The suggestion that quantum mechanics implies that instantaneous action at a distance occurs is normally based on the contention that this follows from the entanglement of particles that share a common origin. My question is: does quantum mechanics predict that this happens even when there is no entanglement? In particular, does this happen when two quantum systems interact in such a way that the wave function of at least one of them changes drastically?
Take, for example, an interaction between a hydrogen atom and a hydrogen-oxide radical: H + HO = H2O. While the hydrogen atom is free, the wave function of its electron allows it to be anywhere in the universe. Or rather, it is everywhere in the universe. Instantly after the interaction has completed, the amplitude of the quantum wave of the same electron is smaller everywhere, except in the very immediate neighbourhood of the water molecule of which it has become a part. In the rest of the universe, the wave function has taken on other values, if not instantaneously – the reaction could take some time – then at least far quicker than light.
One could object that the electron is never really at more than one point at any one time, only we don’t know which until we make a measurement. But that amounts to a refusal to accept quantum mechanics. The effect of a wave on its environment is determined by the totality of the wave, including even those places where its amplitude is partly or entirely imaginary. For example, the hydrogen atoms in a water molecule are positioned at an angle of 108 degrees from each other, as seen from the oxygen nucleus, due to some very particular properties of the wave functions which define the hydrogen-oxygen bonds. That results in water having some very peculiar properties, including the property that its solid form – ice – is less dense than the liquid form and therefore floats on it. Even the mere stability of water molecules is due to the wave function of the electrons which the hydrogen atoms share with the oxygen atom: in this wave function the electrons are as much as near the oxygen atom as the hydrogen atom.