Einstein’s three most important (among others) legacies A revolution in our concept of time. The possibility to convert mass into energy and vice versa. Gravity as curved spacetime.

Time is the only “thing” we everybody all share. It’s like a river Time is the only “thing” we everybody all share! It’s like a river. We all swim in it. River graph. Sharing means the time duration of an event you measure is the same as what I do. Time is absolute, independent of its observers.

Time measurement. Periodic motion. Pendulum Precise clock. Atomic clock.

It could be done with more and more sophistication and accuracy. Atomic clock would error less than one second in 3 million years.

In the beginning of 20th century, it was a great plan to put clocks at grid points in a city to provide or sell accurate time to city people. Commercialization and commoditization of time.

How to Synchronize all the clocks? Use light signal from a central facility to synchronize all the clocks For this to work, we need to subtract the time light travels from the central to the clock. Does the light travel at constant speed?

相對性原則

慣性座標系之間的伽利略變換

慣性座標系之間的 速度與加速度的變換

伽利略變換 物理定律（運動方程式）的形式一模一樣！只是起始條件不同！

非慣性系之間的伽利略變換 v 非定值 X

非慣性座標系之間的 速度與加速度的變換 v 非定值

非慣性系的變換 物理定律（運動方程式）的形式不同！因此可以分辨那個是在運動！

伽利略變換 物理定律（運動方程式）的形式一模一樣！只是起始條件不同！

Physicists long believe if the rule is correct relative to one observer at rest, it should also be true relative to other observers moving in constant speed. You can’t tell whether you are truly at rest or moving. You can only say you are at rest or moving relative to other observers. This is called Relativity Principle.

This is a kind of symmetry. Symmetric objects are beautiful in nature. So people also say physics is beautiful. That’s actually why Einstein insisted to himself that light speed is always the same

The earth is moving in the universe like we run in the air or take a train. It seems highly unlikely that the speed of light will always be the same all the time. So Maxwell’s rule and calculation couldn’t be right for all the observers.

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理論思索：光速與觀察者的運動狀態無關 1860 Maxwell showed that light is a kind of electromagnetic signal, call EM wave, which can be generated by a antenna. He also calculated the speed of EM wave and light is m/s But ………. If we measure from a train…..

直覺與經驗：光速與觀察者的運動狀態相關 The earth is moving in the universe like we run in the air or take a train. It seems highly unlikely that the speed of light will always be the same all the time. So Maxwell’s rule and calculation couldn’t be right for all the observers.

Michelson and Morley (1887) Active Figure 39.4 According to the ether wind theory, the speed of light should be c - v as the beam approaches mirror M2 and c + v after reflection. Fig 39-4, p.1249

The speed of light is always the same no matter how the observer moves. Maxwell方程式在不同的慣性座標系中，型式不變。 伽利略變換必須修正

Relativity of simultaneity 伽利略變換錯在哪裡？ It was Einstein who first realized how the constant light speed implies a total revolution of our concept of time Relativity of simultaneity The two explosions are simultaneous for Sam but not simultaneous for Sally!!!!! Time is no smooth river.

The time observed from rest observer is longer than what it is designed to be. A moving clock looks slowed down from an observer at rest !!!!!

Test of time dilation 1977 Hafele and Keating flew four atomic clocks twice around the globe. Relativity prediction is test within 10%. A few years later, another team flew round and round above Chesapeake bay for 15H. For a sonic jet, the dilation is about 10-8s. Predictions are good within 1%.

The subtle is the lord, but malicious he is not. This is so revolutionary that Albert felt really sorry towards Newton: “Newton, forgive me, you found the only way which, in your age, was just about possible for a man of highest thought, and --creative power.” 1949 The idea of relative time is so mysterious that Einstein felt the need to defend for the god: The subtle is the lord, but malicious he is not.

伽利略變換必須修正 絕對時間是關鍵

羅倫兹變換 Lorentz Transformation 這個變換會給出正確的時間拉長效應：

Time Dilation

長度縮短效應 Length Contraction

星際大戰 未可慮相對論效應 B A的觀點 B的觀點 A I II

仔細分析事件1對齊及事件2發砲的時間差 對齊與發砲是在 A座標系中同時 故還未對齊，已經發砲 B -v A 事件1 O’ O I 事件2 II

仔細分析事件1對齊及事件2發砲的時間差 故還未對齊，已經發砲 事件2 事件1

停車問題

II I I早於II II早於I 時間先後也是相對的

速度加成 光速恆定

4-vector

座標軸旋轉 羅倫茲轉換 不變量 vector 4-vector

Proper Time τ 它是一個羅倫茲變換下的不變量 Proper time 的小變化

動量

牛頓版動量守恆 u u u’ ？ u 完全非彈性碰撞 v=u O’ O 牛頓版的動量守恆遵守伽利略變換下的相對性原則

但？如果考慮相對性效應….. u u u’ ？ u v=u O’ O 牛頓的定義使動量守恆不遵守相對性原則

新的定義 以Proper Time 取代時間 動量P是4-vector 在O’座標系中的動量 如果在O座標系中，Px及Pt都守恆，在O’座標系中，P’x自然保證守恆

u u u’ u v=u O’ O

新定義與舊定義的關係 接近牛頓的定義

P0是什麼？ 可以猜 動量守恆與能量守恆便整合成一個定律。 動量與能量的分別只是表面的

E=mc2 Using the relativity principle, Einstein is able to derive that the energy of an object can be written as For v=c, the energy is infinite. Hence you are never able to push an object faster than the speed of light! Even at rest, an object still contain an energy due to its mass: It opens up the possibility to convert mass into energy or vice versa.

Even at rest, an object still contain an energy due to its mass: It opens up the possibility to convert mass into energy or vice versa. 質量是能量的一種形式，能量守恆蘊含質量可以轉換為其他形式的能量，其他形式的能量亦可轉換為質量，質量不再守恆。

u u 質量不守恆，動能轉換成質量。 反之，質量轉化為能量，也有可能

原子能

If we can smash a coin and destroy it………. This is more than a day’s output of a power plant. Smash a coin and generate power plant.

Nuclei

束縛態

原子核質量 = 質子中子總質量 – 總束縛能/c2 束縛能越大，質量越小

總質量減少，消失的質量以能量形式釋出

Count the mass difference The mass total decreases and the difference turns into energy.

Chain reaction

Atomic bomb

核融合 Fusion

Sun and fusion

deuterium

宇宙核融合

With the current rate of burning, the sun will last for another five billion years.

Tabletop fusion and the scandal