Is Information a conserved quantity or not?

[Pythagorean]

TL;DR Summary

Could a variable who's measured values are a countable infinite set still be a conserved quantity?

I've been wondering about statespace. Classically, we assume statespace is infinite (presumably so that we can depend on smooth, differentiable manifolds). But even in quantum, we assume a smooth space and time on which we define wave functions and operations (at least in undergrad quantum, that was the treatment).

I've been watching Susskin's lectures on Quantum Gravity (don't groan yet) and thinking about the entanglement-wormhole thought experiment and wondering about space topologically. Would these topological treatments around quantum/gravity unification not also suggest infinite states?

If you accept that availability of states is infinite in both classical and quantum treatment, then, by extension is information infinite (I couldn't find a single definition of information)?
And does that imply whether it's a conserved quantity or not?
Can we measure whether information is a conserved quantity or is statespace space more axiomatic in physics than empirical?

 

[anorlunda]

Summary: Could a variable who's measured values are a countable infinite set still be a conserved quantity?

I've been watching Susskin's lectures on Quantum Gravity

Your question is discussed well in lecture 1 of Susskind's Statistical Mechanics course.

 

[Geoffrey Tobin]

Short answer to Summary Question: Yes.
Proof by examples: Angular momentum, Electric Charge, Hadron number, Lepton number.

 

[Mark44]

Thread closed.
The stated summary -- "Could a variable who's measured values are a countable infinite set still be a conserved quantity?" -- seems to me to be meaningless at best.