# Problems

##### This is a list of open questions we have. Any help towards their solution is welcome.

**#001: Classical mechanics as high entropy limit of quantum mechanics**

*Category: Quantum mechanics - Tags: Quantum information, Classical limit, Entropy*

**#002: Properly extend the classical uncertainty relationship to multiple d.o.f.**

*Category: Classical mechanics - Tags: Classical information, Hamiltonian mechanics, Entropy*

**#003: Characterize the expression \( G_{\alpha\beta\gamma} = \partial_\alpha g_{\beta \gamma} - \partial_\beta g_{\alpha \gamma} \)**

*Category: Classical mechanics - Tags: Differential geometry, Riemannian geometry, Symplectic geometry, General relativity*

**#004: See how much of relativity is already there in the particle equation**

*Category: Classical mechanics - Tags: Differential geometry, Riemannian geometry, Symplectic geometry, General relativity*

**#005: Find a better mathematical characterization for quantum states**

*Category: Quantum mechanics - Tags: Vector spaces, Function spaces*

**#006: Is the continuum hypothesis relevant in physics?**

*Category: Mathematical foundations - Tags: Set theory, Topology*

**#007: Can the current logic axioms be simplified?**

*Category: Mathematical foundations - Tags: General theory, Mathematical logic, Boolean algebra, Heyting algebra, sigma-algebra*

**#008: Special relativity as a theory of integration**

*Category: Special relativity - Tags: Classical mechanics, Riemannian geometry, Measure theory*

**#009: Determine whether quantum states are stable equilibria**

*Category: Quantum mechanics - Tags: Hilbert spaces, Vector spaces, Projections*

**#010: A classical analogue for relativistic spin**

*Category: Classical mechanics - Tags: Quantum mechanics, spin, Hamiltonian mechanics, symplectic geometry*

**#011: Determine the relationship between quantum and classical moment problems**

*Category: Probability theory - Tags: Quantum mechanics, Statistics, Measure theory*

**#012: Product of observables**

*Category: Quantum mechanics - Tags: Linear operators, Hilbert spaces, \*-algebra*

**#013: Find correct morphisms for experimental domains**

*Category: Mathematical foundations - Tags: General theory, Category theory, Mathematical logic, Order theory*

**#014: Characterize the space of domain relationships**

*Category: General topology - Tags: General theory, Point-set topology, Order theory*

**#015: More in depth exploration of coordinate invariant measures**

*Category: Measure theory - Tags: General theory, Classical mechanics, Complex analysis*

**#016: Characterize quantum projections and entropy maximization processes with constraints**

*Category: Quantum mechanics - Tags: Quantum mechanics, Quantum information*

**#017: Is space flat?**

*Category: General relativity - Tags: Differential geometry, Riemannian geometry*

**#018: Express Liouville theorem for position and velocity**

*Category: Classical mechanics - Tags: Differential geometry, Riemannian geometry*

**#019: Show equivalence of "inner products"/bilinear forms and trigonometry**

*Category: Linear algebra - Tags: Riemannian geometry, Pseudo-Riemannian geometry, symplectic geometry*

**#020: Ensemble spaces as convex spaces**

*Category: Geometry - Tags: Synthetic geometry, Affine geometry, Projective geometry*