From ec7a5f3cf2249be4b888c2e404090e18b964ad96 Mon Sep 17 00:00:00 2001 From: Vectornaut Date: Fri, 24 Jan 2025 20:58:51 +0000 Subject: [PATCH] Discuss physics perspective --- Elements-and-observables.md | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/Elements-and-observables.md b/Elements-and-observables.md index 7ab2dbd..4ac2b78 100644 --- a/Elements-and-observables.md +++ b/Elements-and-observables.md @@ -1,6 +1,11 @@ ## Separation -Elements don't interact directly with each other, and constraints don't interact directly with each other either. In other words, the graph of direct interactions among elements and constraints is bipartite. +### General thoughts + +* In physics, there's a long and successful tradition of thinking about states and observables as distinct and dual to each other. + * Specifying consistent values for enough observables picks out a state. + * Elements correspond to state space building blocks. +* Elements don't interact directly with each other, and constraints don't interact directly with each other either. In other words, the graph of direct interactions among elements and constraints is bipartite. ### Contrasts @@ -15,6 +20,11 @@ An assembly consisting entirely of elements seems meaningful and potentially use ## Unification +In some physics settings, states can at least resemble observables. + +* A random variable is a function on a measurable space, while a probability distribution is a measure. When the measurable space is finite, however, you can express every probability distribution as a function too, which multiplies the counting measure. +* In a finite-dimensional quantum system, states can be expressed as density operators. + Can we realize constraints as geometric objects? For example: * A real angle constraint might be seen as a pair of infinitesimal ribbons crossing at a fixed angle along a circle