物理与天文2023researchgate.net
薛定谔方程从经典力学中数学地涌现（2012）
Schrödinger equation emerges mathematically from classical mechanics (2012)
专业 · 约 35 分钟读完前置知识：哈密顿力学、量子力学基础、辛几何/李群
导读
这篇论文探讨薛定谔方程能否从经典力学中数学地导出，并将其与不确定性原理、海森堡群联系起来，标题中的"伪量子三元组"暗示作者试图在经典框架内重构量子力学的基本结构。不过论文摘要相当专业，非专家可能难以直接读懂。
HN 关注点：HN 读者既关心"薛定谔方程能否从经典力学推出"这一物理问题，也在讨论该论文的可读性以及去哪里找同行对论文的讨论。
HN 评论精选
这几条评论里：质疑 1 补充 3
补充薛定谔从光学-力学类比出发，通过引入"衍射"概念推导出方程，其推理深度被"只是猜得好"的说法低估。
薛定谔的推理非常了不起。哈密顿从光学出发，发现了光方程与力学方程之间的数学类比：费马的最小时间原理对应力学的最小作用量原理。但最小时间原理不预测衍射，只描述光线的几何路径，当光波长与相互作用对象尺寸相当时就失效了。当时力学方程在小系统上也明显失效。薛定谔的惊人洞察是：力学是否以和光学相同的方式失效？物质在"波长"与相互作用对象尺寸相当时，是否也会表现出某种"衍射"？这能否解释德布罗意把微小粒子当作波的成功？由此，他给物质方程加上了"衍射"，得到了薛定谔方程。如果有物理背景（研究生水平）值得读原文。物理学界流传"薛定谔只是猜得好"，这大大低估了他推理的深度。
alecst查看英文原文
Schrodinger's reasoning was remarkable. The high-level description of classical mechanics was formulated by Hamilton, who was starting from optics. He saw a mathematical analogy between the equations for light and the equations for mechanics. The principle of least time (Fermat's principle) for light became the principle of least action for mechanics. But the principle of least time does not predict diffraction, just the geometric path of a light ray. It fails when the wavelength of the light is large compared to whatever it's interacting with. At the time, the equations for mechanics were clearly failing for small systems. Here's where Schrodinger had his incredible insight: what if mechanics broke in the same way as optics? Could matter itself display a kind of "diffraction" when its "wavelength" was similar in size to the objects it was interacting with? Could this explain the success of de Broglie's work, which treated small particles like waves? Guided by that, he was able to add "diffraction" to the equations of matter and come up with the Schrodinger equation. It's worth reading the original paper if you have a physics background -- probably grad-level (just being realistic.) I've been wanting to write a blog post about this because the physics lore is something like "Schrodinger just made a really good guess" but that totally undersells the depth of his reasoning.
补充论文开放获取，建议使用期刊官方链接而非 ResearchGate。
我不知道是否有关于科学论文链接的规定，但我认为用期刊论文链接更合适。该论文是开放获取的，不需要用 ResearchGate。链接：https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012015
bluish29查看英文原文
I don't know if there is a rule about science papers links, but I think using the journal paper link [1] is more suitable. The paper is open access, so no need for research gate. [https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012015]
补充询问学术界对论文的讨论平台，指出 ResearchGate 缺乏实质讨论。
如果我想知道学界对某篇论文的看法，可以去哪里找相关讨论？我以为 ResearchGate 可能是这样的地方，但通常在那里的论文页面看不到讨论。我知道有时能找到论文发表前的同行评审意见，但我想找的是其他科学家的评论。
danilor查看英文原文
If I wanted to know what the community thought of a particular paper, is there a place where I can find a discussion of it? I thought maybe researchgate was the place, but I usually don't see discussion on the paper submission there. I know sometimes you can find the peer reviewer comments before the paper got published, but what I mean is comments from other scientists.
质疑论文摘要过于专业，非专家难以理解。
好吧，摘要里明明都是英文单词，但我完全不知道它们是什么意思。有没有人能给出一个非专家也能看懂的概述？
ndsipa_pomu查看英文原文
Okay, the abstract clearly had english words in there, but I've got no idea what they mean. Does anyone have an overview that would make sense to a non-expert?
相关资源
从这篇论文所有 HN 讨论帖的全部评论里整理出来的链接。
历次讨论
- 2023Hacker News 讨论帖191 分 · 86 评
同领域还值得读
LIGO 探测到第二个引力波
Second Gravitational Wave Detected at LIGO
LIGO 宣布探测到第二个双黑洞并合产生的引力波信号（GW151226）。
物理与天文2016 · 621 分 · 174 评入门 · 约 20 分钟编辑精选W 玻色子质量测量显示与理论计算存在 7σ 偏差
Measurement of the W boson mass reveals 7σ deviation from calculations
对 W 玻色子质量的测量结果与标准模型理论计算存在 7σ 的偏差，远超统计学显著性标准，可能暗示新物理的存在。
物理与天文2022 · 356 分 · 151 评进阶 · 约 60 分钟编辑精选涌现引力与暗宇宙
Emergent Gravity and the Dark Universe
Verlinde 的这篇论文提出“涌现引力”理论，认为引力并非基本相互作用，而是由时空的量子信息（熵）涌现而来，并据此试图在不引入暗物质粒子的情况下解释星系旋转曲线等通常归因于暗…
物理与天文2016 · 219 分 · 81 评 · 引用 7专业 · 约 120 分钟编辑精选Feynman：用计算机模拟物理（1981）
Feynman: Simulating Physics with Computers (1981)
这是费曼 1981 年的经典演讲论文，探讨用计算机模拟物理系统（尤其是量子系统）的问题。
物理与天文2016 · 187 分 · 22 评入门 · 约 60 分钟编辑精选量子世界中观察者独立性的实验否证
Experimental rejection of observer-independence in the quantum world
报告了一个检验观察者独立性的量子实验，借助多观察者版本的 Wigner's Friend 场景，考察不同观察者获得的测量结果是否能被视为客观、观察者无关的事实。
物理与天文2019 · 187 分 · 111 评 · 引用 4专业 · 约 50 分钟编辑精选