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 whether quantum predictions allow a joint distribution by solving the moment problem

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

#012: Product of observables

Category: Quantum mechanics - Tags: Linear operators, Hilbert spaces

#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