Are wave functions real physical objects? Are wave functions (ex. electron waves) real physical objects or just mathematical tools?. Some researchers say that they have proof that they are real objects. Here's [the link]
(http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392)
Does this mean that wave functions are real objects, after all?
 A: This question was already discussed and under several forms before, see the comments. Though, it addresses directly a problem that in other questions appears as a side-issue. 
The answer is we don't know for sure. Certainly, in experiments on quantum systems, there is a reality travelling through our apparatuses.
So, I would suggest to reformulate the question as: is the wave-function an exact description of that reality, s.t. instead of saying 1) "we have in the apparatus a quantum object prepared in the wave-function $\psi$ ", we can allow ourselves to say 2) "we have in the apparatus the wave-function $\psi$?
Well, the answer is double. As long as the reality in the apparatus was not measured with a classical apparatus, the best description of the reality in the apparatus is the wave-function, we had no bad surprises about this. So, the expression 2) is in fact quite used de facto. But the wave-function is not able to explain the so-called collapse, i.e. why from a set of possible outcomes of a measurement, we get a particular one, i.e. how that one result is chosen. Here, already, we have doubts whether we may use 2) instead of 1).
There are facts that encourage us to use 2) as explained above. Not only the wave-function predicts correctly probabilities of results, but it also explains well (models well) the evolution of the reality in all the stages prior to the measurement with a classical apparatus, i.e. when we pass that reality through fields, different splitters, when we produce entangled systems (again, before we measure them with classical apparatuses). 
