Formally Defining Wavefunction Branches

[LW Meta: This post is (a) about how wavefunction branching explains measurements and why chaotic dynamics don't cause the quantum state to become non-classical-looking (b) the mathematical problem of formally defining wavefunction branches. The former will be familiar to people who've read Eliezer's quantum sequence, but the latter is new to LW to my knowledge!] 2.5.4 The Emergence of Classicality 2.5.4.1 In 2.5.2 I left open two questions about quantum mechanics and seemingly-classical reality. Namely, (b) how does the world stay in a relatively-classical state, and (c) what happens when we take a measurement? It turns out the answer to both questions is the same, and it involves the information-proliferating dynamics discussed in section 2.4. 2.5.4.2 Let's examine the Stern-Gerlach experiment in more detail. In this experiment a stream of neutral silver atoms is propelled through a non-uniform magnetic field and strikes a screen. The interaction of the magnetic field with the spin is described by the Hamiltonian mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0; } mjx-container[jax="CHTML"][display="true"] { display: block; text-align: center; margin: 1em 0; } mjx-container[jax="CHTML"][display="true"][width="full"] { display: flex; } mjx-container[jax="CHTML"][display="true"] mjx-math { padding: 0; } mjx-container[jax="CHTML"][justify="left"] { text-align: left; } mjx-container[jax="CHTML"][justify="right"] { text-align: right; } mjx-msub { display: inline-block; text-align: left; } mjx-TeXAtom { display: inline-block; text-align: left; } mjx-mover { display: inline-block; text-align: left; } mjx-mover:not([limits="false"]) { padding-top: