相對論簡介

1. 相對論簡介 近代物理導論—二

2. 亞里斯多德--「物理的力學」 亞里斯多德提出的假設是「凡是運動著的物體，一定有推動者在推著它運動」。這是建立在日常經驗上。若你看到一個東西在移動，你就會尋找一個推動它的東西（像是我們的手、身體）。當沒什麼東西推它時，它就會停止運動。但是一個推著一個，不能無限制地追溯上去，「必然存在第一推動者」，中古世紀的基督教說「第一推動者」就是指上帝，並將亞里斯多德的學說，與基督教教義結合。

3. 閤下的「物理的力學」已被我的「運動力學」取代了閤下的「物理的力學」已被我的「運動力學」取代了

4. 「牛頓先生，很抱歉推翻了您的理論，不過您的成就是您那個時代一個人的智力和創造力所能達到的顛峰，您所創造的許多觀念直到今日都仍在引導我們的物理思維。雖然我們知道，當我們對宇宙萬物有了更深入的瞭解以後，這些觀念將會被一些更抽象的新觀念所取代。」

5. 光傳播的方式 光速的測量 光的本質 相對論 馬赫原理--- 相對性原理 與牛頓力學的矛盾 鐳的放射性能量 與質量的差異

6. 與牛頓同時的惠更司 ( 荷，Christian Huygens, 1629-95) 是近代光學的先驅。 光的介質是一種：「充滿空間，微妙而富彈性的『以太』。」

7. 光是波還是粒子 • 粒子說：古希臘哲學家認為光是由粒子組成。支持者有：蘇格拉底、柏拉圖、歐基里得、牛頓。 • 波動說：光是呈波動前進的。支持者有：恩培多克力斯、惠更司。 • 光子：愛因斯坦的光電效應理論。光是由一些粒子組成，即沒有質量的濃縮電磁能。 • 量子物理：光具有波動-粒子雙重性，能量高時具粒子性，能量低時具波動性。

8. 光速 • 光有多快？這問題困擾人類許多年。 • 測量方法： • 反射法（伽利略）。 • 燈光明滅法。 • 木星衛星法（羅默）。 • 高速八面鏡法（邁克生）。

9. 光速-反射法 • 測量光束射向遠距離外的鏡子，在反射回來的時間。

10. 光速-燈光明滅法 • 在兩遠遙遙相距的山頂上，利用燈光明滅來測量。

11. 光速-木星衛星法（羅默） • 測量不同時間，木衛一隱沒於木星的陰影裡的時間週期。 • 惠更斯：光速＝多行進的距離/多測量的時間 ＝300,000 km/s

12. 光速-高速八面鏡法（邁克生） • 測量光在一高速旋轉的八面鏡與35公里外一面平面鏡之間來回一次的時間。 • 光速＝來回距離/轉八分之圈所需時間 ＝299,920 km/s 35km 快 慢

13. 波的波動性 • 波的折射與反射：當波由一介質傳播到另一介質的界面時，會產生反射與折射。 • 波的繞射：當波遇到障礙物或狹縫時，會繞過障礙物或穿過狹縫，而向四周傳播，此種現象稱為繞射。 • 波的干涉：當兩波相會時，介質所做的擾動運動，是各單波單獨存在時所產生之擾動的合成，此種合成具相加性，是兩波偏離平衡位置的相加，即振幅的相加。

14. 電磁波 • 電磁波：光是一種能量，由於電荷加速而發出，此能量在部分為電，部分為磁的波中傳播。包含：無線電波、微波、X射線等。

15. 波的反射與折射

16. 波的繞射

17. 波的干涉

18. 干涉與波粒雙重性 • 若用機關槍對著一有雙狹縫的鋼板射擊，那麼牆上的彈痕分佈如何呢？ • 當把機關槍換成電子槍，而把鋼板換成一般狹縫，那麼電子在屏幕上的分佈將如雙狹縫干涉一般。 • 電子單狹縫繞射，電子雙狹縫一、二、三。

19. 波粒雙重性 • 粒子表現出波動的特性：干涉與繞射。顯示粒子與波動在微觀尺度下是不可分辨的。 • 一般觀念下的粒子，如電子、質子、中子、原子等，在微觀下亦可表現出波動性。 • 而光在此一般觀念下認為是波動的，亦可能表現出粒子性，如X光、加碼射線、光電效應等。

20. 透明與不透明物質 • 受光線照射，物質內電子與入射光發生交互作用，決定物質對光的反應。 • 若入射光的頻率接近電子的固有頻率，則入射光會被物質吸收而變成熱。反之，則不會被吸收，而能在物質內傳播。 • 光在透光物質內需藉原子吸收再發射的過程來傳播，因此需耗費時間，所以光在介質內的光速較在真空中為慢。 • 紅外光及紫外光對玻璃是不透明的（請思考其原因）。

21. 陰影 • 光的射線被物體阻擋而無法到達的地方，出現陰影。 • 完整陰影稱本影，部分陰影稱半影。

22. 偏振 • 光是「橫波」，而非「縱波」，來自於光具有「偏振現象」。 • 電子振動產生偏振的電磁波。電子振動方向與光的偏振同向。

23. Basic Problems • Newtonian mechanics fails to describe properly the motion of objects whose speeds approach that of light • Newtonian mechanics is a limited theory • It places no upper limit on speed • It is contrary to modern experimental results • Newtonian mechanics becomes a specialized case of Einstein’s special theory of relativity • When speeds are much less than the speed of light

24. Newtonian Relativity • To describe a physical event, a frame of reference must be established • The results of an experiment performed in a vehicle moving with uniform velocity will be identical for the driver of the vehicle and a hitchhiker on the side of the road

25. Newtonian Relativity, cont. • Reminders about inertial frames • Objects subjected to no forces will experience no acceleration • Any system moving at constant velocity with respect to an inertial frame must also be in an inertial frame • According to the principle of Newtonian relativity, the laws of mechanics are the same in all inertial frames of reference

26. Newtonian Relativity – Example • The observer in the truck throws a ball straight up • It appears to move in a vertical path • The law of gravity and equations of motion under uniform acceleration are obeyed

27. Newtonian Relativity – Example, cont. • There is a stationary observer on the ground • Views the path of the ball thrown to be a parabola • The ball has a velocity to the right equal to the velocity of the truck

28. Newtonian Relativity – Example, conclusion • The two observers disagree on the shape of the ball’s path • Both agree that the motion obeys the law of gravity and Newton’s laws of motion • Both agree on how long the ball was in the air • All differences between the two views stem from the relative motion of one frame with respect to the other

29. Views of an Event • An event is some physical phenomenon • Assume the event occurs and is observed by an observer at rest in an inertial reference frame • The event’s location and time can be specified by the coordinates (x, y, z, t)

30. Views of an Event, cont. • Consider two inertial frames, S and S’ • S’ moves with constant velocity, , along the common x and x’ axes • The velocity is measured relative to S • Assume the origins of S and S’ coincide at t = 0

31. Galilean Transformation of Coordinates • An observer in S describes the event with space-time coordinates (x, y, z, t) • An observer in S’ describes the same event with space-time coordinates (x’, y’, z’, t’) • The relationship among the coordinates are • x’ = x – vt • y’ = y • z’ = z • t’ = t

32. Notes About Galilean Transformation Equations • The time is the same in both inertial frames • Within the framework of classical mechanics, all clocks run at the same rate • The time at which an event occurs for an observer in S is the same as the time for the same event in S’ • This turns out to be incorrect when v is comparable to the speed of light

33. Galilean Transformation of Velocity • Suppose that a particle moves through a displacement dx along the x axis in a time dt • The corresponding displacement dx’ is • u is used for the particle velocity and v is used for the relative velocity between the two frames

34. Speed of Light • Newtonian relativity does not apply to electricity, magnetism, or optics • These depend on the frame of reference used • Physicists in the late 1800s thought light moved through a medium called the ether • The speed of light would be c only in a special, absolute frame at rest with respect to the ether • Maxwell showed the speed of light in free space is c = 3.00 x 108 m/s

35. Michelson-Morley Experiment • First performed in 1881 by Michelson • Repeated under various conditions by Michelson and Morley • Designed to detect small changes in the speed of light • By determining the velocity of the Earth relative to the ether

36. Michelson-Morley Equipment • Used the Michelson interferometer • Arm 2 is aligned along the direction of the Earth’s motion through space • The interference pattern was observed while the interferometer was rotated through 90° • The effect should have been to show small, but measurable, shifts in the fringe pattern

37. Michelson-Morley Results • Measurements failed to show any change in the fringe pattern • No fringe shift of the magnitude required was ever observed • The negative results contradicted the ether hypothesis • They also showed that it was impossible to measure the absolute velocity of the Earth with respect to the ether frame • Light is now understood to be an electromagnetic wave, which requires no medium for its propagation • The idea of an ether was discarded

38. Albert Einstein • 1879 – 1955 • 1905 • Special theory of relativity • 1916 • General relativity • 1919 – confirmation • 1920’s • Didn’t accept quantum theory • 1940’s or so • Search for unified theory - unsuccessful

39. Einstein’s Principle of Relativity • Resolves the contradiction between Galilean relativity and the fact that the speed of light is the same for all observers • Postulates • The principle of relativity: All the laws of physics are the same in all inertial reference frames • The constancy of the speed of light: The speed of light in a vacuum has the same value in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light

40. The Principle of Relativity • This is a sweeping generalization of the principle of Newtonian relativity, which refers only to the laws of mechanics • The results of any kind of experiment performed in a laboratory at rest must be the same as when performed in a laboratory moving at a constant velocity relative to the first one • No preferred inertial reference frame exists • It is impossible to detect absolute motion

41. The Constancy of the Speed of Light • This is required by the first postulate • Confirmed experimentally in many ways • Explains the null result of the Michelson-Morley experiment • Relative motion is unimportant when measuring the speed of light • We must alter our common-sense notions of space and time

42. Consequences of Special Relativity • A time measurement depends on the reference frame in which the measurement is made • There is no such thing as absolute time • Events at different locations that are observed to occur simultaneously in one frame are not observed to be simultaneous in another frame moving uniformly past the first

43. Simultaneity • In special relativity, Einstein abandoned the assumption of simultaneity • Thought experiment to show this • A boxcar moves with uniform velocity • Two lightning bolts strike the ends • The lightning bolts leave marks (A’ and B’) on the car and (A and B) on the ground • Two observers are present: O’ in the boxcar and O on the ground

44. Simultaneity – Thought Experiment Set-up • Observer O is midway between the points of lightning strikes on the ground, A and B • Observer O’ is midway between the points of lightning strikes on the boxcar, A’ and B’

45. Simultaneity – Thought Experiment Results • The light reaches observer O at the same time • He concludes the light has traveled at the same speed over equal distances • Observer O concludes the lightning bolts occurred simultaneously

46. Simultaneity – Thought Experiment Results, cont. • By the time the light has reached observer O, observer O’ has moved • The signal from B’ has already swept past O’, but the signal from A’ has not yet reached him • The two observers must find that light travels at the same speed • Observer O’ concludes the lightning struck the front of the boxcar before it struck the back (they were not simultaneous events)

47. Simultaneity – Thought Experiment, Summary • Two events that are simultaneous in one reference frame are in general not simultaneous in a second reference frame moving relative to the first • That is, simultaneity is not an absolute concept, but rather one that depends on the state of motion of the observer • In the thought experiment, both observers are correct, because there is no preferred inertial reference frame

48. Simultaneity, Transit Time • In this thought experiment, the disagreement depended upon the transit time of light to the observers and does not demonstrate the deeper meaning of relativity • In high-speed situations, the simultaneity is relative even when transit time is subtracted out • We will ignore transit time in all further discussions

49. Time Dilation • A mirror is fixed to the ceiling of a vehicle • The vehicle is moving to the right with speed v • An observer, O’, at rest in the frame attached to the vehicle holds a flashlight a distance d below the mirror • The flashlight emits a pulse of light directed at the mirror (event 1) and the pulse arrives back after being reflected (event 2)

50. Time Dilation, Moving Observer • Observer O’ carries a clock • She uses it to measure the time between the events (∆tp) • She observes the events to occur at the same place • ∆tp = distance/speed = (2d)/c