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:宇宙中最快的东西 但我们依然有办法测量它的速度 如果我们把画面放慢, 我们可以使用时空图来分析光的运动 就像从侧面来看一页页的手翻书 在这堂课里,我们将补充一个实验事实 当任何人测量光的速度的时候 都会得到相同的结果 每秒299 792 458米 这意味着 当我们把光画在时空图上时 光的世界线必须总是呈现相同的角度 但是,我们之前看到 速度,即世界线的角度 会随着不同观察者的视角而改变 为了弄清这个矛盾 让我们来看看如下情况 如果我开始移动 而我站在这里朝着汤姆发射激光 首先,我们需要构造时空图 这意味着 取出对应每一个时刻的每一帧图片 然后把它们叠在一起 从侧面我们看到激光的世界线 有着固定的、正确的角度 就和早先的一样 目前为止一切顺利 但是这个时空图展示的是安德鲁的视角 从我的视角来看是什么样的呢? 在上一课里 我们展示了如何得到汤姆的视角 只需把所有的图片平移一点 直到汤姆的世界线完全垂直 但是仔细看看光的世界线 平移所有图片的话 会使得光的世界线倾斜过度 我所测得的光速将会快于安德鲁所测得的 但是我们所做过的所有实验 我们所有的努力 都表明光速是恒定的 让我们重新开始 在19世纪00年代,有个聪明的家伙叫爱因斯坦 他想出了如何从汤姆的视角 来正确地看待问题 而同时依然能得到正确的光速 首先我们需要把分离的画面都粘合起来 粘成完整的一块 于是我们有了时空 将时间和空间 变成一整块平顺连续的材料 现在,变戏法的时候到了 你要做的是 沿着世界线拉伸你的整块时空 然后在垂直于世界线的方向上 同等数量地压缩时空 唵嘛呢叭咪吽! 汤姆的世界线变得垂直了 所以这代表了他眼中的世界 但是最重要的是 光的世界线从未改变角度 所以汤姆所测量的光速 也是正确的光速 这个杰出的戏法叫做 洛伦兹变换 这可不是骗人的把戏 重新将时空分割为一幅幅画面 你将得到物理上正确的动画 我静止坐在车里 所有东西都朝我移来并经过我身边 而光速依然 是那个恒定的速度 和所有人测量的光速一样 而另一方面 有些奇怪的事情发生了 围栏柱子的间隔不再是一米了 而我妈妈会担心 我看起来瘦了 这不公平!为什么我看起来没瘦? 我以为物理学对每个人都是一样的 的确是一样的,你也看起来瘦了 所有这些,时空的拉伸和压缩 把我们之前认为的 独立的时间和空间 都混合到了一起 这个特别的压缩效应 被称为洛伦兹收缩 好吧,可是我依然看起来不瘦 不,你的确看起来瘦了 现在我们对时空有了更多的了解 我们应该重新画出 我眼中的情形是怎么样的 对你来说,我表现出洛伦兹收缩 而对你来说,我表现出了洛伦兹收缩 对 好吧,至少这是公平的 说到公平 不仅空间被时间搅浑 时间也被空间搅浑 有个效应叫做时间膨胀 虽然在日常的速度下 比如汤姆的车速 实际的效应非常非常地小 比我们刚才展示的要小得多 然而精密的实验 比如观察微小的粒子 在大型强子对撞机里的运动 确认了这些效应是真实存在的 既然现在时空已是被实验验证的事实 我们的野心可以更大一些 我们是否可以开始 考虑时空本身的性质? 我们会在下一个动画里找到答案