陶哲轩博客写数学问题时，通常先把对象定义清楚，再给直觉、反例和证明轮廓。把「Quantum mechanics and Tomb Raider」改写成可阅读的中文笔记，重点是：问题在问什么、已知到哪一步、下一步最容易走偏在哪。原站广告、分享条和导航已去掉。

问题在问什么

This post is derived from an interesting conversation I had several years ago with my friend Jason Newquist on trying to find some intuitive analogies for the non-classical nature of quantum mechanics. It occurred to me that this type of informal, rambling discussion might actually be rather suited to the blog medium, so here goes nothing…

Quantum mechanics has a number of weird consequences, but here we are focusing on three (inter-related) ones:

已知结果和反例

In trying to come up with a classical conceptual model in which to capture these non-classical phenomena, we eventually hit upon using the idea of using computer games as an analogy. The exact choice of game is not terribly important, but let us pick Tomb Raider – a popular game from about ten years ago (back when I had the leisure to play these things), in which the heroine, Lara Croft , explores various tombs and dungeons, solving puzzles and dodging traps, in order to achi

The thing about such games is that there is an “internal universe”, in which Lara interacts with other game elements, and occasionally is killed by them, and an “external universe”, where the computer or console running the game, together with the human who is playing the game, resides. While the game is running, these two universes run more or less in parallel; but there are certain operations, notably the “save game” and “restore game” features, which disrupt this relations

证明或构造的主线

Imagine first that Lara is about to navigate a tricky rolling boulder puzzle, when she hears a distant rumbling sound – the sound of her player saving her game to disk. Let us suppose that what happens next (from the perspective of the player) is the following: Lara navigates the boulder puzzle but fails, being killed in the process; then the player restores the game from the save point and then Lara successfully makes it through the boulder puzzle.

Now, how does the situation look from Lara’s point of view? At the save point, Lara’s reality diverges into a superposition of two non-interacting paths, one in which she dies in the boulder puzzle, and one in which she lives. (Yes, just like that cat .) Her future becomes indeterministic. If she had consulted with an infinitely prescient oracle before reaching the save point as to whether she would survive the boulder puzzle, the only truthful answer this oracle could give i

阅读时建议盯住的点

This simple example shows that the internal game universe can become indeterministic, even though the external one might be utterly deterministic. However, this example does not fully capture the weirdness of quantum mechanics, because in each one of the two alternate states Lara could find herself in (surviving the puzzle or being killed by it), she does not experience any effects from the other state at all, and could reasonably assume that she lives in a classical, determi

So, let’s make the game a bit more interesting. Let us assume that every time Lara dies, she leaves behind a corpse in that location for future incarnations of Lara to encounter. (This type of feature was actually present in another game I used to play , back in the day.) Then Lara will start noticing the following phenomenon (assuming she survives at all): whenever she navigates any particularly tricky puzzle, she usually encounters a number of corpses which look uncannily l

值得单独记下的条目

• Objects can behave both like particles (with definite position and a continuum of states) and waves (with indefinite position and (in confined situations) quantised states);
• The equations that govern quantum mechanics are deterministic, but the standard interpretation of the solutions of these equations is probabilistic; and
• If instead one applies the laws of quantum mechanics literally at the macroscopic scale, then the universe itself must split into the superposition of many distinct “worlds”.

阅读和落地时建议先做的 5 件事

1. 用自己的语言重写定义和结论，不看原文能不能说清对象是什么。
2. 找一个最小反例或边界情形，确认假设少一条会怎样。
3. 把证明拆成可独立检验的引理，每步只保留一个新想法。
4. 若涉及计算或形式化，先写可复现的小例子，再谈一般情形。
5. 记下尚未解决的缺口：缺估计、缺构造，还是缺正确的范畴。

和智能体、形式化工具怎么接

龙虾PRO做 OpenClaw 落地时，数学笔记最有用的部分往往是「可检验的步骤」：定义、反例、引理边界。智能体适合帮忙展开计算和检索，不适合代替你决定哪条假设能扔。

本文侧重全链路风控方法论。落地时请用自身业务单据做回放验证，不要把示例阈值直接当生产策略。 相关：风控体检 · 方案资源