Hydrogen atoms binding and electron/positrons

If you have two hydrogen atoms with electrons with similar spin, they will cause repulsion and do not bind. If you have two hydrogen atoms with electrons with opposite spin, they will attract and bind and stay together.

If you have two electrons they will cause repulsion and do not bind, stay together. If you have an electron and positron they will attract and ‘bind’ and ‘stay together’ as a photon.

Rotational angular momentum and mach paradox

If you have a heat bath at room temperature where a CO molecule sits in. There is enough energy for the CO molecule to be in the l=1 state. Now it can release this energy and send out a photon, it will fall down to the l=0 state. But now the CO molecule stops rotating.

However this seems weird. Because if you have a rotating frame w.r.t. the CO molecule at first he/she will see the CO molecule standing still. Then it will send out a photon and start rotating. This doesn’t make sense to that observer. So then he can conclude that he is in a rotating frame. He also can conclude that all the forces he was seeing (centrifugal, coriolis etc) are actually fake. Seems like you can solve machs problem right there

Opaque derivations

What makes a derivation opaque? Some derivations are obviously rigorous and neat, but so opaque. These should be avoided because nothing can be understood from it, only the truth of the statement. Understanding the machinery of a proof is very important.