jim360 //
I'll have a look at the original papers if I can. But I fancy that I understand QM rather better than Reuters does. It -- and you -- are confusing the concept of superposition, when a particle exists in a number of states simultaenously, but is not being observed, with what happens after it was observed. If you went and watched that particle, you would see it stationary, or in motion, but not both. Before that observation, it could have been both, but it could not have been both while being seen. //
You are confused about the nature of observation. It is as though you believe that the light being reflected into the human eye directly from the object is a special thing.
In this experiment they saw "Each version of the atom interfered with the other in a measurable way". Hence they observed the atom in both positions simultaneously. Otherwise it would not have behaved in this way.
What is important is they did this without bringing it out of the Quantum superpositioned state. It worked because they did not detect the exact location of the atom, just that it behaved as though it was in both those locations at the same time.
This proved beyond any doubt that a common classical reinterpretation of Quantum Mechanics is wrong. Many scientists including Einstein were convinced that the system is in one state or the other and we simply have no way of predicting it prior to the observation.
Or as you put it:
"But while there is no observation being made, our ignorance of its location can be captured by a mathematical statement that implies that, before a measurement, the particle could equally well be in any of two places (or three or four or indeed anywhere). "
It isn't a matter of it being in ANY of the places before the observation, it is a case of it simultaneously being in ALL of those places.
Your misunderstanding is very common.