Light: it's the fastest thing in the universe, but we can still measure its speed if we slow down the animation, we can analyze light's motion using a space-time diagram, which takes a flipbook of animation panels, and turns them on their side. In this lesson, we'll add the single experimental fact that whenever anyone measures just how fast light moves, they get the same answer: 299,792,458 meters every second, which means that when we draw light on our space-time diagram, it's world line always has to appear at the same angle. But we saw previously that speed, or equivalently world line angles, change when we look at things from other people's perspective. To explore this contradiction, let's see what happens if I start moving while I stand still and shine the laser at Tom. First, we'll need to construct the space-time diagram. Yes, that means taking all of the different panels showing the different moments in time and stacking them up. From the side, we see the world line of the laser light at its correct fixed angle, just as before. So far, so good. But that space-time diagram represents Andrew's perspective. What does it look like to me? In the last lesson, we showed how to get Tom's perspective moving all the panels along a bit until his world line is completely vertical. But look carefully at the light world line. The rearrangement of the panels means it's now tilted over too far. I'd measure light traveling faster than Andrew would. But every experiment we've ever done, and we've tried very hard, says that everyone measures light to have a fixed speed. So let's start again. In the 1900s, a clever chap named Albert Einstein worked out how to see things properly, from Tom's point of view, while still getting the speed of light right. First, we need to glue together the separate panels into one solid block. This gives us our space-time, turning space and time into one smooth, continuous material. And now, here is the trick. What you do is stretch your block of space-time along the light world line, then squash it by the same amount, but at right angles to the light world line, and abracadabra! Tom's world line has gone vertical, so this does represent the world from his point of view, but most importantly, the light world line has never changed its angle, and so light will be measured by Tom going at the correct speed. This superb trick is known as a Lorentz transformation. Yeah, more than a trick. Slice up the space-time into new panels and you have the physically correct animation. I'm stationary in the car, everything else is coming past me and the speed of light works out to be that same fixed value that we know everyone measures. On the other hand, something strange has happened. The fence posts aren't spaced a meter apart anymore, and my mom will be worried that I look a bit thin. But that's not fair. Why don't I get to look thin? I thought physics was supposed to be the same for everyone. Yes, no, it is, and you do. All that stretching and squashing of space-time has just muddled together what we used to think of separately as space and time. This particular squashing effect is known as Lorentz contraction. Okay, but I still don't look thin. No, yes, you do. Now that we know better about space-time, we should redraw what the scene looked like to me. To you, I appear Lorentz contracted. Oh but to you, I appear Lorentz contracted. Yes. Uh, well, at least it's fair. And speaking of fairness, just as space gets muddled with time, time also gets muddled with space, in an effect known as time dilation. No, at everyday speeds, such as Tom's car reaches, actually all the effects are much, much smaller than we've illustrated them. Oh, yet, careful experiments, for instance watching the behavior of tiny particles whizzing around the Large Hadron Collider confirmed that the effects are real. And now that space-time is an experimentally confirmed part of reality, we can get a bit more ambitious. What if we were to start playing with the material of space-time itself? We'll find out all about that in the next animation.
光:宇宙中最快的東西。 但我們依然有辦法測量它的速度。 如果我們把畫面放慢, 我們可以使用時空圖來分析光的運動, 就像從側面來看一頁頁的手翻書。 在這堂課裡,我們先補充一個實驗結果: 當任何人所測量的光速, 都會得到相同的結果。 每秒299 792 458公尺。 這意味著 當我們把光畫在時空圖上時, 光的世界線必須總是呈現相同的角度。 但是,我們之前看到 速度即是由世界線的角度來表示 會隨著不同觀察者的視角而改變。 為了弄清這個矛盾 讓我們來看看如下情況: 如果我開始移動, 而我站在這裡朝著湯姆發射雷射光。 首先,我們需要建構出時空圖 這意味著 取出對應每一個時刻的每一幅圖片, 然後把它們疊在一起。 從側面我們看到雷射光的世界線 有著固定的、正確的角度, 就和早先的一樣。 目前為止一切順利。 但是這個時空圖展示的是安德魯的視角。 從我的視角來看是什麽樣的呢? 在上一課裡 我們展示了如何得到湯姆的視角。 只需把所有的圖片平移一點, 直到湯姆的世界線完全垂直。 但是仔細看看光的世界線。 平移所有圖片的話, 會使得光的世界線傾斜過度。 我所測得的光速將會比安德魯所測得的快。 但是我們所做過的實驗, 我們所有的努力, 都證明光速是恒定的。 讓我們重新開始。 在19世紀初,有個聰明的傢伙叫愛因斯坦。 他想出了如何從湯姆的視角 來正確地看待問題, 而同時依然能得到正確的光速。 首先我們需要把分離的畫面都粘合起來, 粘成完整的一塊, 於是我們有了時空。 將時間和空間 變成一整塊平順連續的材料。 現在,變戲法的時候到了。 你要做的是 沿著光的世界線拉伸你的整塊時空, 然後在垂直世界線的方向上 等量地壓縮時空。 唵嘛呢叭咪吽! 湯姆的世界線變得垂直了, 所以這代表了他眼中的世界。 但是最重要的是, 光的世界線從未改變角度。 所以湯姆所測量的光速 也是正確的光速。 這個傑出的戲法叫做 勞侖茲轉換。 這可不是騙人的把戲, 重新將時空分割為一幅幅畫面 你將得到物理上正確的動畫。 我靜止坐在車裡, 所有東西都朝我移來並經過我身邊, 而光速依然 是那個恒定的速度, 和所有人測量的光速一樣。 而另一方面, 有些奇怪的事情發生了, 圍欄柱子的間隔不再是一米了。 而我媽媽會擔心 我看起來變瘦了。 這不公平!為什麼我看起來沒變瘦? 我以為物理學對每個人都是一樣的。 的確是一樣的,你也看起來瘦了。 所有這些,時空的拉伸和壓縮, 把我們之前認為的 獨立的時間和空間 都混合到了一起。 這個特別的壓縮效應, 被稱為勞侖茲收縮。 好吧,可是我依然看起來不瘦。 不,你的確看起來瘦了。 現在我們對時空有了更多的了解, 我們應該重新畫出 我眼中的情形是怎麽樣的。 對你來說,我表現出勞侖茲收縮。 而對你來說,我表現出了勞侖茲收縮。 對。 好吧,至少這是公平的。 說到公平, 不僅空間被時間攪渾, 時間也被空間攪渾。 有個效應叫做時間膨脹。 雖然在日常的速度下, 比如湯姆的車速, 實際的效應非常非常地小, 比我們剛才展示的要小得多。 然而精密的實驗, 比如觀察微小的粒子 在大型強子對撞機裡的運動, 確認了這些效應是真實存在的。 既然現在時空已是被實驗驗證的事實, 我們的野心可以更大一些。 我們是否可以開始 考慮時空本身的性質? 我們會在下一堂課裡找到答案。