A categorical reformulation of nuclear fission physics, treating nuclear states as objects in a symmetric monoidal category and fission processes as morphisms.
Novel perspectives on nuclear physics through the lens of category theory
Nuclear configurations form objects in a symmetric monoidal category. Fission processes are morphisms preserving conservation laws.
B: Nucl → Energy maps configurations to binding energies. Functoriality captures compositional energy accounting.
Charge and baryon conservation emerge as constraints on morphism existence. Illegal transitions have no representation.
Chain reactions modeled as coalgebras over branching functors. Neutron multiplication emerges naturally.
Conservation laws enforced at compile time using GADTs and type families. Invalid fissions fail to compile.
Complete Haskell implementation demonstrates that categorical abstractions translate to working code.
Rigorous categorical foundations for nuclear fission physics
Type-safe, executable categorical physics
-- | The Binding Energy Functor on objects bindingFunctorObj :: SEMFCoefficients -> NuclearConfig -> MeV bindingFunctorObj coef (NuclearConfig ns) = sum $ map (bindingEnergy coef) ns -- | The Binding Energy Functor on morphisms bindingFunctorMor :: SEMFCoefficients -> NuclearMorphism -> MeV bindingFunctorMor coef (NuclearMorphism src tgt _) = bindingFunctorObj coef tgt - bindingFunctorObj coef src
-- | Type-safe fission with conservation laws enforced at compile time data SafeFission src tgt where SafeFission :: (TotalZ src ~ TotalZ tgt, TotalA src ~ TotalA tgt) => TConfig src -> TConfig tgt -> SafeFission src tgt -- This compiles: U-236 → Ba-141 + Kr-92 + 3n (conserves A and Z) exampleFission :: SafeFission '[TNuclide 236 92] '[TNuclide 141 56, TNuclide 92 36, TNuclide 1 0, TNuclide 1 0, TNuclide 1 0] exampleFission = SafeFission source target
Full arXiv-style treatment with rigorous mathematics
Mass–Energy Equivalence, Binding Energy, and Chain-Reaction Dynamics in a Categorical Framework
We present a categorical reformulation of nuclear fission physics, treating nuclear configurations as objects in a symmetric monoidal category and fission processes as morphisms preserving essential structure. The binding energy function is elevated to a functor B: Nucl → Energy, and conservation laws (charge, baryon number, energy-momentum) emerge as natural transformations. Chain-reaction dynamics are modeled coalgebraically, with neutron multiplication captured by coalgebras over a branching functor...