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Discuss physics perspective

Vectornaut 2025-01-24 20:58:51 +00:00
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Elements-and-observables.md

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## 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
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## 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