有人對他說:

"You know, there's a man with an experiment that seems to disagree with special relativity.

"你聽說了嗎, DC Miller作出一項實驗似乎與相對論矛盾,

DC Miller. What about that?" And he would say, "Aw, that'll go away." (Laughter)

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.

所以, 到底為什麼簡潔優美如此成功? 這是關鍵問題.

Now, yeah, what do we mean by beautiful? That's one thing.

現在, 對, 至於我所指的"美"是什麼意思? 這是另一個問題,

I'll try to make that clear -- partially clear.

我會試著解釋清楚, 大致上清楚.

Why should it work, and is this something to do with human beings?

為何美如此成功, 這跟人類的心靈有關嗎?

I'll let you in on the answer to the last one that I offer,

這答案我就直接講了,

and that is, it has nothing to do with human beings.

答案就是, 它跟人類心靈一點關係都沒有.

Somewhere in some other planet, orbiting some very distant star,

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,

maybe in a another galaxy,

在那星球上的某處,

there could well be entities that are at least as intelligent as we are,

住著與我們至少並論的智慧生物,

and are interested in science. It's not impossible; I think there probably are lots.

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.

顯而易見的, 我們相隔過遠無法互動.

But they could be out there, very easily.

但是它們現在可能就在外面, 輕而易舉地.

And suppose they have, you know, very different sensory apparatus, and so on.

假設它們存在, 你也知道, 有著奇特的感覺器官等.

They have seven tentacles, and they have 14 little funny-looking compound eyes,

可能有七肢觸手, 14個可笑的複眼, 及

and a brain shaped like a pretzel.

一個長得像中國繩結的腦.

Would they really have different laws?

那它們會有不同的物理定律嗎?

There are lots of people who believe that, and I think it is utter baloney.

有許多人是這樣認為的, 但我認為那是一派胡言.

I think there are laws out there,

我認為世上存在著終極正確的物理定律組,

and we of course don't understand them at any given time very well

當然人類至今從未真正的掌握它們,

-- but we try. And we try to get closer and closer.

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

或許有那麼一天, 我們真的解出有關粒子與其作用力

of the particles and forces, what I call the "fundamental law."

的 終極 統一 基本物理理論, 我稱之為"基本定律".

We may not even be terribly far from it.

我們離此目標也許已非遙不可及.

But even if we don't run across it in our lifetimes,

但就算在我們有生之年還未能達成,

we can still think there is one out there,

我們可以相信那是存在的,

and we're just trying to get closer and closer to it.

並朝此目標慢慢靠近.

I think that's the main point to be made.

我覺得這就是我想傳達的.

We express these things mathematically.

我們用數學去描述定律.

And when the mathematics is very simple --

當我指數學型式很簡潔時,

when in terms of some mathematical notation,

只要利用一些已知數學符號,

you can write the theory in a very brief space, without a lot of complication --

就可以將整個理論寫下來, 且用很小的空間, 也不會很複雜.

that's essentially what we mean by beauty or elegance.

這就是我所指的美或優雅.

Here's what I was saying about the laws. They're really there.

這裡是我剛才對於物理定律所談的. 它們真的存在.

Newton certainly believed that.

牛頓也深信不疑.

And he said, here, "It is the business of natural philosophy to find out those laws."

他說過, 在這, "找出那些定律是科學的主要工作."

The basic law, let's say -- here's an assumption.

讓我們對"基本定律"作個假設:

The assumption is that the basic law really takes the form

"假定基本定律真的將

of a unified theory of all the particles.

所有基本力與粒子的量子理論 統一了."

Now, some people call that a theory of everything.

現在, 有些人稱它為 無所不知理論(上帝不擲骰子).

That's wrong because the theory is quantum mechanical.

那是錯的, 因為這理論與量子力學有關.

And I won't go into a lot of stuff about quantum mechanics and what it's like, and so on.

我不會講一堆量子力學的東西, 或試著去解釋它之類的.

You've heard a lot of wrong things about it anyway. (Laughter)

反正你們早就聽過許多, 但錯誤, 的訊息了. (笑聲)

There are even movies about it with a lot of wrong stuff.

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.

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)

Now, sometimes those probabilities are near certainties.

好 ,有時候測不準的範圍非常小, 接近準確.

And in a lot of familiar cases, they of course are.

對許多日常熟悉的現象, 一像也都是如此準確.

But other times they're not, and you have only probabilities for different outcomes.

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.

So what that means is that the history of the universe is not determined just by the fundamental law.

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,

It's the fundamental law and this incredibly long series of accidents,

是由基本定律, "和"無時無刻不斷的意外,

or chance outcomes, that are there in addition.

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.

基本定律並"不能算出"隨機下的結果,

So it's not a theory of everything. And in fact, a huge amount of the information

所以它不是"無所不知理論". 事實上, 在宇宙中

in the universe around us comes from those accidents,

有非常大量的資訊都是因種種意外產生

and not just from the fundamental laws.

而不僅僅基本定律在作用而已.

Now, it's often said that getting closer and closer

現在, 常有人提到, 為了要越來越接近基本定律,

to the fundamental laws by examining phenomena at low energies, and then higher energies,

需要研究低能量物理, 而後是高能量,

and then higher energies, or short distances, and then shorter distances,

接著再更高, 或是縮小量測尺度, 然後再小一點,

and then still shorter distances, and so on, is like peeling the skin of an onion.

接著再更小, 等等. 類似剝洋蔥皮.

And we keep doing that,

我們奉行不渝,

and build more powerful machines, accelerators for particles.

建造更強大的機器, 例粒子加速器.

We look deeper and deeper into the structure of particles,

我們越來越深入研究粒子的內在結構.

and in that way we get probably closer and closer to this fundamental law.

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,

現在, 當我們實行這些事, 或剝掉層層洋蔥皮時,

and we get closer and closer to the underlying law,

也越來越靠近其蘊藏的定律,

we see that each skin has something in common with the previous one,

我們發現每一層皮與前一層有某些相似之處,

and with the next one. We write them out mathematically,

對下一層也是. 當用數學表示時,

and we see they use very similar mathematics.

發現它們使用的數學很類似.

They require very similar mathematics.

所需的數學工具很類似.

That is absolutely remarkable, and that is a central feature

這是絕對值得關注的, 這也是我今天

of what I'm trying to say today.

試著想表達的重點.

Newton called it -- that's Newton, by the way -- that one.

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,

這位是愛因斯坦. 嗨, 小愛! 言歸正傳),

he said, "nature conformable to herself" -- personifying nature as a female.

他說:"大自然遵循她自己". (將大自然擬人化為女性)

And so what happens is that the new phenomena,

所以當我們探究新的現象時,

the new skins, the inner skins of the slightly smaller skins of the onion

也就是洋蔥新的一層皮 (稍小且位於內層的皮,

that we get to, resemble the slightly larger ones.

相較於稍大的舊皮).

And the kind of mathematics that we had for the previous skin

我們研究舊皮所得的數學知識,

is almost the same as what we need for the next skin.

與瞭解新皮所需的數學知識大致相等.

And that's why the equations look so simple.

由於所需的數學已被研究過了,

Because they use mathematics we already have.

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,

舉個平凡的例子: 牛頓發現了重力,

which goes like one over the square of the distance between the things gravitated.

其力的強弱隨兩物體間距的平方衰減.

Coulomb, in France, found the same law for electric charges.

庫倫, 法國人, 發現電荷間的作用力 也是依間距平方衰減.

Here's an example of this similarity.

這就是一個數學相似例子.

You look at gravity, you see a certain law.

當你看重力時, 你得到一個定律.

Then you look at electricity. Sure enough. The same rule.

當你看電力時. 當然, 也是同樣一個定律.

It's a very simple example.

這是一個簡單的例子.

There are lots of more sophisticated examples.

還有許多複雜的例子,

Symmetry is very important in this discussion.

其中, "對稱性"非常重要.

You know what it means. A circle, for example,

你也知道的. 比如說, 一個圓

is symmetric under rotations about the center of the circle.

就轉動而言, 是對稱於其圓心.

You rotate around the center of the circle, the circle remains unchanged.

當你將它繞著其圓心旋轉, 其外形不會改變.

You take a sphere, in three dimensions, you rotate around the center of the sphere,

或是有一個三維立體的球殼, 將之繞其球心旋轉,

and all those rotations leave the sphere alone.

不管怎麼轉, 它的外形還是不變.

They are symmetries of the sphere.

這就是球殼的對稱性.

So we say, in general, that there's a symmetry

所以我們可將之推廣: "若某物在一特定的操作下,

under certain operations if those operations leave the phenomenon,

其本身持有的現象或特徵沒有改變,

or its description, unchanged.

我們就說它, 在那操作之下是對稱的."

Maxwell's equations are of course symmetrical

麥克斯威(Maxwell)方程組, 當然,

under rotations of all of space.

在空間中的旋轉下是對稱的.

Doesn't matter if we turn the whole of space around by some angle,

也就是說, 我們可以任意改變觀察的角度,

it doesn't leave the -- doesn't change the phenomenon of electricity or magnetism.

但不會讓...不會改變電磁效應的實驗結果.

There's a new notation in the 19th century that expressed this,

19世紀時, 對於這種 旋轉對稱 有新的數學符號,

and if you use that notation, the equations get a lot simpler.

若你使用了這種符號, 麥克斯威方程組 可被大大的簡化.

Then Einstein, with his special theory of relativity,

接著, 愛因斯坦 透過特殊的座標轉換理論,

looked at a whole set of symmetries of Maxwell's equations,

更看到了 麥克斯威方程組 裡新的對稱性,

which are called special relativity.

也就是狹義相對論.

And those symmetries, then, make the equations even shorter, and even prettier, therefore.

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.

你來看. 你不須要瞭解這些東西的意義, 沒什麼差.

But you can just look at the form. (Laughter) You can look at the form.

你只須看它的外形. (笑聲) 你可以看它的外形.

You see above, at the top, a long list

看上面, 在頂端, 有一長列清單

of equations with three components for the three directions of space: x, y and z.

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.

Then, using vector analysis, you use rotational symmetry, and you get this next set.

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.

Then you use the symmetry of special relativity and you get an even simpler set

若再運用 狹義相對論 裡的對稱性, 甚至能更加精簡至

down here, showing that symmetry exhibits better and better.

在下面這, 其對稱性已展露無遺.

The more and more symmetry you have, the better you exhibit the simplicity and elegance of the theory.

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

最後兩行, 第一個方程式表示電荷與電流會

give rise to all the electric and magnetic fields.

產生電場及磁場.

The next -- second -- equation says that there is no magnetism other than that.

下一個...第二個方程式表示, 沒有其它辦法可以生成磁場.

The only magnetism comes from electric charges and currents.

磁場產生唯一的來源, 就只能是電流.

Someday we may find some slight hole in that argument.

或許有天我們能找出此論點的小漏洞,

But for the moment, that's the case.

但目前為止, 就是這樣.

Now, here is a very exciting development that many people have not heard of.

好, 物理有一個非常另人興奮的突破, 許多人可能沒聽過.

They should have heard of it, but it's a little tricky to explain in technical detail,

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,

so I won't do it. I'll just mention it. (Laughter)

所以我不幹. 我只會帶過. (笑聲)

But Chen Ning Yang, called by us "Frank" Yang -- (Laughter)

楊振寧(英名: 富蘭克林), 我們稱他"阿富", (笑聲)

-- and Bob Mills put forward, 50 years ago,

與 米爾斯(Bob Mills) 50年前提出

this generalization of Maxwell's equations, with a new symmetry.

更廣義的 麥克斯威方程式 與其蘊涵的新的對稱性質.

A whole new symmetry.

前所未見的對稱性.

Mathematics very similar, but there was a whole new symmetry.

數學上很類似, 不過是全新的對稱性.

They hoped that this would contribute somehow to particle physics

他們希望這能對 粒子物理 多少有些貢獻,

-- didn't. It didn't, by itself, contribute to particle physics.

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!

後來有些粒子物理學家將之更進一步推廣, 終於成功了!

And it gave a very beautiful description of the strong force and of the weak force.

對於強, 弱作用力 給出了非常漂亮的解釋.

So here we say, again, what we said before:

所以我們可以說, 老話一句:

that each skin of the onion shows a similarity to the adjoining skins.

相鄰的洋蔥皮保有許多相似處.

So the mathematics for the adjoining skins is very similar to what we need for the new one.

所以探究新的皮所需俱備的數學工具, 與舊皮非常相似.

And therefore it looks beautiful

理論看起來很美,

because we already know how to write it in a lovely, concise way.

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.

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.

Steps toward unification exhibit the simplicity.

理論相互不斷地統合導致簡化.

Symmetry exhibits the simplicity.

對稱性也使之趨向簡化.

And then there is self-similarity across the scales -- in other words,

且物理在不同的尺度下, 都有許多相似處. 換句話說,

from one skin of the onion to another one.

對不同層的洋蔥皮,

Proximate self-similarity. And that accounts for this phenomenon.

彼此類似. 這解釋了一個現象,

That will account for why beauty is a successful criterion for selecting the right theory.

解釋了為什麼"美"對於正確的理論這麼重要.

Here's what Newton himself said:

這裡是牛頓他説曾說的:

"Nature is very consonant and conformable to her self."

"大自然始終如一的遵循她自己."