Placeholder Image

字幕表 動画を再生する

  • Thank you for putting up these pictures of my colleagues over here.


  • (Laughter) We'll be talking about them.

    (笑)これから 彼らの話をしますが

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

    その前に 実験です 理論家なので普段はしませんが

  • 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.

    なるほど さて かつて私は素粒子を研究していました

  • 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,

    素粒子に関する法則は 万物に適用できます

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


  • We know a lot about four forces. There must be a lot more,

    四つの力は よくわかっています もっと多いはずですが

  • but those are at very, very small distances,


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

    まだ あまりその存在を認識できていません

  • 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.

    美しさこそ 確実に正しい理論を選択するための基準になるということです

  • And why on earth could that be so?

    いったい なぜなのでしょう?

  • 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,

    1957年 3人か4人の仲間で

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

    力の一つ「弱い力」について 部分的ながら完ぺきな理論を提案しました

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

    しかし この理論は 七つの実験結果と一致しませんでした 七つもです

  • Experiments were all wrong.

    でも 実験結果の方がすべて間違いでした

  • And we published before knowing that,

    我々は 結果を知らずに発表しました

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

    とても美しいのだから正しい と思ったからです

  • The experiments had to be wrong, and they were.

    実験は間違いのはずで 実際に間違いでした

  • Now our friend over there, Albert Einstein,


  • used to pay very little attention when people said,

    こんなことを言われても あまり耳を貸しませんでした

  • "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)

    D.C. ミラーだ どうする?」彼は答えました「すぐに消えるよ」(笑)

  • Now, why does stuff like that work? That's the question.

    なぜ 上手くいくのでしょう? 不思議ですね

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

    美しさとは 何を意味するのでしょう? それは ただ一つのことです

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

    これについて 部分的ながら明らかにしていきます

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

    なぜ上手くいくのでしょうか? 人類に関係あるのでしょうか?

  • 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,

    はるか遠くにある恒星のまわりを公転している別の惑星 ―

  • maybe in a another galaxy,


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

    どこかに 我々と同じような知性をもつ生命が実在して

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

    科学に興味があるでしょう 否定はできません たぶん多いでしょう

  • Very likely, none is close enough to interact with us.

    おそらく 会えるほど近くにいないだけです

  • But they could be out there, very easily.


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

    感覚器官などは かなり違っているのではないでしょうか

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

    触手が7本 小さくて変な形の複眼が14個

  • and a brain shaped like a pretzel.


  • Would they really have different laws?

    そこには 地球とは違う法則があるのでしょうか?

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

    そう信じる人は多いのですが まったくばかばかしい話です

  • I think there are laws out there,


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

    どんなに時間があっても 理解し尽くせないでしょう

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

    それでも 挑戦して 理解を深めていくつもりです

  • And someday, we may actually figure out the fundamental unified theory

    いつか人類は 素粒子と力に関する基本的な統一理論を見つけるでしょう

  • 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,

    どこかに存在すると信じて そこに近づこうと

  • 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 --

    複雑でなく 非常にすっきりと表記できることが

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


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

    これは 基本法則についてお話した内容です 基本法則は実在します

  • 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.

    基本法則について ちょっと仮定してみましょう

  • 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.

    間違いです その理論は量子力学的なものだからです

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

    量子力学がどういったものかは 深入りしませんが

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

    いずれにせよ これにまつわる誤解はよく耳にされるでしょう(笑)

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


  • But the main thing here is that it predicts probabilities.

    重要なのは 量子力学が可能性を測るということです

  • Now, sometimes those probabilities are near certainties.


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

    身近な例では たいていそうなりますが

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

    違う場合もあります 様々な結果が生じる可能性だけがわかります

  • 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,

    基本法則に加えて 途方もない偶然の連続

  • or chance outcomes, that are there in addition.


  • And the fundamental theory doesn't include those chance outcomes; they are in addition.

    基本法則は偶然の産物を考慮しません 偶然は付加的なものです

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

    だから万物の理論とはいえないのです 現実においても

  • in the universe around us comes from those accidents,

    この宇宙を取り巻く膨大な情報は 偶然の産物であって

  • 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,

    低エネルギー 高エネルギー 超高エネルギーでの現象を順に調べること

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

    あるいは どんどん距離を縮めて調べることで

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

    徐々に基本法則に近づくことは 玉ねぎの皮をむくようなものです

  • 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.

    そうすることで 基本法則にどんどん近づいています

  • 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,

    どの皮も 前後の皮と共通点があることに気づきます

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


  • and we see they use very similar mathematics.

    数学的表記が そっくりになります

  • They require very similar mathematics.


  • That is absolutely remarkable, and that is a central feature

    これは 注目に値することです

  • of what I'm trying to say today.

    これこそ 今日私が言いたいことなのです

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

    ニュートンは ― ところでニュートンはあちらです

  • This one is Albert Einstein. Hi, Al! And anyway,

    こちらはアルバート・アインシュタインです やあアル!

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

    ニュートンは「自然は 彼女自身に整合する」と言いました 自然を女性に見立てています

  • And so what happens is that the new phenomena,

    新しい現象 新しい皮 つまり

  • 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.


  • A trivial example is this: Newton found the law of gravity,

    簡単な例を紹介します ニュートンは重力の法則を発見しました

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


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

    フランスのクーロンは 電荷について同じ法則を発見しました

  • Here's an example of this similarity.


  • You look at gravity, you see a certain law.

    重力を調べていたら ある法則を発見し

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

    電気を調べていたら 同じ法則を発見したのです

  • 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,

    ご存じでしょうが 例えば

  • is symmetric under rotations about the center of the circle.

    円は その中心まわりに回転対称になっています

  • 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,

    3次元の場合には 球を

  • 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.

    一般的に 対称性があるといいます

  • Maxwell's equations are of course symmetrical

    マクスウェル方程式は 空間内のあらゆる回転に対して

  • under rotations of all of space.

    もちろん 対称です

  • 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,

    19世紀には これを表現する新しい表記法が現れました

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

    その表記法を使えば この方程式がずっと簡潔になります

  • Then Einstein, with his special theory of relativity,

    アインシュタインは 特殊な相対性理論を利用し

  • 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.

    そのような対称性によって この方程式が一層短くて美しくなりました

  • Let's look. You don't have to know what these things mean, doesn't make any difference.

    見てください 意味は分からなくて結構です

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

    形を見るだけでいいですよ(笑) 形だけ見てください

  • 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.

    ベクトル解析と回転対称を利用すると 真ん中の式になります

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


  • down here, showing that symmetry exhibits better and better.

    一番下です 対称性がどんどん良くなる様子が表れています

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

    対称性が高いほど 理論の簡潔さや美しさをはっきりと表記できます

  • The last two, the first equation says that electric charges and currents

    一番下にある二つの式のうち 一つ目は

  • give rise to all the electric and magnetic fields.

    電荷と電流から あらゆる電磁場が発生することを示しています

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

    二つ目の式は 磁場だけでは存在できないことを示しています

  • The only magnetism comes from electric charges and currents.

    磁場だけは 電荷と電流から発生します

  • Someday we may find some slight hole in that argument.

    いつかはこの理論にも 多少矛盾が出てくるでしょうが

  • But for the moment, that's the case.


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

    実は ほとんどの方が知らない 驚くような進展があります

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

    知っておくべきですが 専門的に詳しく説明するのはやっかいですから

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

    それはやめて 言っておくだけにします(笑)

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

    フランク・ヤンと呼ばれていた楊振寧と ―(笑)

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

    ボブ・ミルズは 50年前に

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

    新しい対称性を利用して マクスウェル方程式を一般化しました

  • A whole new symmetry.


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

    数学的にそっくりですが 全く新しい対称性があります

  • They hoped that this would contribute somehow to particle physics

    彼らは これが何らかの形で素粒子物理学に役立つと期待していたのですが

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


  • But then some of us generalized it further. And then it did!

    ところが 我々の仲間がこれを更に一般化した結果 役に立つものとなりました

  • 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.

    玉ねぎの皮は どれも隣の皮に似ています

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

    隣の皮の数学的表記は 次の皮で必要とされるものにとても似ているのです

  • And therefore it looks beautiful


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


  • So here are the themes. We believe there is a unified theory underlying all the regularities.

    こんなテーマがあります 我々はすべての秩序を支える統一理論の存在を信じているということです

  • Steps toward unification exhibit the simplicity.


  • Symmetry exhibits the simplicity.


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

    大きさの違いをまたいで 玉ねぎの1枚の皮から別の皮へとつながる

  • from one skin of the onion to another one.


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

    近接した場所での自己相似性です それがこの現象を作り上げています

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

    だから 正しい理論を選択する基準として美しさが適していると言えるのです

  • Here's what Newton himself said:


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

    こう言いました「自然は自らに調和し 相似する」

  • One thing he was thinking of is something that most of us take for granted today,

    彼の考えていたことの一つが 今では当然だと思われていますが

  • 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.

    本当なのか定かではないのですが よく言われる話があります

  • Four sources told it. That when they had the plague in Cambridge,

    情報元は四つあります ケンブリッジで疫病がはやったとき

  • and he went down to his mother's farm -- because the university was closed --

    彼は母親の農場を訪れました 大学が閉鎖されたからです

  • 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.


  • That was a big unification for those days, although today we take it for granted.

    今ではあたりまえですが その時代には 重要といえる統一でした

  • 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 ... "

    とんでもない奇人だと思われるのを避けるためであり ―」

  • That's what we all have to watch out for, (Laughter) especially at this meeting.

    これは我々も注意しないといけません(笑) この講演では特にそうです

  • " ... and so prejudice my readers against all those things which were the main design of the book."


  • Now, who today would claim that as a mere conceit of the human mind?

    今それを 単に頭に浮かんだ奇想だと言う人はいませんね?

  • 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.

    だれでも知っています それが重力の性質です

  • It's not something in the human mind. The human mind can, of course, appreciate it

    これは心の中だけのものではありません 人の心はこれを評価したり

  • and enjoy it, use it, but it's not -- it doesn't stem from the human mind.

    楽しんだり 利用したりすることができますが 心の中から生まれたのではなく

  • It stems from the character of gravity.


  • And that's true of all the things we're talking about.

    それは すべてに当てはまります

  • They are properties of the fundamental law.

    それが 基本法則の特徴なのです

  • The fundamental law is such that the different skins of the onion resemble one another,

    基本法則とはそういうものなので 玉ねぎの皮は互いに似ているのです

  • and therefore the math for one skin allows you to express beautifully and simply

    だから1枚の皮を表す数学的表記を使って 次の皮の現象を

  • the phenomenon of the next skin.


  • I say here that Newton did a lot of things that year:

    ニュートンはその年 様々な実績を上げました

  • gravity, the laws of motion, the calculus, white light composed of all the colors of the rainbow.

    重力 運動の法則 微積分 虹色の集合が白色となることなどです

  • 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.

    これらの原則を 独立した形而上学的な仮定だと考える必要はありません

  • 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.

    さらに何かを得るために さらに何かが必要なわけではありません

  • That's what emergence means.


  • Life can emerge from physics and chemistry, plus a lot of accidents.

    生命の誕生は 物理的過程と化学的過程に多くの偶然が関与して生じます

  • The human mind can arise from neurobiology and a lot of accidents,

    人の心は 神経生物学と多くの偶然が関与して生まれます

  • the way the chemical bond arises from physics and certain accidents.

    そうやって 物理学的過程にある種の偶然が関与して 化学結合が生まれます

  • It doesn't diminish the importance of these subjects

    もっと基本的な要素に 偶然が重なって生まれるものだとわかっても

  • to know that they follow from more fundamental things, plus accidents.


  • That's a general rule, and it's critically important to realize that.

    それが大原則であり それに気づくことが非常に重要です

  • You don't need something more in order to get something more.

    さらに何かを得るために さらに何かが必要なわけではありません

  • People keep asking that when they read my book, "The Quark and the Jaguar,"

    私の著書「クォークとジャガー」の読者からいつも 質問を受けます

  • and they say, "Isn't there something more beyond what you have there?"