Physics and math are not what I was taught


This is a running list of corrections to things I thought I knew at one time but which have either proven to be untrue or at least been called into question.

  • Schrödinger did not claim that quantum mechanics says that a cat can be both alive and dead at the same time. (Schrödinger’s cat is a reductio ad absurdum.)
  • Photons are not particles.
  • Spacetime may not be curved.
  • Wormholes may not exist (spacetime may be simply connected).
  • ‘Hidden variable’ theories are possible. (von Neumann was wrong, Feynman was wrong because he believed von Neumann).
  • Particles in quantum mechanics do not travel in straight lines, even in the absence of external forces.
  • Mathematics is not hierarchical except by how it is taught. (You don’t need to know trig to learn calculus.)
  • A rotation through 360° does not return an object in physical 3D space to the same point. A rotation through 720° does.
  • Pauli spin matrices do not arise from quantum mechanics. (They are a matrix representation of quaternions which are perfectly good classical mechanics.)
  • Dirac matrices do not arise from quantum mechanics and specifically are not unique to the Dirac equation. (They are a matrix representation of rotations in 4-dimensional space and are perfectly good relativistic mechanics.)
  • Linear algebra is not the same thing as matrix algebra.