This is a mathematical fact which makes no reference to where the particles are located in space. It is true for the ground state of a hydrogen atom, in which the electron and proton are on top of each other, as well as for the situation we consider next in which particle \(a\) is in Alice’s laboratory and \(b\) in Bob’s laboratory some distance away. Suppose that Alice measures \(S_{az}\) for her particle and Bob measures \(S_{bz}\) for his. Then using \([\psi_0]\) as a pre-probability, subsection 3.5, one can show that the outcomes, although they are random, will always be opposite: if Alice obtains \(+1/2\) (in units of \(\hbar\)), Bob will find \(-1/2\); if Alice obtains \(-1/2\), Bob will find \(+1/2\).