阿爾伯特•愛因斯坦發表光電效應理論
確立他在量子力學中的地位。
但他始終對其論述有所質疑。
雖然我們大多知道他推導出E=MC^2，
但他最後的偉大貢獻 應是1935年的論文，
與他年輕的同事鮑里斯•波多爾斯基 和納森•羅森共同發表(EPR論文)。
到1980年代仍被視為哲學上的悖論，
但近年來EPR論文的重要性日漸提升， 也為量子力學帶來新視角。
其中尤為重要的是
對弔詭現象糾纏態的描述。
Entangled states
論文起頭假設來自同源的成對粒子，
每個粒子具兩種可測量的屬性，
兩種屬性測量後各有兩種可能的結果
且機率一樣。
我們假設第一種量測量結果非1即0，
第二種結果可能為A或是B。
一經量測，
同一粒子同一種量的後續觀測
都會得到相同的結果。
這情況下衍生出弔詭的論調，
其一為單一粒子的狀態
在未測量之前都是不確定的，
其二為測量的行為決定了狀態。
甚至發現，測量結果會相互影響。
如果測量一粒子的結果為1，
再進行第二種屬性的測量，
得到A或B的結果各一半，
但如果重複第一種屬性的測量，
仍有50%的機會結果會是0，
即便先前已經測量過的結果顯示為1。
改變測量的屬性，就會重寫原本的測量結果，
有機會得到一個不同的隨機測量值。
更加難懂的是，如果同時考量兩個粒子，
任一粒子都會有隨機的結果，
但如果比較兩者，
可以發現兩者相依相存。
例如若兩者量測結果皆為0，
這個相對關係永遠不變。
兩者的狀態糾纏在一起。
測量其一，則可確定另一個的結果。
Einsteins mistake
但這種糾纏現象似乎 牴觸愛因斯坦的相對論
因為粒子間的距離沒有上限。
如果距離拉大，如在紐約正午測量其一，
十億分之一秒後在舊金山測量另一個，
兩者該得到相同的結果。
但如果量測的行為決定狀態，這表示
一方得傳送某種訊息給另一方 來確定彼此狀態，
傳遞速度還得是 光速的一千三百萬倍，
以相對論來說這是不可能的。
因此，愛因斯坦稱為 「spukhafte fernwirkung」，
也就是，鬼魅似的遠距作用。
他堅信量子力學有不完備處，
所以不足以揭露並解釋
兩個粒子具有的深層先??K狀態。
支持正統量子理論的尼爾斯•波耳一派
認為量子狀態確實是不確定的，
而糾纏現象讓某一粒子的狀態，
與距離甚遠的另一粒子緊密相關。
三十年來，物理陷入僵局，
直到約翰•貝爾想出試驗EPR論點的方法，
關鍵在於討論涉及兩個粒子 不同測量的狀況。
愛因斯坦、波多爾斯基和羅森 支持的局域隱變數理論
嚴格限制得到的固定結果， 如1A或是B0的次數，
因為這些結果事先已經固定。
貝爾從純量子的方法著手，
也就是說測量前屬性確實無法確定，
這樣的狀況下有不同的限制 且預示混雜的測量結果，
其結果不可能在事先 安排好的狀況下達成。
貝爾一提出驗證EPR論點的方法，
物理學家紛紛出馬試驗。
起於70 年代的約翰·克勞澤 及80年代早期的阿蘭•阿斯佩，
許許多多的實驗 反覆驗證EPR預測，
全數得到相同的結論：
證明量子力學是正確的。
具不確定性的兩糾纏粒子間 確實存在相關性。
沒有更進一步的變數可以解釋此現象。
Conclusion
EPR論文雖然不成立，但是個精彩的錯誤。
它引領物理學家深究量子力學的根基，
使理論得以更為完備，
也有更多研究投入各個面向， 好比量子資訊，
現在是個熱門的領域， 有潛力發展出效能無敵的電腦。
但礙於測量結果的隨機性，
科幻場景還是不可能成真，
好比利用粒子糾纏現象以超光速傳遞訊息。
所以相對論暫時還站得住腳。
但量子的世界，確實難搞， 不像愛因斯坦堅信的客觀實在。
Einstein's brilliant mistake: Entangled states - Chad Orzel
Albert Einstein played a key role in launching quantum mechanics through his theory of the photoelectric effect but remained deeply bothered by its philosophical implications. And though most of us still remember him for deriving E=MC^2, his last great contribution to physics was actually a 1935 paper, coauthored with his young colleagues Boris Podolsky and Nathan Rosen. Regarded as an odd philosophical footnote well into the 1980s, this EPR paper has recently become central to a new understanding of quantum physics, with its description of a strange phenomenon now known as entangled states. Entangled states The paper begins by considering a source that spits out pairs of particles, each with two measurable properties. Each of these measurements has two possible results of equal probability. Let's say zero or one for the first property, and A or B for the second. Once a measurement is performed, subsequent measurements of the same property in the same particle will yield the same result. The strange implication of this scenario is not only that the state of a single particle is indeterminate until it's measured, but that the measurement then determines the state. What's more, the measurements affect each other. If you measure a particle as being in state 1, and follow it up with the second type of measurement, you'll have a 50% chance of getting either A or B, but if you then repeat the first measurement, you'll have a a 50% chance of getting zero even though the particle had already been measured at one. So switching the property being measured scrambles the original result, allowing for a new, random value. Things get even stranger when you look at both particles. Each of the particles will produce random results, but if you compare the two, you will find that they are always perfectly correlated. For example, if both particles are measured at zero, the relationship will always hold. The states of the two are entangled. Measuring one will tell you the other with absolute certainty. Einsteins mistake But this entanglement seems to defy Einstein's famous theory of relativity because there is nothing to limit the distance between particles. If you measure one in New York at noon, and the other in San Francisco a nanosecond later, they still give exactly the same result. But if the measurement does determine the value, then this would require one particle sending some sort of signal to the other at 13,000,000 times the speed of light, which according to relativity, is impossible. For this reason, Einstein dismissed entanglement as "spuckafte ferwirklung," or spooky action at a distance. He decided that quantum mechanics must be incomplete, a mere approximation of a deeper reality in which both particles have predetermined states that are hidden from us. Supporters of orthodox quantum theory lead by Niels Bohr maintained that quantum states really are fundamentally indeterminate, and entanglement allows the state of one particle to depend on that of its distant partner. For 30 years, physics remained at an impasse, until John Bell figured out that the key to testing the EPR argument was to look at cases involving different measurements on the two particles. The local hidden variable theories favored by Einstein, Podolsky and Rosen, strictly limited how often you could get results like 1A or B0 because the outcomes would have to be defined in advanced. Bell showed that the purely quantum approach, where the state is truly indeterminate until measured, has different limits and predicts mixed measurement results that are impossible in the predetermined scenario. Once Bell had worked out how to test the EPR argument, physicists went out and did it. Beginning with John Clauster in the 70s and Alain Aspect in the early 80s, dozens of experiments have tested the EPR prediction, and all have found the same thing: quantum mechanics is correct. The correlations between the indeterminate states of entangled particles are real and cannot be explained by any deeper variable. Conclusion The EPR paper turned out to be wrong but brilliantly so. By leading physicists to think deeply about the foundations of quantum physics, it led to further elaboration of the theory and helped launch research into subjects like quantum information, now a thriving field with the potential to develop computers of unparalleled power. Unfortunately, the randomness of the measured results prevents science fiction scenarios, like using entangled particles to send messages faster than light. So relativity is safe, for now. But the quantum universe is far stranger than Einstein wanted to believe.
授課教師
陳永忠 ycchen@thu.edu.tw