Why our universe might exist on a knife-edge | Gian Giudice

996,659 views ・ 2013-10-24

TED


請雙擊下方英文字幕播放視頻。

譯者: Candie Lin 審譯者: Yuexin Gao
00:13
So last year, on the Fourth of July,
0
13179
2344
去年7月4號
00:15
experiments at the Large Hadron Collider
1
15523
2499
在大型強子對撞機(LHC)的實驗裡
00:18
discovered the Higgs boson.
2
18022
2290
希格斯玻色子被發現了
00:20
It was a historical day.
3
20312
1968
那是歷史性的一刻
00:22
There's no doubt that from now on,
4
22280
2295
無庸置疑地,從現在開始
00:24
the Fourth of July will be remembered
5
24575
1834
7月4號不再被認為是 美國獨立紀念日
00:26
not as the day of the Declaration of Independence,
6
26409
2442
00:28
but as the day of the discovery of the Higgs boson.
7
28851
3834
而是發現希格斯玻色子的重要日子
00:32
Well, at least, here at CERN.
8
32685
2432
至少對歐洲核子研究組織是這樣的
00:35
But for me, the biggest surprise of that day
9
35117
4155
但是對我而言,那天最大的驚喜
00:39
was that there was no big surprise.
10
39272
2499
就是沒有太大的驚喜
00:41
In the eye of a theoretical physicist,
11
41771
2599
在物理理論學家的眼中
00:44
the Higgs boson is a clever explanation
12
44370
1893
希格斯玻子是一個很絕妙的解釋
00:46
of how some elementary particles gain mass,
13
46263
3523
它解釋了一些基本粒子如何獲得質量
00:49
but it seems a fairly unsatisfactory
14
49786
2836
但是這看來就是個不盡滿意
00:52
and incomplete solution.
15
52622
2206
而且不夠完整的解答
00:54
Too many questions are left unanswered.
16
54828
3024
太多問題都無法回答
00:57
The Higgs boson does not share the beauty,
17
57852
2835
希格斯玻色子不夠美麗
01:00
the symmetry, the elegance,
18
60687
1885
不夠均稱,不夠優雅
01:02
of the rest of the elementary particle world.
19
62572
2728
不足以和基本粒子世界相比
01:05
For this reason, the majority of theoretical physicists
20
65300
3622
因此,大多數理論學家
01:08
believe that the Higgs boson could not
21
68922
2942
不相信希格斯玻色子就是所有的真相
01:11
be the full story.
22
71864
2482
01:14
We were expecting new particles and new phenomena
23
74346
2854
我們希望新的粒子和新的現象
01:17
accompanying the Higgs boson.
24
77200
2450
能隨著希格斯玻色子出現
01:19
Instead, so far, the measurements
25
79650
2318
但目前從LHC對撞機得來的測量 卻沒有顯示什麼新的粒子和新的現象
01:21
coming from the LHC show no signs of new particles
26
81968
3758
01:25
or unexpected phenomena.
27
85726
2149
01:27
Of course, the verdict is not definitive.
28
87875
3653
當然,目前的論斷並不是絕對的
01:31
In 2015, the LHC will almost double
29
91528
3994
2015年,LHC對撞機將會加倍
01:35
the energy of the colliding protons,
30
95522
2691
質子撞擊的能量
01:38
and these more powerful collisions
31
98213
2071
這些更強烈的撞擊
01:40
will allow us to explore further the particle world,
32
100284
4584
能讓我們進一步了探索粒子世界
01:44
and we will certainly learn much more.
33
104868
3132
我們一定能從中知道更多
01:48
But for the moment, since we have found
34
108000
3146
但當下我們還沒找到新現象的證據
01:51
no evidence for new phenomena, let us suppose
35
111146
3149
讓我們假設我們今天知道的粒子
01:54
that the particles that we know today,
36
114295
3164
01:57
including the Higgs boson,
37
117459
1856
包含希格斯玻色子
01:59
are the only elementary particles in nature,
38
119315
3285
是自然界中僅有的基本粒子
02:02
even at energies much larger
39
122600
2744
即使它們能爆發的能量 比我們今天所知的多上更多
02:05
than what we have explored so far.
40
125344
2766
02:08
Let's see where this hypothesis is going to lead us.
41
128110
4632
我們來看看這個假設會帶來什麼事
02:12
We will find a surprising and intriguing result
42
132742
3432
我們會發現宇宙驚奇又迷人的結果
02:16
about our universe, and to explain my point,
43
136174
3799
在我繼續解釋之前
02:19
let me first tell you what the Higgs is about,
44
139973
3876
先讓我說明希格斯玻色子是什麼
02:23
and to do so, we have to go back
45
143849
3134
要說明的話,我們必須回到
02:26
to one tenth of a billionth of a second
46
146983
4357
宇宙大爆炸之後的百億分之一秒
02:31
after the Big Bang.
47
151340
1531
02:32
And according to the Higgs theory,
48
152871
2041
根據希格斯理論
02:34
at that instant, a dramatic event took place
49
154912
3366
在那瞬間 一件非常戲劇化的事件在宇宙中發生
02:38
in the universe.
50
158278
1591
02:39
Space-time underwent a phase transition.
51
159869
4791
時空經歷轉變期
02:44
It was something very similar to the phase transition
52
164660
3077
這個轉變期 和水在零度以下結冰的過程非常像
02:47
that occurs when water turns into ice
53
167737
3545
02:51
below zero degrees.
54
171282
1961
02:53
But in our case, the phase transition
55
173243
2940
但這個例子裡
轉變期不是分子在物質裡的重新排列
02:56
is not a change in the way the molecules
56
176183
2531
02:58
are arranged inside the material,
57
178714
2286
03:01
but is about a change
58
181000
1888
而是時空結構的改變
03:02
of the very fabric of space-time.
59
182888
3626
03:06
During this phase transition, empty space
60
186514
2626
在這段轉變期,空間充滿物質
03:09
became filled with a substance
61
189140
2672
03:11
that we now call Higgs field.
62
191812
3032
就是我們說的希格斯場
03:14
And this substance may seem invisible to us,
63
194844
2329
這種物質我們可能看不見
03:17
but it has a physical reality.
64
197173
2678
但卻擁有物理性質
03:19
It surrounds us all the time,
65
199851
2058
它隨時環繞我們
03:21
just like the air we breathe in this room.
66
201909
3701
就像我們在這房間內呼吸的空氣一樣
03:25
And some elementary particles interact
67
205610
2318
有些基本粒子和這種物質互動 從過程中獲得能量
03:27
with this substance, gaining energy in the process.
68
207928
3828
03:31
And this intrinsic energy is what we call
69
211756
3075
這種內在的能量 就是我們今天說的粒子質量
03:34
the mass of a particle,
70
214831
2133
03:36
and by discovering the Higgs boson, the LHC
71
216964
3253
而藉由發現希格斯玻色子
LHC對撞機證實這種物質是真的
03:40
has conclusively proved that this substance is real,
72
220217
4532
03:44
because it is the stuff the Higgs bosons are made of.
73
224749
3919
因為希格斯玻色子正由這種物質組成
03:48
And this, in a nutshell, is the essence of the Higgs story.
74
228668
3444
簡單來說,這就是希格斯故事的梗概
03:52
But this story is far more interesting than that.
75
232112
4743
但更有趣的在後頭
03:56
By studying the Higgs theory,
76
236855
2311
研究希格斯理論的同時
03:59
theoretical physicists discovered,
77
239166
2360
理論學家發現
04:01
not through an experiment
78
241526
1904
並非經由實驗,而只是數學演算
04:03
but with the power of mathematics,
79
243430
2476
04:05
that the Higgs field does not necessarily exist
80
245906
3712
他們發現希格斯場並不是 只以我們今日發現的形式存在
04:09
only in the form that we observe today.
81
249618
3337
04:12
Just like matter can exist as liquid or solid,
82
252955
5045
就像物質可以有液態和固態兩種狀態
04:18
so the Higgs field, the substance that fills all space-time,
83
258000
4572
所以希格斯場 也就是那填滿時空的物質
04:22
could exist in two states.
84
262572
3354
可以存在於兩種狀態下
04:25
Besides the known Higgs state,
85
265926
2310
除了已知的希格斯場之外
04:28
there could be a second state in which the Higgs field
86
268236
3147
希格斯場還可能比現在 所知的高出幾十億密度存在
04:31
is billions and billions times denser
87
271383
3536
04:34
than what we observe today,
88
274919
2045
04:36
and the mere existence of another state
89
276964
3487
光是另一種希格斯場的可能存在
04:40
of the Higgs field poses a potential problem.
90
280451
4245
就帶來了潛在的問題
04:44
This is because, according to the laws
91
284696
3238
因為根據量子力學定律
04:47
of quantum mechanics, it is possible
92
287934
2693
兩種狀態之間的轉變是有可能的
04:50
to have transitions between two states,
93
290627
2832
04:53
even in the presence of an energy barrier
94
293459
2949
即使兩個狀態之間有能量差間隔
04:56
separating the two states,
95
296408
2628
04:59
and the phenomenon is called,
96
299036
2209
詞如其名,這個現象被稱為量子穿隧
05:01
quite appropriately, quantum tunneling.
97
301245
4142
05:05
Because of quantum tunneling,
98
305387
1891
因為量子穿隧效應
05:07
I could disappear from this room
99
307278
2533
我可以從這間房間消失
05:09
and reappear in the next room,
100
309811
3322
再從另外一個房間出現
05:13
practically penetrating the wall.
101
313133
3395
簡單來說就是穿越牆壁
05:16
But don't expect me to actually perform the trick
102
316528
2815
但別期待我會真的在你們面前表演
05:19
in front of your eyes, because the probability
103
319343
2578
05:21
for me to penetrate the wall is ridiculously small.
104
321921
4388
因為讓我能穿越牆壁的機率十分渺小
05:26
You would have to wait a really long time
105
326309
2598
在這發生之前你們得等上好一陣子
05:28
before it happens, but believe me,
106
328907
2132
但相信我 量子穿隧是一個真實存在的現象
05:31
quantum tunneling is a real phenomenon,
107
331039
3177
05:34
and it has been observed in many systems.
108
334216
3195
且已經被很多機制發現
05:37
For instance, the tunnel diode,
109
337411
2562
例如,穿隧兩極真空管 一個在電子學中常用的組件
05:39
a component used in electronics,
110
339973
2197
05:42
works thanks to the wonders
111
342170
2422
因為量子穿隧效應而被製造出來
05:44
of quantum tunneling.
112
344592
2320
05:46
But let's go back to the Higgs field.
113
346912
2292
但讓我們再回到希格斯場
05:49
If the ultra-dense Higgs state existed,
114
349204
4563
如果超濃度的希格斯場存在
05:53
then, because of quantum tunneling,
115
353767
2354
那,因為量子穿隧效應
05:56
a bubble of this state could suddenly appear
116
356121
3713
在這狀態下的泡泡 可以突然出現在宇宙中的特定時空
05:59
in a certain place of the universe at a certain time,
117
359834
3242
06:03
and it is analogous to what happens when you boil water.
118
363076
3765
就和我們煮滾水的時候一樣
06:06
Bubbles of vapor form inside the water,
119
366841
3089
蒸氣泡泡從水中蒸發
06:09
then they expand, turning liquid into gas.
120
369930
3856
然後膨脹,從液態變成氣態
06:13
In the same way, a bubble of the ultra-dense Higgs state
121
373786
4804
同理,一顆泡泡在超濃度的希格斯場
06:18
could come into existence because of quantum tunneling.
122
378590
3427
可以因為量子穿隧效應而出現
06:22
The bubble would then expand at the speed of light,
123
382017
2837
泡泡會以光速膨脹,佔領空間
06:24
invading all space, and turning the Higgs field
124
384854
3486
將希格斯場從熟悉帶到全新的狀態
06:28
from the familiar state into a new state.
125
388340
3649
06:31
Is this a problem? Yes, it's a big a problem.
126
391989
4161
這是個問題嗎?
是,很大的問題
06:36
We may not realize it in ordinary life,
127
396150
2745
在日常生活中可能難以理解
06:38
but the intensity of the Higgs field is critical
128
398895
3205
但希格斯場的密度 對於物質構造非常重要
06:42
for the structure of matter.
129
402100
2645
06:44
If the Higgs field were only a few times more intense,
130
404745
4073
如果希格斯場密度只是比一般高一點
06:48
we would see atoms shrinking, neutrons decaying
131
408818
2944
我們就會看到原子核中原子收縮
中子衰變,核子解體
06:51
inside atomic nuclei, nuclei disintegrating,
132
411762
3686
06:55
and hydrogen would be
133
415448
2340
氫會變成宇宙中 唯一可能存在的化學元素
06:57
the only possible chemical element in the universe.
134
417788
4352
07:02
And the Higgs field, in the ultra-dense Higgs state,
135
422140
3011
而超濃度的希格斯場
07:05
is not just a few times more intense than today,
136
425151
3814
並不是只比今天的希格斯場 密度高上幾倍
07:08
but billions of times,
137
428965
2195
而是幾十億倍
07:11
and if space-time were filled by this Higgs state,
138
431160
3202
如果時空被這個希格斯場填滿
07:14
all atomic matter would collapse.
139
434362
3153
所有原子物質都會崩解
07:17
No molecular structures would be possible, no life.
140
437515
4490
沒有任何分子結構能夠存在 沒有生命
07:22
So, I wonder, is it possible
141
442005
3338
所以我想
未來希格斯場有可能會經歷轉變期
07:25
that in the future, the Higgs field
142
445343
2586
07:27
will undergo a phase transition and,
143
447929
2565
07:30
through quantum tunneling, will be transformed
144
450494
3129
和量子穿隧效應
07:33
into this nasty, ultra-dense state?
145
453623
4687
進入這個恐怖,高濃度的狀態嗎?
07:38
In other words, I ask myself, what is the fate
146
458310
3525
換句話說,我問自己
希格斯場在宇宙中的命運是什麼?
07:41
of the Higgs field in our universe?
147
461835
3083
07:44
And the crucial ingredient necessary
148
464918
2251
而回答這個問題的關鍵 在於希格斯玻色子的質量
07:47
to answer this question is the Higgs boson mass.
149
467169
4386
07:51
And experiments at the LHC found that the mass
150
471555
4111
在一次LHC的實驗裡發現
07:55
of the Higgs boson is about 126 GeV.
151
475666
4274
希格斯玻色子的質量 是1260億電子伏特
07:59
This is tiny when expressed in familiar units,
152
479940
3036
用我們熟悉的單位表示的話其實不多
08:02
because it's equal to something like
153
482976
1320
差不多是10的負22次方公克
08:04
10 to the minus 22 grams,
154
484296
2207
08:06
but it is large in particle physics units,
155
486503
3970
但是對粒子單位來說很大
08:10
because it is equal to the weight
156
490473
2104
它就等於是整個DNA分子的重量
08:12
of an entire molecule
157
492577
2246
08:14
of a DNA constituent.
158
494823
2420
08:17
So armed with this information from the LHC,
159
497243
3387
有了從LHC得到的資料
08:20
together with some colleagues here at CERN,
160
500630
1944
再加上從歐洲核子研究組織得到的
08:22
we computed the probability
161
502574
1909
我們試著計算
08:24
that our universe could quantum tunnel
162
504483
3015
宇宙經過量子穿隧 進入高濃度希格斯場的可能性
08:27
into the ultra-dense Higgs state,
163
507498
3118
08:30
and we found a very intriguing result.
164
510616
3677
結果非常有趣
08:34
Our calculations showed
165
514293
2149
我們的計算顯示
08:36
that the measured value of the Higgs boson mass
166
516442
3172
希格斯玻色子的質量非常特別
08:39
is very special.
167
519614
1845
08:41
It has just the right value
168
521459
2919
它的質量剛剛好
08:44
to keep the universe hanging
169
524378
2693
可以讓宇宙處在一個不安定的狀態
08:47
in an unstable situation.
170
527071
2570
08:49
The Higgs field is in a wobbly configuration
171
529641
3256
希格斯場的結構至今為止 仍處於搖擺不定的狀態
08:52
that has lasted so far
172
532897
2049
08:54
but that will eventually collapse.
173
534946
3045
但最終還是會崩塌
08:57
So according to these calculations,
174
537991
3179
根據我們的計算
09:01
we are like campers
175
541170
2030
我們就像露營的人
09:03
who accidentally set their tent
176
543200
2452
不小心將帳篷搭在懸崖邊
09:05
at the edge of a cliff.
177
545652
1794
09:07
And eventually, the Higgs field
178
547446
1790
最後,希格斯場會經歷轉變期
09:09
will undergo a phase transition
179
549236
1936
09:11
and matter will collapse into itself.
180
551172
3044
然後所有的物質會自我毀滅
09:14
So is this how humanity is going to disappear?
181
554216
3444
所以人類文明就是這樣消失的嗎?
09:17
I don't think so.
182
557660
1755
我不這樣覺得
09:19
Our calculation shows that quantum tunneling
183
559415
3353
我們的計算顯示
09:22
of the Higgs field is not likely to occur
184
562768
3656
希格斯場的量子穿隧
在接下來的10年到100年 不太可能會發生
09:26
in the next 10 to the 100 years,
185
566424
3504
09:29
and this is a very long time.
186
569928
3042
這是一段很長的時間
09:32
It's even longer than
187
572970
1768
甚至比義大利成立穩定的政府還要長
09:34
the time it takes for Italy to form a stable government.
188
574738
3669
09:38
(Laughter)
189
578407
2407
09:40
Even so, we will be long gone by then.
190
580814
3791
即使發生了,我們也已經不在了
09:44
In about five billion years,
191
584605
2608
在約50億年後
09:47
our sun will become a red giant,
192
587213
2457
太陽會變成紅巨星
09:49
as large as the Earth's orbit,
193
589670
2513
和地球繞日的軌跡一樣大
09:52
and our Earth will be kaput,
194
592183
3277
地球會毀掉
09:55
and in a thousand billion years,
195
595460
2357
1兆年之後
09:57
if dark energy keeps on fueling
196
597817
2286
如果黑暗能量還在供給
10:00
space expansion at the present rate,
197
600103
2835
太空依現在的速度膨脹
10:02
you will not even be able to see as far as your toes,
198
602938
4177
你連到腳趾頭這麼短的距離都看不到
10:07
because everything around you
199
607115
1697
因為你身邊的事物
10:08
expands at a rate faster than the speed of light.
200
608812
3701
都在以比光速還要快的速度膨脹
10:12
So it is really unlikely
201
612513
1985
所以要我們看到希格斯場膨脹 真的不怎麼可能
10:14
that we will be around to see the Higgs field collapse.
202
614498
3870
10:18
But the reason why I am interested
203
618368
3579
我對希格斯場轉換感興趣的原因是
10:21
in the transition of the Higgs field
204
621947
2012
10:23
is because I want to address the question,
205
623959
3285
因為我想問:
10:27
why is the Higgs boson mass so special?
206
627244
4965
為何希格斯玻色子的質量如此特別?
10:32
Why is it just right to keep the universe
207
632209
2974
為何它剛剛好讓宇宙
10:35
at the edge of a phase transition?
208
635183
3490
處於轉變的邊緣?
10:38
Theoretical physicists always ask "why" questions.
209
638673
3862
理論學家永遠喜歡問"為什麼"
10:42
More than how a phenomenon works,
210
642535
2675
不只是想要知道現象的成因
10:45
theoretical physicists are always interested in
211
645210
2472
理論學家更感興趣的是
10:47
why a phenomenon works in the way it works.
212
647682
3232
為何一個現象會以現在這個方式運作
10:50
We think that this these "why" questions
213
650914
3362
我們覺得這些"為什麼"可以給我們線索
10:54
can give us clues
214
654276
1723
10:55
about the fundamental principles of nature.
215
655999
3538
找尋自然的基本定律
10:59
And indeed, a possible answer to my question
216
659537
3905
而能解答我問題的可能答案
11:03
opens up new universes, literally.
217
663442
4364
開啟了整個宇宙 真的是字面上的開啟
11:07
It has been speculated that our universe
218
667806
3441
一直有人懷疑
我們的宇宙只是 眾多宇宙泡沫堆中的一個泡泡
11:11
is only a bubble in a soapy multiverse
219
671247
4133
11:15
made out of a multitude of bubbles,
220
675380
2563
眾多宇宙裡有數以萬計的泡泡
11:17
and each bubble is a different universe
221
677943
2216
每個泡泡都是一個不同的宇宙
11:20
with different fundamental constants
222
680159
1894
擁有不同的內容物
11:22
and different physical laws.
223
682053
1865
還有不同的定律
11:23
And in this context, you can only talk about
224
683918
2006
在這個假設下
11:25
the probability of finding a certain value of the Higgs mass.
225
685924
4711
我們只能討論確定希格斯質量的可能性
11:30
Then the key to the mystery
226
690635
2343
那麼解開謎團的關鍵
11:32
could lie in the statistical properties
227
692978
3263
就在這眾多宇宙中的統計特性
11:36
of the multiverse.
228
696241
2228
11:38
It would be something like what happens
229
698469
2414
它可能類似沙灘上的沙丘
11:40
with sand dunes on a beach.
230
700883
2237
11:43
In principle, you could imagine to find sand dunes
231
703120
2872
基本上你可以想像 在沙灘上的任何坡度找到沙丘
11:45
of any slope angle in a beach,
232
705992
2430
11:48
and yet, the slope angles of sand dunes
233
708422
4161
但是沙丘的坡度通常都在30到35度左右
11:52
are typically around 30, 35 degrees.
234
712583
3470
11:56
And the reason is simple:
235
716053
1668
原因很簡單
11:57
because wind builds up the sand, gravity makes it fall.
236
717721
3678
因為風堆起沙子,重力讓沙子掉下來
12:01
As a result, the vast majority of sand dunes
237
721399
2884
所以大部分的沙丘
12:04
have slope angles around the critical value,
238
724283
3919
都擁有剛好接近崩塌的斜度
12:08
near to collapse.
239
728202
1984
12:10
And something similar could happen
240
730186
2997
類似的事情也可能 發生於眾多宇宙中的希格斯玻色子
12:13
for the Higgs boson mass in the multiverse.
241
733183
4537
12:17
In the majority of bubble universes,
242
737720
2872
在眾多宇宙的泡泡中
12:20
the Higgs mass could be around the critical value,
243
740592
3057
希格斯的質量 可能也在希格斯場接近崩塌的邊緣
12:23
near to a cosmic collapse of the Higgs field,
244
743649
3596
12:27
because of two competing effects,
245
747245
1947
就像在沙丘的例子裡 有兩個互相抗衡的效應一樣
12:29
just as in the case of sand.
246
749192
3586
12:32
My story does not have an end,
247
752778
3145
我的故事不會結束
12:35
because we still don't know the end of the story.
248
755923
3735
因為我們還不知道故事的結局
12:39
This is science in progress,
249
759658
3288
科學一直在前進
12:42
and to solve the mystery, we need more data,
250
762946
3834
為了解開謎團,我們需要更多數據
12:46
and hopefully, the LHC will soon add new clues
251
766780
4616
希望LHC不久後 又會為這個故事提供更多新線索
12:51
to this story.
252
771396
2621
12:54
Just one number, the Higgs boson mass,
253
774017
3830
光是發現希格斯玻色子的質量
12:57
and yet, out of this number we learn so much.
254
777847
5329
就讓我們知道這麼多
13:03
I started from a hypothesis, that the known particles
255
783176
3047
我一開始假設 已知的粒子都在宇宙之中
13:06
are all there is in the universe,
256
786223
2036
13:08
even beyond the domain explored so far.
257
788259
2706
甚至超出我們所知的宇宙
13:10
From this, we discovered that the Higgs field
258
790965
3768
從這我們發現能跨越時空的希格斯場
13:14
that permeates space-time may be standing
259
794733
3443
可能處在刀鋒 隨時可能引起宇宙崩塌
13:18
on a knife edge, ready for cosmic collapse,
260
798176
4557
13:22
and we discovered that this may be a hint
261
802733
3550
我們發現這可能提醒我們
13:26
that our universe is only a grain of sand
262
806283
4033
我們的宇宙 只是眾多宇宙沙灘中的一顆沙粒
13:30
in a giant beach, the multiverse.
263
810316
3613
13:33
But I don't know if my hypothesis is right.
264
813929
3251
但我並不知道我的假設正不正確
13:37
That's how physics works: A single measurement
265
817180
3683
這就是物理學的運作方式
一套測量可將我們推向認識宇宙的新路
13:40
can put us on the road to a new understanding
266
820863
2864
13:43
of the universe
267
823727
1663
13:45
or it can send us down a blind alley.
268
825390
3019
也可以送我們進死胡同
13:48
But whichever it turns out to be,
269
828409
2564
但不論結果如何
13:50
there is one thing I'm sure of:
270
830973
3192
有一件事我很確定:
13:54
The journey will be full of surprises.
271
834165
3349
這趟旅程將會充滿驚喜
13:57
Thank you.
272
837514
1373
謝謝
13:58
(Applause)
273
838887
5248
關於本網站

本網站將向您介紹對學習英語有用的 YouTube 視頻。 您將看到來自世界各地的一流教師教授的英語課程。 雙擊每個視頻頁面上顯示的英文字幕,從那裡播放視頻。 字幕與視頻播放同步滾動。 如果您有任何意見或要求,請使用此聯繫表與我們聯繫。

https://forms.gle/WvT1wiN1qDtmnspy7