AlbertYang的甘苦滋味

Someone, one of my friend, has written that moon doesn't exist unless you "perceive" and "observe" it from philosopher's point of view. This is kind of perverting the fundamental idea from the great masters who are famous for their pioneering work on quantum mechanics. In order to elucidate the spirit of quantum mechanics, I'll try to explain "absolute size" and "superposition principle" in the following context as possible as I can.
First of all, it alsway been hold, either classical mechanics or quantum mechanics, that we must interact with our target if we wants to make an observation on it. Observation causes disturbances. Classical mechanics assume that we can always make object being big and neglect disturbance when makeing observation on it. Size is "relative". For example, when we throw a billiard ball at that wall, the wall is "big" and the ball is "small". That is, size depends on the object and your experimental technique, so the classical system obey the causality, i. e. an observation doesn't scatter the system we interested in. Quantum mechanics is fundamentally different from classical mechanics in the way it treats size. Dirac assumes that there is a limit to the fineness of our powers of observation and the smallness of the accompanying disturbance, a limit which is inherent in the nature of things and can never be surpassed by improved technique or increased skill on the part of the observer. That is, for a small object, an unavoidable limiting disturbance is not negligible even if we improve our experimental technique. Size is absolute. On the contrary, classical mechanics doesn't set up to describe objects that are small in an absolute sense. Due to unavoidable limiting disturbance, observation on a microscopic system breaks down the causality, and uncertainty comes in calculation of observables. The experimental result accompanies with probability.
What happened before making observation on a system? A famous example is "Schrödinger's cat." The whole story can be found on Wiki. The state of such system can be described by the following equation
To get statistical result, we perpare many similar boxes. By opening these boxes, we get the probability finding the cat is dead or alive. But we still don't know the real situation before we open these black boxes. It seems strange, and alittle bit distracting from my another main topic: "Superposition principle." All I do is to desribe our interested system by using linear combination (superposition) of a set base kets (vectors). In quantum mechanics, superposition of states is central theoretical description of nature. Observation on a superposition of A (ex: "alive") and B (ex: "dead"), which are basis, gives either a or b. Never gives anything else. Probability of getting result a or b depends on relative weights of A and B in the superposition. A great conclusion comes from Dirac: "The intermediate character of the state formed by superposition thus expresses itself through the probability of a particular result for an observation being 'intermediate' between the corresponding probabilities for the original state, not through the result itself being intermediate between the corresponding results for the original states." "Absolute size" and "Superposition principle" are intimately linked. Maybe the example about the cat is untouchable, I strongly recommendated the book, Elementary Quantum Mechanics, which is written by Michael D. Fayer. He illustrate the two ideas in an attainable way. All quantum mechanics do is to calculate probabilities about our interested system.
Reference Link:
http://www.stanford.edu/group/fayer/

古典的量子論學習中  最經典的模型就是  粒子於一維盒子中的運動描述(波函數)推導  及其能量量化的導式
這邊藉由簡單的一維駐波模型方式推得粒子於一維盒子中
我們知道粒子於一維盒子中的假設(如下圖)