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