academia.edu上的一位资深物理学人士有关本文第2个问题的答复： 【Ron — That is not a basic question at all. It is actually the deepest conceptual leap in quantum mechanics, and the way you phrased it shows you have spotted exactly where the confusion lies. Let me walk you through it step by step. --- ### 1. Classical probability (what you learned in school) In classical probability, we deal with **events** that are either **true or false**, and we assign a number \(P\) between 0 and 1 to how likely that event is. - \(P(A)\) = probability that event A occurs. - \(P(B)\) = probability that event B occurs. If A and B are **independent**, the probability that **both** A and B occur is: \[ P(A \text{ and } B) = P(A) \times P(B) \] If A and B are **mutually exclusive** (they cannot both happen), the probability that **either** A or B occurs is: \[ P(A \text{ or } B) = P(A) + P(B) \] This is the logic you learned. It is the logic of **coins, dice, and cards**. It works perfectly for macroscopic objects. --- ### 2. Quantum mechanics does not deal with probabilities directly Quantum mechanics does not start with probabilities. It starts with **probability amplitudes**. These are complex numbers (they have a magnitude and a phase, like a vector or a wave). We usually denote them with the Greek letter \(\psi\) (psi). For a particle that can be in state A or state B, the quantum state is: \[ \psi = \psi_A + \psi_B \] This is **superposition**. It is a sum of *amplitudes*, not a sum of probabilities. --- ### 3. How do we get a probability from an amplitude? The probability \(P\) is **not** the amplitude itself. It is the **square of the magnitude** of the amplitude: \[ P = |\psi|^2 \] So if \(\psi = \psi_A + \psi_B\), then: \[ P = |\psi_A + \psi_B|^2 \] Now, because these are complex numbers (or vectors), the square of a sum is **not** simply the sum of the squares. There is an extra term: \[ P = |\psi_A|^2 + |\psi_B|^2 + 2 \times \text{(interference term)} \] The interference term is what we call **quantum interference**. It comes from the cross-product between the two amplitudes. Depending on the relative phase (the "alignment") of \(\psi_A\) and \(\psi_B\), this interference term can be **positive** (constructive) or **negative** (destructive). --- ### 4. What does "P1 + P2" or "P1 and P2 cancel" actually mean? When people say "probabilities cancel" or "probabilities interfere", they are speaking loosely. What actually cancels are the **amplitudes**, not the probabilities. Let me give you the classic example: **the double-slit experiment**. - If you close slit B and only open slit A, you get a certain pattern on the screen. The probability of a particle landing at a specific point is \(P_A = |\psi_A|^2\). - If you close slit A and only open slit B, you get \(P_B = |\psi_B|^2\). Now, **if quantum mechanics were classical**, opening both slits would just give: \[ P = P_A + P_B \] You would see the two patterns simply added together. **But that is not what happens.** What actually happens is: \[ P = |\psi_A + \psi_B|^2 = P_A + P_B + \text{interference} \] At some points on the screen, the interference term is large and positive, so the pattern is **brighter** than \(P_A + P_B\) (constructive interference). At other points, the interference term is large and negative, so the pattern is **darker** than \(P_A + P_B\)—sometimes completely **dark** (destructive interference). So when we say "P1 and P2 cancel", we really mean: *the amplitudes \(\psi_A\) and \(\psi_B\) are out of phase (one is positive, the other negative), so their sum is zero, and therefore the final probability \( |\psi_A + \psi_B|^2 \) is zero.* The probabilities \(P_A\) and \(P_B\) are still individually positive, but the *interference term* has cancelled them out.】 我的回复： 【 Dear Ian, Thanks for your answer. But your interpretation makes QM even worse. They stole the name of Hamilton, but their not Hamilton, they stole the name of probability, but they are not. They built their mansion from the air without ANY foundation so that they need to scramble up their definitions for their prop! Cheers, Ron】 他的跟进： 【 Well Ron, the way I look at it, dealing with assessing reality with any formal system in the end it cannot say anything about reality because all formal systems, including mathematics, are inherently incomplete. Even in the beginning of physics. We say distance x is velocity over time, t. That is x=vt. We want to know what is distance (space) we see it is measured in terms of velocity (distance per time), v=x/t. Substitute that into the equation x=(x/t)t and we get x=x. Which means the very of foundations of physics does to tell us what reality is. It tells us space is space. But it is still a useful tool that will land us on the Moon. 】 我的回复： 【 Rongqing Dai 3 hrs ago But they should not call it probability if they invented a new math. If their dynamics was not derived from Hamilton rigorously, they should not pretend to be. Cheers, Ron 】 。。。。。。 看来理论物理学界真正从哲学根子上出了问题。。。。积重难返！ |
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