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TED2008

Garrett Lisi: An 8-dimensional model of the universe

ギャレット・リージ「万物の理論」

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物理学者でありサーファーでもあるギャレット・リージが紹介するのは、議論を巻き起こしている新たな宇宙のモデルで、重要な問題はこれですべて解決できる可能性があります。物質と力の素粒子を表す一番美しい8次元モデルです。

- Physicist
Physicist Garrett Lisi has proposed a new "theory of everything" -- a grand unified theory that explains all the elementary particles, as well as gravity. Full bio

Whoa, dude. Check out those killer equations. Sweet. (Laughter)
おぉすごいな! このすごい方程式を見て いいねぇ
00:21
Actually, for the next 18 minutes I'm going to do the best I can
今から18分 できる限り式を使わず
00:30
to describe the beauty of particle physics without equations.
素粒子物理の美を説明します
00:34
It turns out there's a lot we can learn from coral.
サンゴは 学ぶ所が多く
00:38
Coral is a very beautiful and unusual animal.
とても美しい 特異な生物です
00:41
Each coral head consists of thousand of individual polyps.
サンゴの突起は 無数のポリプの集合体です
00:44
These polyps are continually budding and branching
ポリプは出芽と分岐を繰り返し
00:48
into genetically identical neighbors.
同じ遺伝子をもつ複製を作ります
00:50
If we imagine this to be a hyper-intelligent coral,
これを高知能なサンゴだとして
00:53
we can single out an individual and ask him a reasonable question.
個体を一つ選んで 気になる質問をしましょう
00:55
We can ask how exactly he got to be in this particular location
みんなと違って ちょうどその位置にいるのは
00:59
compared to his neighbors --
なぜ?
01:02
if it was just chance, or destiny, or what?
単なる偶然? 運命か何か?
01:04
Now, after admonishing us for turning the temperature up too high,
ポリプは 温暖化に苦言を呈してから
01:08
he would tell us that our question was completely stupid.
ばかな質問だと言うでしょう
01:11
These corals can be quite kind of mean, you see,
サンゴは意地悪になるんです
01:15
and I have surfing scars to prove that.
私もサーフィンで傷を負いました
01:17
But this polyp would continue and tell us
ポリプは続けます
01:20
that his neighbors were quite clearly identical copies of him.
「隣のポリプは 私の完全な複製物だ 私は
01:21
That he was in all these other locations as well,
すべての場所に
01:25
but experiencing them as separate individuals.
同時に存在し それぞれを体験する」
01:27
For a coral, branching into different copies
サンゴにとって 多くの複製に分岐することは
01:30
is the most natural thing in the world.
当然なので
01:33
Unlike us, a hyper-intelligent coral would be uniquely prepared
人類とは違い 高知能なサンゴらしく 量子力学を
01:35
to understand quantum mechanics.
理解します
01:39
The mathematics of quantum mechanics very accurately
量子力学の数学で 宇宙の仕組みが
01:42
describes how our universe works.
正確に表現され
01:44
And it tells us our reality is continually branching
現実が多くの可能性に分岐し続けることがわかります
01:46
into different possibilities, just like a coral.
まさにサンゴのようです
01:49
It's a weird thing for us humans to wrap our minds around,
人類がこれを理解しがたいのは
01:53
since we only ever get to experience one possibility.
一つの可能性しか経験しないからです
01:55
This quantum weirdness was first described
量子力学の奇妙さを示したのは
01:58
by Erwin Schrödinger and his cat.
シュレーディンガーの猫が最初です
02:00
The cat likes this version better.
猫なら
02:02
(Laughter)
こっちのほうが好きでしょう(笑)
02:04
In this setup, Schrödinger is in a box with a radioactive sample
放射性物質とシュレーディンガーが 箱に入っています
02:08
that, by the laws of quantum mechanics, branches into a state
量子力学の法則によれば 試料から
02:11
in which it is radiated and a state in which it is not.
放射線が出る状態と
02:14
(Laughter)
出ない状態に分岐します(笑)
02:18
In the branch in which the sample radiates,
放射した方では
02:22
it sets off a trigger that releases poison and Schrödinger is dead.
毒が放出されて シュレーディンガーは死んでいますが
02:23
But in the other branch of reality, he remains alive.
他方の現実では生きたままです
02:27
These realities are experienced separately by each individual.
二つの現実は 各シュレーディンガーが別々に経験します
02:30
As far as either can tell, the other one doesn't exist.
各世界に 相手の世界は存在しません
02:33
This seems weird to us, because each of us
人は一つの現実しか経験できず
02:36
only experiences an individual existence,
別の現実を見られないので
02:38
and we don't get to see other branches.
奇妙に感じます
02:40
It's as if each of us, like Schrödinger here, are a kind of coral
シュレーディンガーと同様 私たちはサンゴのように
02:42
branching into different possibilities.
多くの可能性に分岐します
02:45
The mathematics of quantum mechanics tells us
量子力学の数学でわかるように
02:49
this is how the world works at tiny scales.
これが微小世界の仕組みです
02:51
It can be summed up in a single sentence:
一言でいうと
02:53
Everything that can happen, does.
「起こりうる全てが起こる」
02:56
That's quantum mechanics.
これが量子力学です
02:58
But this does not mean everything happens.
でも 全て起こるわけではありません
03:00
The rest of physics is about describing what can happen
ほかの物理学は 起こる事と起こらない事を
03:02
and what can't.
示します
03:05
What physics tells us is that everything comes down to geometry
物理学が示すのは 素粒子の相互作用と幾何学に
03:07
and the interactions of elementary particles.
すべて行き着くということです
03:10
And things can happen only if these interactions
何かが起こるのは 相互作用が完全に平衡な場合
03:12
are perfectly balanced.
だけです
03:15
Now I'll go ahead and describe how we know about these particles,
その粒子を知る方法 その実体
03:19
what they are and how this balance works.
平衡がどう作用するのか説明します
03:21
In this machine, a beam of protons and anti-protons
この装置では 陽子と反陽子のビームが
03:25
are accelerated to near the speed of light
光速近くまで加速して衝突し
03:28
and brought together in a collision, producing a burst of pure energy.
一体化して 混じりけのないエネルギーが放射されて
03:30
This energy is immediately converted into a spray
原子より小さな粒子の放射に
03:34
of subatomic particles,
変換され
03:36
with detectors and computers used to figure out their properties.
検出器とコンピュータで解析されます
03:38
This enormous machine -- the large Hadron Collider
この巨大な加速器LHCは
03:41
at CERN in Geneva --
ジュネーブのCERNにあり
03:43
has a circumference of 17 miles
一周27km
03:45
and, when it's operating, draws five times as much power
稼働時にはモントレー市の
03:46
as the city of Monterey.
5倍の電力を消費します
03:48
We can't predict specifically what particles will be produced
衝突ごとに どの粒子が生まれるかは
03:51
in any individual collision.
予測できません
03:54
Quantum mechanics tells us all possibilities are realized.
量子力学は すべての可能性が
03:56
But physics does tell us what particles can be produced.
実在するといい 物理学は生成可能な粒子を示します
03:59
These particles must have just as much mass and energy
生成された粒子のエネルギーは必ず
04:03
as is carried in by the proton and anti-proton.
陽子と反陽子が運ぶエネルギーに等しく
04:05
Any particles more massive than this energy limit
このエネルギー限界を超える粒子は
04:09
aren't produced, and remain invisible to us.
生まれず 目にできません
04:11
This is why this new particle accelerator is so exciting.
この新型加速器がすごいのは そこです
04:15
It's going to push this energy limit seven times
エネルギー限界が従来より7倍
04:18
beyond what's ever been done before,
高いのです
04:20
so we're going to get to see some new particles very soon.
新しい素粒子はすぐ見つかります
04:22
But before talking about what we might see,
予測する前に
04:26
let me describe the particles we already know of.
既知の素粒子について説明します
04:27
There's a whole zoo of subatomic particles.
いわゆる「素粒子動物園」です
04:31
Most of us are familiar with electrons.
電子は身近ですね
04:33
A lot of people in this room make a good living
みなさんは
04:35
pushing them around.
これを使って
04:36
(Laughter)
いい暮らしをしています(笑)
04:37
But the electron also has a neutral partner called the neutrino,
電子には中性の仲間がいます
04:40
with no electric charge and a very tiny mass.
無電荷で質量がとても小さいニュートリノです
04:42
In contrast, the up-and-down quarks have very large masses,
アップクォークとダウンクォークは 質量が膨大で
04:46
and combine in threes to make the protons and neutrons
三つで 陽子と中性子を作ります
04:49
inside atoms.
物質の素粒子には
04:51
All of these matter particles come in left- and right-handed varieties,
右回りと左回りがあり
04:53
and have anti-particle partners that carry opposite charges.
逆の電荷をもった反粒子が相棒です
04:55
These familiar particles also have less familiar
身近な素粒子には
05:01
second and third generations, which have the same charges as the first
聞き慣れない第2 第3世代があります 第1世代と電荷は同じですが
05:02
but have much higher masses.
質量ははるかに大きいものです
05:06
These matter particles all interact with the various force particles.
物質の素粒子は 力の素粒子と相互作用します
05:10
The electromagnetic force interacts with electrically charged matter
「電磁力」は 電荷をもつ物質と相互作用します
05:13
via particles called photons.
光子という素粒子が媒介します
05:16
There is also a very weak force called, rather unimaginatively,
非常に弱い力もあります
05:18
the weak force, that interacts
安直に「弱い力」と呼ばれていて
05:21
only with left-handed matter.
左回りの物質とだけ相互作用します
05:24
The strong force acts between quarks which carry
「強い力」は クォークに働きます
05:27
a different kind of charge, called color charge,
クオークは 色荷というチャージをもち
05:29
and come in three different varieties: red, green and blue.
色荷には 赤 緑 青の3種があります
05:31
You can blame Murray Gell-Mann for these names --
この命名はマリー・ゲルマンの
05:34
they're his fault.
あやまちです
05:36
Finally, there's the force of gravity, which interacts with matter
最後は「重力」です 質量とスピンを介して
05:38
via its mass and spin.
物質と相互作用します
05:41
The most important thing to understand here
一番重要なのは 力ごとに
05:44
is that there's a different kind of charge associated
別のチャージが対応する
05:46
with each of these forces.
ということです
05:48
These four different forces interact with matter
4種の力は その力に対応した
05:50
according to the corresponding charges that each particle has.
各素粒子のチャージに応じて 物質と作用します
05:52
A particle that hasn't been seen yet, but we're pretty sure exists,
未発見ながら確実に存在するのが
05:57
is the Higgs particle, which gives masses to all these other particles.
ヒッグス粒子です 他の素粒子に質量を与えます
05:59
The main purpose of the Large Hadron Collider
LHCの主目的は
06:04
is to see this Higgs particle, and we're almost certain it will.
ヒッグス粒子の発見です ほぼ確実ですが
06:05
But the greatest mystery is what else we might see.
ほかに何を発見できるかが 最大の神秘です
06:09
And I'm going to show you one beautiful possibility
ここからは すごい可能性を一つ
06:13
towards the end of this talk.
お話しします
06:15
Now, if we count up all these different particles
素粒子を
06:19
using their various spins and charges, there are 226.
スピンやチャージを考慮して数え上げると226個です
06:20
That's a lot of particles to keep track of.
多いのです
06:25
And it seems strange that nature would have
自然界にそれほど多種の素粒子が
06:27
so many elementary particles.
あるのは奇妙にも思えますが
06:29
But if we plot them out according to their charges,
チャージに基づいて描画すると
06:32
some beautiful patterns emerge.
美しいパターンが現れます
06:34
The most familiar charge is electric charge.
一番身近なのは電荷ですね
06:38
Electrons have an electric charge, a negative one,
電子の電荷はマイナス1
06:41
and quarks have electric charges in thirds.
クォークの電荷は1/3の倍数
06:43
So when two up quarks and a down quark are combined
アップクォーク二つと ダウンクォーク一つで
06:45
to make a proton, it has a total electric charge of plus one.
陽子を作ります 電荷の合計はプラス1です
06:47
These particles also have anti-particles, which have opposite charges.
素粒子には 逆の電荷をもつ反粒子が存在します
06:51
Now, it turns out the electric charge is actually
電荷は
06:55
a combination of two other charges:
別の二つのチャージの組み合わせです
06:56
hypercharge and weak charge.
ハイパーチャージとウィークチャージです
06:59
If we spread out the hypercharge and weak charge
2次元チャージ空間に
07:02
and plot the charges of particles in this two-dimensional charge space,
ハイパーチャージとウィークチャージを展開して 各粒子のチャージをプロットすると
07:03
the electric charge is where these particles sit
電荷は
07:08
along the vertical direction.
縦方向に示されます
07:10
The electromagnetic and weak forces interact with matter
ハイパーチャージとウィークチャージに基づいて
07:13
according to their hypercharge and weak charge,
電磁力と弱い力が物質と
07:15
which make this pattern.
相互作用します
07:17
This is called the Unified Electroweak Model,
これは
07:19
and it was put together back in 1967.
1967年に統一された電弱統一モデルです
07:20
The reason most of us are only familiar with electric charge
身近なのは電荷だけで
07:24
and not both of these is because of the Higgs particle.
両方ではないのは ヒッグス粒子が原因です
07:26
The Higgs, over here on the left, has a large mass
左側にあるヒッグスは質量が大きくて
07:30
and breaks the symmetry of this electroweak pattern.
電弱パターンの対称性を破ります
07:33
It makes the weak force very weak
弱い素粒子の
07:36
by giving the weak particles a large mass.
質量を大きくし 弱い力を弱めます
07:37
Since this massive Higgs sits along the horizontal direction
大質量のヒッグスが図の横方向に位置しているので
07:39
in this diagram, the photons of electromagnetism remain massless
電磁力を担う光子は質量をもたずに チャージ空間の縦方向で
07:42
and interact with electric charge along the vertical direction
電荷と相互作用を
07:46
in this charge space.
します
07:48
So the electromagnetic and weak forces are described
電磁力と弱い力は 2次元空間で
07:52
by this pattern of particle charges in two-dimensional space.
素粒子のチャージのパターンとして示されます
07:54
We can include the strong force by spreading out
強い力を2チャージ方向に展開して
07:58
its two charge directions and plotting the charges
クォークに働く力の素粒子のチャージを描くと
08:00
of the force particles in quarks along these directions.
強い力を導入することができます
08:03
The charges of all known particles can be plotted
既知のすべての素粒子の
08:07
in a four-dimensional charge space, and projected down
チャージを 4次元チャージ空間に描画して
08:09
to two dimensions like this so we can see them.
2次元に投影できます
08:12
Whenever particles interact, nature keeps things in a perfect balance
素粒子が相互作用するとき 4チャージ方向で
08:15
along all four of these charge directions.
完全に平衡が保たれます
08:18
If a particle and an anti-particle collide, it creates a burst of energy
粒子と反粒子が衝突すると エネルギーが放出されて
08:21
and a total charge of zero in all four charge directions.
全4チャージ方向でチャージの和がゼロになります
08:24
At this point, anything can be created as long as it has
エネルギーが同じで チャージの和がゼロであれば
08:28
the same energy and maintains a total charge of zero.
何でも作れます
08:31
For example, this weak force particle and its anti-particle
例えば この弱い力の粒子と反粒子は
08:34
can be created in a collision.
衝突で生まれます
08:37
In further interactions, the charges must always balance.
さらに相互作用しても チャージは常に平衡します
08:39
One of the weak particles could decay into an electron
弱い力は 電子と反電子ニュートリノに
08:42
and an anti-neutrino,
崩壊しますが
08:45
and these three still add to zero total charge.
三つのチャージの和はゼロのままです
08:47
Nature always keeps a perfect balance.
いつも完全に平衡が保たれます
08:50
So these patterns of charges are not just pretty.
チャージパターンは綺麗なだけでなく
08:53
They tell us what interactions are allowed to happen.
どんな相互作用が発生し得るかを読み取れます
08:55
And we can rotate this charge space in four dimensions
4次元でこのチャージ空間を回転させれば
08:58
to get a better look at the strong interaction,
強い相互作用を見られます
09:01
which has this nice hexagonal symmetry.
六角形状に対称です
09:03
In a strong interaction, a strong force particle, such as this one,
強い相互作用では 例えばこの強い力の素粒子が
09:06
interacts with a colored quark, such as this green one,
例えばこの緑のカラークォークと相互作用して
09:10
to give a quark with a different color charge -- this red one.
別の色荷をもつ この赤いクォークとなります
09:13
And strong interactions are happening millions of times
体中の原子では 毎秒
09:18
each second in every atom of our bodies,
強い相互作用が 無数に発生して
09:20
holding the atomic nuclei together.
原子核を一体に保っています
09:23
But these four charges corresponding to three forces
3種の力に対応した4種のチャージだけでは
09:27
are not the end of the story.
終わりません
09:30
We can also include two more charges
重力に対応した
09:32
corresponding to the gravitational force.
2チャージも導入できます
09:33
When we include these, each matter particle
このとき 物質の素粒子は それぞれ
09:35
has two different spin charges, spin-up and spin-down.
上下二つのスピンチャージをもちます
09:38
So they all split, and give a nice pattern
6次元チャージ空間にすべて分かれて
09:42
in six-dimensional charge space.
きれいなパターンを描きます
09:44
We can rotate this pattern in six dimensions,
6次元でパターンを回転させると
09:46
and see that it's quite pretty.
かなり綺麗になります
09:48
Right now, this pattern matches our best current knowledge
素粒子レベルの微小スケールで自然の仕組みを示す最有力の思想と
09:53
of how nature is built at the tiny scales
これが一致
09:57
of these elementary particles.
しています
09:59
This is what we know for certain.
確かに一致しています
10:01
Some of these particles are at the very limit
いくつかの素粒子で
10:03
of what we've been able to reach with experiments.
すでに装置限界に達しています
10:04
From this pattern, we already know the particle physics
微小スケールでの素粒子物理は
10:07
of these tiny scales. The way the universe works
このパターンから明らかとなりました
10:10
with these tiny scales is very beautiful.
微小スケールの宇宙の仕組みは とても美しいのです
10:13
But now I'm going to discuss some new and old ideas
未知の世界について 新旧交えて
10:17
about things we don't know yet.
お話しします
10:19
We want to expand this pattern using mathematics alone,
数学だけを使い パターンを拡張して
10:22
and see if we can get our hands on the whole enchilada.
全体像をつかめるか試します
10:24
We want to find all the particles and forces
宇宙を完璧に描く 素粒子と力を
10:27
that make a complete picture of our universe.
すべて見つけたいのです
10:29
And we want to use this picture to predict new particles
もっと高エネルギーの実験で見つかる
10:32
that we'll see when experiments reach higher energies.
新しい素粒子を予測したいのです
10:34
So there's an old idea in particle physics
素粒子物理学には昔から
10:39
that this known pattern of charges, which is not very symmetric,
対称性に欠ける この既知のチャージパターンは
10:41
could emerge from a more perfect pattern that gets broken --
完璧なパターンが崩壊して生まれたという考えがあります
10:45
similar to how the Higgs particle breaks the electroweak pattern
ヒッグス粒子が電弱パターンを破って
10:49
to give electromagnetism.
電磁力を生むのと
10:51
In order to do this, we need to introduce new forces
似ています そのためには 新しい力とチャージ方向を
10:53
with new charge directions.
導入する必要があります
10:56
When we introduce a new direction, we get to guess
新しいチャージ方向を導入すれば
11:00
what charges the particles have along this direction,
素粒子のチャージが明らかになり ほかと一緒に
11:02
and then we can rotate it in with the others.
回転可能になります
11:05
If we guess wisely, we can construct the standard charges
上手くやれば6チャージ次元の標準的なチャージが
11:08
in six charge dimensions as a broken symmetry
もっと綺麗な7チャージ次元パターンの対称性を
11:11
of this more perfect pattern in seven charge dimensions.
破った形だといえることになります
11:14
This particular choice corresponds to a grand unified theory
この選択は 1973年にパティとサラムが提唱した
11:18
introduced by Pati and Salam in 1973.
大統一理論に対応するものです
11:21
When we look at this new unified pattern,
この新たな統一パターンを見ると
11:24
we can see a couple of gaps where particles seem to be missing.
素粒子が欠けたような穴が二つあります
11:27
This is the way theories of unification work.
統一理論がうまくいった例です
11:31
A physicist looks for larger, more symmetric patterns
実証済みのパターンを内包した
11:34
that include the established pattern as a subset.
大きくて対称的なパターンを探すのが物理学者です
11:36
The larger pattern allows us to predict the existence
大きなパターンから 未知の素粒子の
11:40
of particles that have never been seen.
存在を予測できます
11:42
This unification model predicts the existence of these two
この統一モデルから 弱い力によく似た
11:45
new force particles, which should act a lot like the weak force,
新しい力の素粒子を二つ予測できます
11:48
only weaker.
弱い方だけです
11:52
Now we can rotate this set of charges in seven dimensions
7次元でチャージ群を回転させると
11:54
and consider an odd fact about the matter particles:
物質の素粒子について奇妙な事実が浮かびます
11:56
the second and third generations of matter
物質の素粒子を 6次元チャージ空間で見ると
11:59
have exactly the same charges in six-dimensional charge space
第2 第3世代のチャージが 第1世代と
12:02
as the first generation.
全く同じなのです
12:05
These particles are not uniquely identified by their six charges.
6チャージでは区別できずに
12:08
They sit on top of one another in the standard charge space.
標準のチャージ空間で重なっています
12:12
However, if we work in eight-dimensional charge space,
ところが8次元チャージ空間で考えると
12:16
then we can assign unique new charges to each particle.
各素粒子に固有のチャージを新しく割り当てられます
12:19
Then we can spin these in eight dimensions,
8次元で回転させて
12:23
and see what the whole pattern looks like.
パターンの全貌を見てみましょう
12:26
Here we can see the second and third generations of matter now
物質の第2 第3世代が
12:30
related to the first generation by a symmetry called "triality."
「三重性」という対称性で 第1世代に結びついています
12:32
This particular pattern of charges in eight dimensions is actually
8次元で示された 特有のチャージパターンは
12:38
part of the most beautiful geometric structure in mathematics.
数学的に最も美しい幾何学模様の一種です
12:41
It's a pattern of the largest exceptional Lie group, E8.
最大の例外型リー群E8のパターンです
12:46
This Lie group is a smooth, curved shape with 248 dimensions.
このリー群は 248次元の滑らかな曲線を描きます
12:50
Each point in this pattern corresponds to a symmetry
そのパターンの各点が この複雑で美しい形状と
12:54
of this very complex and beautiful shape.
同じ対称性をもつのです
12:57
One small part of this E8 shape can be used
E8形状の一部に重力を説明した
13:00
to describe the curved space-time of Einstein's general relativity,
アインシュタインの一般相対性理論でいう時空の歪みが
13:02
explaining gravity.
示されています
13:05
Together with quantum mechanics, the geometry of this shape
量子力学を組み合わせると この幾何学形状から
13:07
could describe everything about how the universe works
微小スケールでの宇宙の仕組みを
13:10
at the tiniest scales.
全て説明できます
13:12
The pattern of this shape living in eight-dimensional charge space
8次元チャージ空間に存在するこのパターンは
13:14
is exquisitely beautiful,
比類のない美しさです
13:17
and it summarizes thousands of possible interactions
素粒子間に生じ得る相互作用が
13:21
between these elementary particles, each of which
無数に集約されていて それぞれが
13:23
is just a facet of this complicated shape.
複雑な形状の一面を構成しています
13:25
As we spin it, we can see many of the other intricate patterns
回転させると 複雑なパターンが
13:30
contained in this one.
数多く現れます
13:32
And with a particular rotation, we can look down through this pattern
ある特定の回転を加えると
13:36
in eight dimensions along a symmetry axis
対称軸に沿って8次元パターンを見下ろして
13:38
and see all the particles at once.
素粒子を一望できます
13:41
It's a very beautiful object, and as with any unification,
非常に美しく どの統一モデルにも見られるように
13:44
we can see some holes where new particles are required
新たな素粒子の入るべき空所が
13:47
by this pattern.
見てとれます
13:49
There are 20 gaps where new particles should be,
ここには20ヶ所あります
13:52
two of which have been filled by the Pati-Salam particles.
2ヶ所はパティとサラムの粒子です
13:55
From their location in this pattern, we know that these new particles
位置からすると 新しい素粒子は
13:58
should be scalar fields like the Higgs particle,
ヒッグス粒子のようなスカラー場のはずですが
14:00
but have color charge and interact with the strong force.
色荷を持って 強い力と作用します
14:03
Filling in these new particles completes this pattern,
新たな素粒子で埋まれば
14:06
giving us the full E8.
完全なE8が出来上がります
14:08
This E8 pattern has very deep mathematical roots.
このE8パターンは非常に深い数学的根拠に基づいています
14:10
It's considered by many to be the most beautiful structure
数学的に最も美しい構造になると 多くの人が
14:13
in mathematics.
感じています
14:16
It's a fantastic prospect that this object of great
数学的にも見事なこの模様が
14:17
mathematical beauty could describe the truth of particle interactions
微小スケールでの素粒子の相互作用を示すという展望は
14:20
at the smallest scales imaginable.
素晴らしいと思います
14:23
And this idea that nature is described by mathematics
数学が自然を説明するという思想は
14:25
is not at all new.
決して新しいものではなく
14:30
In 1623, Galileo wrote this:
1623年 ガリレオは言いました
14:32
"Nature's grand book, which stands continually open to our gaze,
「自然の崇高な規範は 常に観察を受け入れ
14:36
is written in the language of mathematics.
数学的表現で記述できる
14:39
Its characters are triangles, circles and other geometrical figures,
その要素は 三角や円などの幾何学形状である
14:42
without which it is humanly impossible to understand
さもなくば人間の理解は
14:45
a single word of it;
全く及ばず
14:47
without these, one is wandering around in a dark labyrinth."
暗い迷宮をさまようことになる」
14:49
I believe this to be true, and I've tried
これを信じてガリレオに従い
14:54
to follow Galileo's guidance in describing the mathematics
三角や円などの幾何学形状だけで
14:56
of particle physics using only triangles, circles
素粒子物理の数学を表現することに
14:58
and other geometrical figures.
挑みました
15:01
Of course, when other physicists and I actually work on this stuff,
ほかの物理学者と取り組む中で
15:03
the mathematics can resemble a dark labyrinth.
この数学は 暗い迷宮にも思えましたが
15:06
But it's reassuring that at the heart of this mathematics
本質に触れると 純粋で美しい幾何学だと
15:11
is pure, beautiful geometry.
再認識させられました
15:14
Joined with quantum mechanics, this mathematics
量子力学を併用すると
15:18
describes our universe as a growing E8 coral,
美しいパターンに基づいて
15:20
with particles interacting at every location in all possible ways
あらゆる可能性のもと各所で素粒子が相互作用する 成長するE8サンゴとして
15:22
according to a beautiful pattern.
宇宙を説明できます
15:26
And as more of the pattern comes into view using new machines
LHCのような新しい装置で
15:30
like the Large Hadron Collider, we may be able to see
もっとパターンが見えてくれば
15:32
whether nature uses this E8 pattern or a different one.
自然がE8パターンに従うのか そうでないのか 明らかになります
15:35
This process of discovery is a wonderful adventure to be involved in.
この探索は 素晴らしい冒険です
15:40
If the LHC finds particles that fit this E8 pattern,
LHCで E8パターンに合う素粒子が見つかれば
15:44
that will be very, very cool.
やったぜと思うでしょうが
15:47
If the LHC finds new particles, but they don't fit this pattern --
パターンから外れる新しい素粒子が見つかれば
15:50
well, that will be very interesting, but bad for this E8 theory.
かなり興味は引かれますが E8理論的には困ります
15:53
And, of course, bad for me personally.
個人的には困るのです
15:58
(Laughter)
(笑)
16:00
Now how bad would that be?
どれくらい?
16:03
Well, pretty bad.
かなり最悪!
16:04
(Laughter)
(笑)
16:06
But predicting how nature works is a very risky game.
自然の仕組みを予測するゲームは
16:10
This theory and others like it are long shots.
リスクが大きく この理論も ほかの理論も 博打です
16:13
One does a lot of hard work knowing that most of these ideas
たいていは失敗に終わるとわかりつつ
16:17
probably won't end up being true about nature.
熱中します
16:20
That's what doing theoretical physics is like:
理論物理は
16:22
there are a lot of wipeouts.
失敗ばかりです
16:24
In this regard, new physics theories are a lot like start-up companies.
新しい物理理論は新興企業にそっくりです
16:26
As with any large investment, it can be emotionally difficult
大きな投資をして 失敗したとき
16:32
to abandon a line of research when it isn't working out.
研究をやめるのはつらいですね
16:34
But in science, if something isn't working, you have to
でも 科学では ダメなら
16:37
toss it out and try something else.
切り替えが必要
16:39
Now, the only way to maintain sanity and achieve happiness
不安になりつつ 正気を保って幸せをつかむには
16:42
in the midst of this uncertainty is to keep balance
生活バランスと展望の維持こそ
16:45
and perspective in life.
唯一の解決策です
16:47
I've tried the best I can to live a balanced life.
私は生活のバランスを維持しようと
16:51
(Laughter)
ベストを尽くしてきました(笑)
16:53
I try to balance my life equally between physics, love and surfing --
「物理」「愛」「サーフィーン」のバランスを保っています
16:56
my own three charge directions.
私の3チャージ方向です
16:59
(Laughter)
(笑)
17:01
This way, even if the physics I work on comes to nothing,
だから 物理で成果が出なくても
17:03
I still know I've lived a good life.
いい人生だったと思えます
17:05
And I try to live in beautiful places.
美しい場所に住むようにしていて
17:08
For most of the past ten years I've lived on the island of Maui,
この10年はほとんど マウイ島で過ごしています
17:10
a very beautiful place.
本当に美しい所です
17:13
Now it's one of the greatest mysteries in the universe to my parents
私の親にとって 宇宙で最大の謎は
17:15
how I managed to survive all that time without engaging
就職もせずに その間 どうやって
17:18
in anything resembling full-time employment.
生き延びたのかということです
17:21
(Laughter)
(笑)
17:23
I'm going to let you in on that secret.
秘密を明かします
17:27
This was a view from my home office on Maui.
これは
17:31
And this is another, and another.
マウイの仕事部屋から見た景色です
17:35
And you may have noticed that these beautiful views
美しい眺めは どれも似ていますが
17:39
are similar, but in slightly different places.
場所が少し違っています
17:41
That's because this used to be my home and office on Maui.
マウイでは これが家であり職場だったからです
17:45
(Laughter)
(笑)
17:48
I've chosen a very unusual life.
異色の生活でしたが
17:50
But not worrying about rent allowed me to spend my time
家賃なしの生活で 時間を自由に
17:53
doing what I love.
使えました
17:55
Living a nomadic existence has been hard at times,
放浪生活は大変な時もありましたが
17:57
but it's allowed me to live in beautiful places
美しい場所で生活できました
17:59
and keep a balance in my life that I've been happy with.
幸せな生活でバランスを保てました
18:01
It allows me to spend a lot of my time hanging out
高知能なサンゴと
18:05
with hyper-intelligent coral.
よく遊んだりもしました
18:07
But I also greatly enjoy the company of hyper-intelligent people.
知能の高い人にも会えてうれしいです
18:11
So I'm very happy to have been invited here to TED.
今日 ここに招待いただいて光栄です
18:14
Thank you very much.
ありがとうございました
18:17
(Applause)
(拍手)
18:18
Chris Anderson: I probably understood two percent of that,
(クリス)
18:31
but I still absolutely loved it. So I'm going to sound dumb.
理解できたのは2%だけど良かったよ くだらない質問だと思うかもしれないけど
18:32
Your theory of everything --
あなたのいう万物の理論は
18:38
Garrett Lisi: I'm used to coral.
(ギャレット)サンゴだよ
18:41
CA: That's right. The reason it's got a few people
(クリス)それが興味を引くのは
18:42
at least excited is because, if you're right, it brings
あなたが正しければ 重力と量子論が
18:44
gravity and quantum theory together.
一体化されるからですけど
18:47
So are you saying that we should think of the universe,
宇宙の本質には
18:50
at its heart -- that the smallest things that there are,
最小のもの ―
18:53
are somehow an E8 object of possibility?
可能性を示すE8的なものがあると考えるべきでしょうか?
18:56
I mean, is there a scale to it, at the smallest scale,
つまり 最小スケールで測るものを
19:03
or ...?
想定しているとか?
19:05
GL: Well, right now the pattern I showed you that corresponds
(ギャレット)私がお見せした
19:06
to what we know about elementary particle physics --
素粒子物理学の通説に対応したパターンは
19:09
that already corresponds to a very beautiful shape.
すでに とても綺麗な形状をしています
19:13
And that's the one that I said we knew for certain.
確実な部分です
19:16
And that shape has remarkable similarities -- and the way it fits
かなりの類似点のあるその形状を
19:18
into this E8 pattern could be the rest of the picture.
E8パターンにどう当てはめるかが後の説明です
19:22
And these patterns of points that I've shown for you
点でできたあのパターンは
19:26
actually represent symmetries of this high-dimensional object
この高次元のモデルの対称性をよく表しています
19:29
that would be warping and moving and dancing
このモデルは 私たちの体験する時空を超えて 歪んだり
19:33
over the space time that we experience.
動いたり跳ねたりします
19:36
And that would be what explains all these
これが 全ての素粒子を
19:39
elementary particles that we see.
説明してくれます
19:41
CA: But a string theorist,
(クリス)私の理解では弦理論家は電子を
19:42
as I understand it, explains electrons in terms of much smaller
振動する微小な弦で説明します
19:45
strings vibrating --
弦理論は
19:47
I know you don't like string theory -- vibrating inside it.
嫌いでしょうけど
19:48
How should we think of an electron in relation to E8?
E8との関連では 電子をどうとらえればいいのですか?
19:51
GL: No, it would be one of the symmetries of this E8 shape.
(ギャレット)E8形状の対称性の一つです
19:57
So what's happening is, as the shape is moving over space-time,
その形状が時空を超えて動くときに
20:01
it's twisting. And the direction it's twisting as it moves
ねじれが生じます その移動に伴うねじれ方向で
20:05
is what particle we see. So it would be --
どの素粒子か決まります
20:09
CA: The size of the E8 shape,
(クリス)E8形状の大きさは 電子と
20:11
how does that relate to the electron?
どう関係する?
20:13
I kind of feel like I need that for my picture.
理解するには それが必要なんです
20:14
Is it bigger? Is it smaller?
大きい?小さい?
20:16
GL: Well, as far as we know electrons are point particles,
(ギャレット)知る限りでは
20:17
so this would be going down to the smallest possible scales.
電子は点ですから 最小ということになります
20:20
So the way these things are explained in quantum field theory
場の量子論で説明すると
20:24
is, all possibilities are expanding and developing at once.
全ての可能性が同時に拡張し進展しているということになります
20:26
And this is why I use the analogy to coral.
だからサンゴに例えるのです
20:30
And in this way, the way that E8 comes in is
E8を適用する場合には
20:33
it will be as a shape that's attached at each point in space-time.
それは時空の各点に結びついた形状となります
20:40
And, as I said, the way the shape twists --
屈曲した表面を動きながら
20:45
the directional along which way the shape is twisting
その形状のねじれる方向が
20:49
as it moves over this curved surface --
どの素粒子かを
20:51
is what the elementary particles are, themselves.
決めるのです
20:52
So through quantum field theory, they manifest themselves
場の量子論では 点として表現されて そのように
20:56
as points and interact that way.
相互作用します
21:00
I don't know if I'll be able to make this any clearer.
これ以上わかりやすくできないな
21:02
(Laughter)
(笑)
21:04
CA: It doesn't really matter.
(クリス)大丈夫ですよ
21:08
It's evoking a kind of sense of wonder, and I certainly
知りたいという気持ちがわいてきました
21:09
want to understand more of this.
ぜひもっと理解したいと思います
21:13
But thank you so much for coming. That was absolutely fascinating.
ありがとう 面白かったよ
21:16
(Applause)
(拍手)
21:18
Translated by Satoshi Tatsuhara
Reviewed by Lily Yichen Shi

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About the speaker:

Garrett Lisi - Physicist
Physicist Garrett Lisi has proposed a new "theory of everything" -- a grand unified theory that explains all the elementary particles, as well as gravity.

Why you should listen

Working from principles of differential geometry, physicist Garrett Lisi is developing a new unified theory that purports to explain all the elementary particles, and gravity, in one elegant model. His theory is based on a mathematical shape called E8. With 248 symmetries, E8 is large, complex and beautiful -- and Lisi believes the relationships of its symmetries correspond to known particles and forces, including gravity.

His work, explained in his paper "An Exceptionally Simple Theory of Everything," and in an ongoing discussion on FQXi, is still on science's speculative fringe. But some physicists believe he could be pointing the way toward a truly unified theory.

More profile about the speaker
Garrett Lisi | Speaker | TED.com