[파인만 양자역학] 1-6. 전자 관찰하기 [2/2] (Watching the Electron)
[참조] 차교수의 물리 산책/파인만 양자역학 1장 7강[링크][원문]
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파인만 양자역학을 내맘대로 번역하고 약간의 해설을 달아 봤습니다. 한글 해석과 덧붙인 [주]는 저의 개인적인 생각 이므로 그대로 받아 들이진 말아 주세요. 하지만 칭찬, 동의, 반론, 지적등 어떤 식으로든 의견은 환영 합니다.
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Chapter 1. Quantum Behavior
1장. 양자역학이 지배하는 대상의 행동
1–6. Watching the electrons
1-6. 전자 관찰하기 [2/2]
Let us try the experiment with longer waves. We shall keep repeating our experiment, each time with light of a longer wavelength. At first, nothing seems to change. The results are the same. Then a terrible thing happens.
[관찰하지 않으면 전자의 분포곡선이 파동 처럼 간섭 곡선을 그린다. 관찰하면 입자처럼 간섭 곡선이 나오지 않았다. 그 이유로, 전자가 광자에 의해 밀쳐져 경로가 틀어져서 간섭받은 분포 곡선이 나오지 않았다는 설명을 실험으로 보이기 위해서] 파장이 긴 광원을 사용해 실험해 보자. 언뜯 보기에 변화는 없었다. 결과는 동일했다. 그리곤 끔찍한 일이 벌어졌다.
You remember that when we discussed the microscope we pointed out that, due to the wave nature of the light, there is a limitation on how close two spots can be and still be seen as two separate spots. This distance is of the order of the wavelength of light. So now, when we make the wavelength longer than the distance between our holes, we see a big fuzzy flash when the light is scattered by the electrons. We can no longer tell which hole the electron went through!
현미경에 대하여 이야기 했던 걸 상기해보자. 빛의 파동성으로 인해 두 지점을 구분할 수 있는 한계가 있다고 했었다. 이 거리[분해능 한계]는 빛의 파장 만큼이다. 이제 우리 실험에 두 구 멍의 간격보다 긴 파장의 빛을 써보자. 빛이 전자에 의해 산란되자 아주 커다란 뿌연 섬광이 일었다. 더이상 전자가 [섬광이 있었으나] 어느 구멍을 통과했다고 말할 수 없게 됐다.
We just know it went somewhere! And it is just with light of this color that we find that the jolts given to the electron are small enough so that P′12 begins to look like P12 - that we begin to get some interference effect. And it is only for wavelengths much longer than the separation of the two holes (when we have no chance at all of telling where the electron went) that the disturbance due to the light gets sufficiently small that we again get the curve P12 shown in Fig. 1-3.
그냥 지나갔다는 것만 알고있다! 그리고 이 빛의 색으로는 전자를 밀침이 아주 작아서 P'_12가 P_12 처럼 되었다. 그러니까 밀침이 적으면 관측했어도 간섭이 일어났다. 그 결과는 관측에 사용된 빛의 파장이 두 구멍의 간격이 보다 길었을 때 였다. 이 때는 전자가 어디로 갔다고 특정할 수 없다. 그러니까 빛의 방해가 아주 작아서 그림 1-3 에 보인 P_12을 다시 얻게 됐다.
[주] 관찰용 광원을 켜두고, 두 전자의 경로를 확인 할 수 있
In our experiment we find that it is impossible to arrange the light in such a way that one can tell which hole the electron went through, and at the same time not disturb the pattern. It was suggested by Heisenberg that the then new laws of nature could only be consistent if there were some basic limitation on our experimental capabilities not previously recognized.
우리 실험에서 전자가 어느 구멍을 통해 나갔는지 확정하면서도 동시에 무늬를 흐트러트리지 않는 그런 빛을 마려하기란 불가능 하다는 것을 알게 됐다. 하이젠버그는 새로운 자연의 법칙을 제안했는데
He proposed, as a general principle, his uncertainty principle, which we can state in terms of our experiment as follows: “It is impossible to design an apparatus to determine which hole the electron passes through, that will not at the same time disturb the electrons enough to destroy the interference pattern.” If an apparatus is capable of determining which hole the electron goes through, it cannot be so delicate that it does not disturb the pattern in an essential way. No one has ever found (or even thought of) a way around the uncertainty principle. So we must assume that it describes a basic characteristic of nature.
그가 제안한 일반론으로 제안한 불확정성 원리를 우리가 한 실험의 용어로 표현하면 다음과 같다.
장비를 설계하기는 불가능하다. 전자가 지나갈 구멍
간섭무늬를 무너트릴 만큼 충분한 전자를 방해할
만일 그 장치가 가능하다면
The complete theory of quantum mechanics which we now use to describe atoms and, in fact, all matter, depends on the correctness of the uncertainty principle. Since quantum mechanics is such a successful theory, our belief in the uncertainty principle is reinforced. But if a way to “beat” the uncertainty principle were ever discovered, quantum mechanics would give inconsistent results and would have to be discarded as a valid theory of nature.
“Well,” you say, “what about Proposition A? Is it true, or is it not true, that the electron either goes through hole 1 or it goes through hole 2?” The only answer that can be given is that we have found from experiment that there is a certain special way that we have to think in order that we do not get into inconsistencies. What we must say (to avoid making wrong predictions) is the following. If one looks at the holes or, more accurately, if one has a piece of apparatus which is capable of determining whether the electrons go through hole 1 or hole 2, then one can say that it goes either through hole 1 or hole 2. But, when one does not try to tell which way the electron goes, when there is nothing in the experiment to disturb the electrons, then one may not say that an electron goes either through hole 1 or hole 2. If one does say that, and starts to make any deductions from the statement, he will make errors in the analysis. This is the logical tightrope on which we must walk if we wish to describe nature successfully.
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If the motion of all matter—as well as electrons—must be described in terms of waves, what about the bullets in our first experiment? Why didn’t we see an interference pattern there? It turns out that for the bullets the wavelengths were so tiny that the interference patterns became very fine. So fine, in fact, that with any detector of finite size one could not distinguish the separate maxima and minima. What we saw was only a kind of average, which is the classical curve. In Fig. 1–5 we have tried to indicate schematically what happens with large-scale objects. Part (a) of the figure shows the probability distribution one might predict for bullets, using quantum mechanics. The rapid wiggles are supposed to represent the interference pattern one gets for waves of very short wavelength. Any physical detector, however, straddles several wiggles of the probability curve, so that the measurements show the smooth curve drawn in part (b) of the figure.
Fig. 1-5.Interference pattern with bullets: (a) actual (schematic), (b) observed.
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