愛因斯坦用彎曲時空(廣義相對論)解釋重力現象
愛因斯坦在研究彎曲時空時
找了同學grossmann協助數學問題
古典物力的時空觀-兩個電子因交換光子而有電磁(庫倫力)作用。
時空不受物質影響而獨立存在。
絕對時空-
牛頓以來我們對時空觀念是"時空是絕對的，不隨時間改變的"
古典時空觀念被愛因斯坦改變了：
狹義相對論的2基本假設(special relativity)
一、所有慣性座標系中的物理定律都有相同形式(沒有任何慣性座標系有特殊性(相對性原理)。
二、任何慣性座標系所測得的光速都是C。
在物理上，我們把無法在往下深究原因的事實稱為原理(principle)，以此為接受的出發點。
慣性座標系，例如：等速前進的太空船。兩個慣性座標系之間有固定的相對速度(相對性原理(一般叫做Galileo Principle)，Galileo Principle應始於Galileo之前，但他在書裡特別強調這點，故後人稱為加利略原理)。Galileo以(等速平穩前進的)船為例解釋相對性原理(若不往窗外看，則不知道船在動)。在相對性原理之下，所有觀測者都是等價的，沒有人是絕對的，也就是說速度是相對的。所有運動都是相對的不是絕對的，動或不動是以觀察者的座標來看。
但上述理論遇見光就出問題了，
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| pic from google search |
Maxwell認為光速在乙太(靜止座標)中，速度才會是C。若我們相對於乙太的速度不為0，則量到的光速就不是C。這論點就之前的假設而言是合理的。
但實驗學家卻發現，無論在哪種座標下量測光速，都是C。
傳統觀念中，速度是相對的，沒有絕對速度存在，如何解釋？
....愛因斯坦想了10年(16歲開始想)，26歲(1905年)想出須重新檢討時間的定義，或何謂"同時"。
如果光速真的是絕對的，那應反過來思考我們過去對時間和空間的觀念是否需要修正。
如果我們接受光速是絕對的，那時間(同時)就變成相對的概念。
若A在等速直線前進的火車的正中間，與B相會時向前後發射兩道光，以A而言，兩道光會同時射達車廂前後牆壁，但就在月台觀察的B而言，向後的光會比較早射達車壁。
對A而言，
兩束光線會同時到達兩端的時鐘。
對B而言，
兩束光線將不同時到達兩端的時鐘。
左邊的圖是我按照老師影片中的插圖重繪的。
<<<REF 以下岔出去找些資料>>>
Simultaneilty Video
by nsf October 5, 2007http://www.nsf.gov/news/mmg/mmg_disp.cfm?med_id=55657&from=vid
影片註記：
月台上的男士看到火車前後光線同時射出，且同時到達他的眼裡；他同時認為車裡的朋友會先看到前方的光束，因為前方的光束以光速迎向向前行進的女士，而因為遠離後方發出的光束，所以較晚看到後方的光束。
火車裡的女士的確先看到前方的光線，但因為在女士的參考座標中所測出光速一樣是C，而光線經過的前後距離一樣，所以她認為先看到前面的光束是因為前方的光束較後方光束要早射出。
究竟是在月台的男士認為光線是同時射出正確？還是在車裡的女士認為前方的光束先射出才正確？
--愛因斯坦認為兩人以各自的參考座標所下的結論都對。
--這是愛因斯坦特殊相對論的基礎，也就是說，在不同的參考座標中，對"同時"的觀點永遠不會一致。
Time Dilation Video
by: nsf October 4, 2007 http://www.nsf.gov/news/mmg/mmg_disp.cfm?med_id=55655&from=vid
The Twin Paradox Narrative Explained (Animated)
http://youtu.be/Sa81lP9MR0I動的物體，時間走的比較慢。
Time Dilation不合用於twin paradox，因為離開地球那一方的座標有加速度，非慣性座標。
Click on the pic on the left and view the lectures, Physics for the future presidents, by Richard A. Muller.
Time Dilation
If you're going 99% of speed of light. Then you'll slow down by a factor of 7. That's dramatic. If I'm going that fast. You'll time it and till I've gone for 7 years. When I come out, I'll be 1 year older. I'll have experienced less time.
Length Contraction
When I'm moving at 99% of speed of light, I'm actually 7 times thinner. It looks like a pancake. It only contracts in the direction of movement. Side way directions don't change. A sphere becomes a pancake. It doesn't think it's a pancake. In it's frame of reference. It hasn't changed. You'll have changed. You'll become pancakes. It leads to a famous paradox.
Think of it as a train in a tunnel. The train is coming along real fast and because it's going so fast, it gets short. It goes through a tunnel. The tunnel isn't very long. But the train's going so fast, it fits inside anyway. As soon as it's inside, he closes the open doors and the train is trapped inside the tunnel.
Now let's analyze it in the point of view of the train. You're going really fast and you're not shortened up at all. In fact, in terms of frame of reference, the train is coming toward you. And now the tunnel is super short.
So from the tunnel point of view, the train's gotten short and then it'll fit inside. From the train point of view, the tunnel's gotten short. How can it possibly fit inside.
The pics blow are all taken from the lecture clips.
In the theory of relativity, there're two parts to the energy. One is exactly the same as Newton's, at least low velocities, one half m0v2, There's a new term now called rest energy, m0C2
<<REF end>>
運動中的基本粒子受命較長。Time Dilation
運動中的尺比較短。Length Contraction
Time Dilation不合用於twin paradox，因為離開地球那一方的座標有加速度，非慣性座標。
 |
| http://youtu.be/nNgzqpKZwhE |
Time Dilation
If you're going 99% of speed of light. Then you'll slow down by a factor of 7. That's dramatic. If I'm going that fast. You'll time it and till I've gone for 7 years. When I come out, I'll be 1 year older. I'll have experienced less time.
Length Contraction
When I'm moving at 99% of speed of light, I'm actually 7 times thinner. It looks like a pancake. It only contracts in the direction of movement. Side way directions don't change. A sphere becomes a pancake. It doesn't think it's a pancake. In it's frame of reference. It hasn't changed. You'll have changed. You'll become pancakes. It leads to a famous paradox.
Think of it as a train in a tunnel. The train is coming along real fast and because it's going so fast, it gets short. It goes through a tunnel. The tunnel isn't very long. But the train's going so fast, it fits inside anyway. As soon as it's inside, he closes the open doors and the train is trapped inside the tunnel.
Now let's analyze it in the point of view of the train. You're going really fast and you're not shortened up at all. In fact, in terms of frame of reference, the train is coming toward you. And now the tunnel is super short.
So from the tunnel point of view, the train's gotten short and then it'll fit inside. From the train point of view, the tunnel's gotten short. How can it possibly fit inside.
The pics blow are all taken from the lecture clips.
In the theory of relativity, there're two parts to the energy. One is exactly the same as Newton's, at least low velocities, one half m0v2, There's a new term now called rest energy, m0C2
<<REF end>>
運動中的基本粒子受命較長。Time Dilation
運動中的尺比較短。Length Contraction
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