Analogy of Quantum Spin and Matrix Array with Electromagnetic and Gravitational Waves Produced from Pure Mathematics

Abstract

This short article was inspired by the astronomy/astrophysics course “Greatest Unsolved Mysteries of the Universe”. It was prepared by ANU (the Australian National University), was put on the Internet by edX, and the two presenters in the course’s videos are Dr. Paul Francis and Brian Schmidt (yes, the winner of the Nobel Prize for Physics himself). In the video “V5.8: 21 centimetre radiation and the first stars”, Brian said “(To get emission from the hydrogen atom) we're going to have to resort to a little trick of quantum mechanics that is provided for the hydrogen atom, which is that the proton and electron within quantum mechanics have a spin. It's analogous to a top spinning. It turns out that the hydrogen atom has a different energy if those spins are in opposite directions. It turns out it actually has a lower energy and so you can have an energy transition when that flip occurs and a photon comes out.” Then Paul said, “It's a bit like having two bar magnets. If you have them with north pole to north pole, or north pole to south pole, you'll feel a different amount of force between them; a different energy between these two things. When these things are spinning the same way or the opposite way there's a little tiny energy difference between them.” The following explains analogy of quantum spin to maths’ matrix and how, using that analogy, the statements by Brian and Paul can be converted into a mathematical origin of electromagnetism and gravitation.