Mathematics Blog

Exploring mathematical concepts, one post at a time

ω F_cf F_cor Centrifugal & Coriolis Forces
Geometric Origin of Fictitious Forces via Christoffel Symbols
Exploring how centrifugal and Coriolis forces arise naturally as connection terms (Christoffel symbols) of curved, coordinate-dependent reference frames in flat spacetime.
July 2026 Mathematical Physics
t x τ₁ τ₂ τ₃ Clock Hypothesis & Observers
Clock Hypothesis and Observer in General Relativity
Exploring clock hypothesis and its application to observers on general trajectories within curved spacetime manifolds.
June 2026 General Relativity
Ω Ω' εθ δS = δS(boundary) + δS(internal) Boundary deformations in Noether's theorem
Noether's Theorem Done Right: Boundaries Matter
A rigorous derivation of Noether's conserved currents, paying careful attention to surface terms, domain deformations, and gauge invariance where the Lagrangian changes by a total derivative.
May 4, 2026 Classical Mechanics
Solenoid with magnetic flux A ≠ 0 where B = 0: Aharonov-Bohm effect
The Aharonov-Bohm Effect: Why topology of domain matters
Exploring how the vector potential A can have physical effects even in regions where the magnetic field B is zero. A quantum mechanical phenomenon that reveals the topological nature of electromagnetism.
December 31, 2025 Quantum Mechanics