薛丁格的貓
奧地利物理學家薛丁格 是量子力學的創始人之一，
但最讓他出名的 其實是一件他從沒做過的事情：
一個關於貓的思想實驗。
他想像將一隻貓 放進一個密封的盒子中，
接下來的一小時內， 貓有50％的機率會被盒中的儀器殺死。
一小時過去後，他問道： "這隻貓現在是何種狀態呢？"
常識告訴我們， 這隻貓要麼活著，要麼死了。
但是薛丁格指出，根據量子力學，
在盒子打開的那一刻之前，
這隻貓在同一時刻，既是死的也是活的；
只有在盒子被打開的那一刻， 我們才能看見單一固定的狀態。
在那之前，貓的生死純粹是 模糊的概率問題。
一半是死、一半是活。
這似乎很荒謬， 但這正是薛丁格想要指出的。
他發現量子力學 在哲學上是如此令人煩惱，
以至於讓他徹底放棄了這個 他幫助建立起來的理論，
轉而投向生物學的研習。
量子力學的波粒二象性
儘管這個實驗聽上去很荒謬， 但薛丁格的貓卻十分真實。
實際上，它甚為關鍵。
如果量子物體不能夠 以兩種狀態同時存在的話，
那你用來看這段影片的電腦 也就不會存在了。
疊加的量子現象
是一切物質波粒二象性的結果，
一個物體要有波長，
就必須擴展空間範圍，
這就意味著它必須 同時佔據許多位置。
物質的波長限制在很小的空間中，
不能明確定位，
所以它同時存在於許多不同的波長中。
我們在日常事物中無法看到這些波，
因為波長會隨著動量的增加而遞減。
而貓的體積相對較大、質量也較重，
如果我們將一個原子放大到太陽系大小，
那麼貓奔向物理學家時產生的波長，
才相當於太陽系裡的原子般大小。
因小到難以探測，所以 我們從未看到貓的波動性。
然而，例如電子般的粒子，
卻是證明波粒二象性存在的證據。
如果我們把一個電子射向雙狹縫裝置，
電子另一側的位置馬上會被探測到，
就像粒子一樣。
但如果我們大量重複此實驗，
將每個檢測結果記錄下來，
你會發現它們的軌跡表現出波的特徵，
條紋區間內集聚了大量電子，
夾雜在沒有電子的區間之中。
一旦遮擋住一個狹縫， 條紋區間隨之消失，
顯示電子的集聚形態因為同一時刻
有兩個狹縫可供穿過的作用結果。
單個電子無法選擇通過哪個狹縫，
但是，電子束卻是同時通過兩個狹縫。
此種疊加狀態也使許多現代科技成真。
繞原子核旋轉的電子 存在於延伸出的似波軌道中，
當兩個原子相互靠近時，
電子不需要選擇原子軌道，
只需要共用軌道，
這就是一些化學鍵的形成方式。
一個分子中的電子並不是純粹 A原子或B原子所擁有，而是兩者共有。
如果你加入更多原子， 電子們就會分布得更加分散，
同時被許多個原子所共用，
固體中的電子並非固定在某個原子上，
而是在一個較大空間中延展開， 被不同的原子所共用。
這種巨大的疊加狀態，
決定了原子構成物質的形式，
可能是導體、絕緣體或半導體。
電晶體
理解電子是如何被原子所共用，
能夠讓我們得以精確控制半導體的性質，
例如矽半導體。
將不同的半導體以正確的形式合成，
使讓我們製造作出極小的電晶體，
在一小片電腦晶片上 就有上百萬個電晶體。
而那些晶片，以及其中流動的電子，
使你用來觀看此短片的電腦得以運作。
有個老套的笑話： 因網路的存在， 讓人們得以分享貓咪影片。
然而從一個很深刻的層次來說： 網路的存在，
恰恰是源於一個奧地利物理學家 和他想像出來的貓。
Schroedinger's Cat
Austrian physicist Erwin Schroedinger is one of the founders of quantum mechanics, but he's most famous for something he never actually did: a thought experiment involving a cat. He imagined taking a cat and placing it in a sealed box with a device that had a 50% chance of killing the cat in the next hour. At the end of that hour, he asked, "What is the state of the cat?" Common sense suggests that the cat is either alive or dead, but Schr??丼inger pointed out that according to quantum physics, at the instant before the box is opened, the cat is equal parts alive and dead, at the same time. It's only when the box is opened that we see a single definite state. Until then, the cat is a blur of probability, half one thing and half the other. This seems absurd, which was Schr??丼inger's point. He found quantum physics so philosophically disturbing, that he abandoned the theory he had helped make and turned to writing about biology. As absurd as it may seem, though, Schr??丼inger's cat is very real. In fact, it's essential. If it weren't possible for quantum objects to be in two states at once, the computer you're using to watch this couldn't exist. The quantum phenomenon of superposition is a consequence of the dual particle and wave nature of everything. In order for an object to have a wavelength, it must extend over some region of space, which means it occupies many positions at the same time. The wavelength of an object limited to a small region of space can't be perfectly defined, though. So it exists in many different wavelengths at the same time. We don't see these wave properties for everyday objects because the wavelength decreases as the momentum increases. And a cat is relatively big and heavy. If we took a single atom and blew it up to the size of the Solar System, the wavelength of a cat running from a physicist would be as small as an atom within that Solar System. That's far too small to detect, so we'll never see wave behavior from a cat. A tiny particle, like an electron, though, can show dramatic evidence of its dual nature. If we shoot electrons one at a time at a set of two narrow slits cut in a barrier, each electron on the far side is detected at a single place at a specific instant, like a particle. But if you repeat this experiment many times, keeping track of all the individual detections, you'll see them trace out a pattern that's characteristic of wave behavior: a set of stripes - regions with many electrons separated by regions where there are none at all. Block one of the slits and the stripes go away. This shows that the pattern is a result of each electron going through both slits at the same time. A single electron isn't choosing to go left or right but left and right simultaneously. This superposition of states also leads to modern technology. An electron near the nucleus of an atom exists in a spread out, wave-like orbit. Bring two atoms close together, and the electrons don't need to choose just one atom but are shared between them. This is how some chemical bonds form. An electron in a molecule isn't on just atom A or atom B, but A+ B. As you add more atoms, the electrons spread out more, shared between vast numbers of atoms at the same time. The electrons in a solid aren't bound to a particular atom but shared among all of them, extending over a large range of space. This gigantic superposition of states determines the ways electrons move through the material, whether it's a conductor or an insulator or a semiconductor. Understanding how electrons are shared among atoms allows us to precisely control the properties of semiconductor materials, like silicon. Combining different semiconductors in the right way allows us to make transistors on a tiny scale, millions on a single computer chip. Those chips and their spread out electrons power the computer you're using to watch this video. An old joke says that the Internet exists to allow the sharing of cat videos. At a very deep level, though, the Internet owes its existance to an Austrian physicist and his imaginary cat.
授課教師
陳永忠 ycchen@thu.edu.tw