Download presentation
Presentation is loading. Please wait.
4
愛因斯坦的時空 狹義相對論 的時空 廣義相對論 – 等效原理 (Equivalence Principle)，時空扭曲
重力透鏡 (Gravitational lens): 扭曲的時空 黑洞(Black holes): 倒置的時空 宇宙膨脹: 動態的時空 超越愛因斯坦?
5
狹義相對論的時空
6
時空 想像每隔一米及每一秒定下標記→時空網 牛頓: 同一時空網貫穿全宇宙→絕對時空＝客觀的大舞臺
狹義相對論: 不同速度的觀察者有不同的時空網 均速! x t v ~ c x t 0 < v < c x t v ~ 0
7
Einstein had spent a lot of time wondering about the nature of light…
8
Gedanken (Thought) experiments
It was impossible to achieve the kinds of speeds necessary to test his ideas (especially while working in the patent office…), so Einstein used Gedanken experiments or Thought experiments. Einstein pic: Lightning and space ship: Young Einstein
9
光速的絕對性 對所有以均速運動的觀測者來說，光在真空中的速度皆恆常不變。光速是絕對的。
與日常生活經驗(速度相加減)相違背！但已被無數實驗驗證。 相對論的「奇怪」後果多由此而來。
10
什麼是相對性原理？ 在高速飛行的客機中 (或是在船上，或是在火車上‧‧‧)
11
就好像在地面上一樣？Yes! 這是大家熟悉的事實！ 完全一樣？Yes! 為什麼這樣？沒人知道!
這件「顯而易見」的事實其實是大自然很奧妙的本性之一。 物理上我們稱無法再往下深究為什麼的事實為原理。
12
同時之相對性 均速 A 從火車正中心同時向C 及D 放射兩束光。A 所見﹕二光束以相同速度走相同距離→同時到達C及D，不論u 的數值(只能知道相對的均速運動，沒有絕對的均速運動)。
13
→「同時」是相對的！→沒有絕對的時鐘！→時間是相對的！
B 見到的情況? 兩件事件（光到達C及光到達D）相對A為同時，相對B卻不是同時！ 他看到 C 追向光束，而D在移離。因此光束應先到C，後到D。 →「同時」是相對的！→沒有絕對的時鐘！→時間是相對的！
14
Sam 對Sam來說同時發射的兩道光……
15
Frank 對Frank來說，兩道光一定不是同時發射！
16
Figure 1.10 (a) A mirror is fixed to a moving vehicle, and a light pulse leaves O’ at rest in the vehicle. (b) Relative to a stationary observer on Earth, the mirror and O’ move with a speed v. Note that the distance the pulse travels measured by the stationary observer on Earth is greater than 2d. (c) The right triangle for calculating the relationship between t and t’. Fig. 1-10, p. 15
17
Length Contraction v E Consider a spaceship moving with a velocity between two stars. Two observers, one on earth at rest with respect to the stars and the other on the ship measure the distance.
18
總之， 動的鐘走的比較慢 動的尺長度比較短 你的同時不必然是我的同時
20
space + time → spacetime 3維 1維 4維
時間成了座標之ㄧ，會隨觀測者而變。 時間與空間不再是相互獨立的概念，我們必需將兩者結合起來，將它們看成是不可分割的一體 也就是說 空間 + 時間 → 時空 space + time → spacetime 3維 1維 維 愛因斯坦的數學老師閔考斯基(Minkowski)首先強調4維時空的幾何意義，所以我們 也常將4維時空稱為閔考斯基時空。
21
廣義相對論 (General Relativity)
如何把重力與相對論結合？
22
廣義相對論 1915 時空的彎曲曲率 能量（質量） Photo: Orren Jack Turner, Prints & Photographs Division, Library of Congress, LC-USZ
23
Albert Einstein 1879-1955 Spooky Action at a Distance
According to Newton if the Sun disappeared in an instant, so would its gravitational field at the Earth, millions of miles away; yet light from the Sun, with its finite speed, would continue for another 8 minutes - this troubled Einstein.
24
愛因斯坦注意到，當年伽利略所指出來，重力很特別的一個性質！
如果沒有空氣，所有物體，無論輕重落地時間相同 就如特殊相對論由光速恆定現象出發，整個廣義相對論就由以上觀察出發！
25
一道光會不會有拋體運動？ 光沒有質量，那會不會受到地球的重力的作用？ 光沒有質量 m = 0 , F = 0 ？
26
“the happiest thought of my life”
On one day in 1907, I was sitting in a chair in the patent office at Bern, when all of a sudden, a thought occurred to me….. “the happiest thought of my life”
27
Albert Einstein's Happiest Thought - 1907
An observer falling freely from the roof of a house will not feel his own weight. If that person drops other bodies while falling, then these remain in a state of rest relative to him. Gravitational mass is the same as inertial mass, gravity equals acceleration
28
愛因斯坦一生最快樂的念頭 自由下跌物體沒有重量! 自由下墜 50 kg 0 kg !
30
向上加速可以增大重力 加速與重力等效 向下加速可以抵消重力
31
等效原理 (Principle of Equivalence)
密封太空船內不能分辨太空船在星球表面(重力場)或在太空(無重力)向「上」加速 有重力沒有加速=有加速沒有重力
32
有重力下的靜止觀察者，與無重力下的加速觀察者，是等效的。
愛因斯坦推論這樣的對應關係適用於任何物理現象，包括光的傳播！
33
Light Deflection 在重力下光是否會偏轉，就考慮在無重力情況下的加速觀察者看來，光會不會偏轉就可以了。
34
Tests of General Relativity
光即使沒有質量，還是會受到重力的作用而彎曲其路徑。
35
One of Eddington's photographs of the total solar eclipse of 29 May 1919, presented in his 1920 paper announcing its success, confirming Einstein's theory that light bends
36
NY Times, Nov 10, 1919
37
重力透鏡 Abell 2218。照片由美國太空總署 (NASA) 以哈勃太空望遠鏡拍得。
重力透鏡示意圖。遠方星光被星系團折射而「聚焦」於地球。
38
Black Holes If the gravitational attraction is large enough (either through high mass or small distance), there will be a place where the escape velocity is greater than the speed of light. This is a Black Hole.
39
Schwarzschild radius Derivation is wrong and picture is wrong, but the result is correct
41
光無法離開黑洞！
43
Event horizon
44
加速度=時空彎曲 狹義相對論: 不同速度的觀測者時間、空間間隔都不同 加速度→不同位置有不同速度 不同速度→不同位置有不同空間間隔
時間的扭曲: 每空間點有不同速度的時鐘 →時空「網」 x t v ~ c x t 0 < v < c x t v ~ 0
45
重力=時空扭曲 重力場→加速度→時空間隔每點不同 t x
47
Massive objects deform spacetime - causes gravitational lensing
Warping of spacetime affects path of light and matter. It affects light in space by bending the path of light ray and affects light in time by slowing down light rays. The impact in time is used in GPS technology. Massive objects deform spacetime - causes gravitational lensing
49
The Persistence of Memory (1931) His most famous painting, challenges the idea that time is rigid. It is also said to be an interpretation of Einstein’s theory of relativity–the warping of space & time by gravity.
50
物質決定時空的曲率 能量（質量） 時空的彎曲曲率 愛因斯坦重力方程式(1915) 時空曲率決定物質(粒子)如何運動 → 粒子沿著極端線前進
51
Matter tells spacetime how to curve.
John Archibald Wheeler Matter tells spacetime how to curve. Spacetime tells matter how to move. 物質告訴時空如何彎曲， 時空告訴物質如何運動。
52
重力對光的影響 彎曲軌跡及紅移
53
Gravitational redshift
Einstein(1911) :物體在重力場 ,下落 d 距離 ,會獲得能量 energy conservation 光也會得到同樣的重力位能( ) 所以得出光在重力埸中行進 ,會改變頻率 依時間和頻率的倒數關係 ,我們得知時間會隨重力場而改變。 d
55
黑洞 重力紅移: 光波長被重力拉長; 重力愈大，紅移愈大 光波長若被拉至無限長: 沒有光逃出＝黑洞
56
史瓦西黑洞 (Schwarzschild black hole)
廣義相對論的一個特別解 = 靜止、不轉動、球對稱的黑洞 史瓦西半徑(Schwarzschild radius)＝臨界半徑＝事件穹界(Event Horizon) 奇點(singularity):密度趨無限大，進入事件穹界的物質必到達奇點。但已知物理定律不再適用 例:太陽 ~ 三公里，地球~一公分 人~ 公分
57
史瓦西黑洞
58
史蒂芬·霍金（Stephen William Hawking）
出生於 1942 年 得到牛津大學第一等榮譽獎項, 但在那之後 “沒有得到太多的工作” 在就讀牛津大學的期間，就有神經肌肉方面的病症出現 1966年劍橋大學博士( singularity theorem ) 1974年發現霍金輻射( Hawking radiation) “A Brief History of Time” 年出版 得到許多的榮譽學位和獎項 公開支持世界和平主義，關注殘疾人士的福利和現今社會議題
59
Amyotrophic Lateral Sclerosis
肌萎縮性脊髓側索硬化症 別稱：Lou Gehrig’s disease（漸凍症） 症狀: 難以站立、走路、奔跑 行動不便、笨拙 – 常常跌倒 手部運動不靈活，諸如扣鈕扣、寫作、轉動鑰匙等等 手部肌肉萎縮 舌頭萎縮 難以咀嚼食物 很難吞嚥(dysphagia) 不太能說話 肌肉痙攣
60
解析黑洞 A non-rotating black hole is particularly simple.
黑洞的中心點叫做 singularity (奇異點).奇異點的大小是零,密度是無限大. 事實上,現今的物理知識仍然不能解釋奇異點的性質 The event horizon (穹界) 是一個以奇異點為中心的球體,黑洞的半徑為黑洞的Schwarzschild radius 我們現今仍對event horizon(穹界)裡面感到未知,因為就連光也無法逃脫出來 event horizon singularity
61
Singularity – In Relativity
In general relativity singularity is a region of space-time in which the curvature becomes so strong that the laws of general relativity break down and the laws of quantum gravity take over.
62
Cosmic Censorship Conjecture: Nature Forbids Naked Singularity
Under general physical conditions, the singularity is enclosed by the event horizon. Information within the event horizon cannot be transmitted to the external world. We say the singularity is concealed or dressed. Those which are not dressed are called naked singularities. Mathematically, naked singularities can exist, but physical considerations suggest cosmic censorship: all singularities are enclosed (Roger Penrose). Hawking bet on cosmic censorship (and conceded too early in 1997).
63
BH have NO HAIR By J.A. Wheeler
64
No-hair Theorem 在這裡頭髮指的是複雜的東西(e.g. 不同型態, 顏色,燙髮,… 等等). 黑洞是 no hair ,因為他很單純. 只要三個東西就可以描述黑洞(Hawking 1972): 質量mass 角動量angular momentum 電荷electric charge
66
合併成一個大黑洞後 , 質量 、半徑和面積分別為
兩個小黑洞 ,質量分別為 ,半徑分別為 。 它們的面積分別是 合併成一個大黑洞後 , 質量 、半徑和面積分別為 合併後的面積大於合併前的面積 這過程是允許的。反之 ,大黑洞分裂成兩個小黑洞,分裂後面 積將減小 ,違反面積定理 ,因而是不可能的。 time space
67
Area Theorem time space
This implies that the surface area of a black hole is a measure of the entropy. If an object has nonzero entropy, then it has a temperature, and it must radiate! At first, Hawking himself could not accept this implication.
69
Real Pairs Created Near a black hole, the tidal force is so strong that the virtual pairs are pulled apart. The two virtual particles can become real.
70
Black holes aren’t black!
A black hole is a true black body, and radiates at the Hawking temperature: TH = h c3 8GMkB So a solar mass black hole has a temperature of about 60 nK! But very small black holes have high temperatures, and evaporate very quickly. Can these be formed?
71
General Relativity and Quantum Mechanics
General relativity and quantum mechanics are two major achievements of 20th century physics. General relativity deals with the very large. Quantum mechanics deals with the very small. Physicists attempted to unify the two.
72
Humour: Hawking Style Einstein (on quantum mechanics): God does not play dice with the universe. Bohr (defending quantum mechanics): Einstein should not tell God what to do! Hawking (on radiation from black holes): God not only plays dice but also sometimes throws them where they cannot be seen.
75
更驚人的結果正才要出現！ Now Einstein again! 他發現如右圖的扭曲時空是廣義相對論所容許的！ 奇異點 singularity 另一個正常世界 Schwarzschild metric 史瓦西度規 Einstein–Rosen bridge
77
Einstein–Rosen bridge
如同連接兩個獨立空間的橋 John Archibald Wheeler 1955 這兩個獨立空間可能在遠方是連在一起的！
78
John Archibald Wheeler 1955
Wormhole 蟲洞
79
星際效應電影 從土星附近，高等文明所創造的蟲洞，到達遠方銀河，尋找遷居地。
80
星際效應
81
Grandfather Paradox
82
Exotic matter in wormholes
In the sense of gravitational deflection of light, a black hole acts as a positive lens and the surrounding vacuum fluctuations act as an additional, negative lens. Positive lens Negative lens
83
If a wormhole is stable, it must contain exotic matter
Photons that enter the wormhole travelling radially inward leave it travelling radially outward without their paths crossing, like a negative lens would do; this gravitational defocussing of light can only be accomplished with negative energy-density material, since a positive energy density would have focussed them to a point before they could diverge, as a positive lens would. Figure from Thorne,Black holes and time warps.
84
Conclusion Hawking’s contribution to the theory of black holes (structure, no hair theorem, radiation, information and entropy). Hawking’s work is confirmed by experiments (Cygnus X-1). Hawking’s openmindedness (bet concessions). Hawking’s attitude towards life (adversity, science, humour). Hawking’s eagerness to popularize science.
85
在《時間簡史》中霍金寫道：“希望不久宇宙學的前沿理論也可以總结得像古典物理學那樣簡結，能為每一個中學生所理解”。
「能夠生在這個時代研究理論物理是很輝煌的一件事 。若是能對人類認識宇宙有一點貢獻,我會覺得快活無比。」
86
Sources 國立師範大學物理系 張嘉弘教授的網站 Tom Kreiting (2009) : Stephen Hawking
K.Y.Michael Wong ( 2006): Hawking and Black Holes 香港中文大學物理系朱明中教授 :愛因斯坦的宇宙 還有更多 ……
Similar presentations
