This is a very simplified colloquial way of stating a concept that also makes it seem mysterious. The state of an electron is described by a vector 'v' in a 2D complex vector space. Now, to actually talk about the vector concretely you should choose a basis. Suppose your basis is one in which the vector 'v' is not parallel to any of the basis vectors. Then you can say the vector v is "somewhere in between basis vectors e1 and e2". No magic in the way I have stated it. There is a little bit of fake magic when you start thinking about the random measurement results you get when you measure the electron in state 'v'. But these effects can be simulated in a classical deterministic universe.
The real magic of quantum mechanics is in entanglement which can't be simulated in a classical deterministic universe. But that is a much longer story.
Now to answer your question, yes there is lots of physical evidence that this non-deterministic description of systems is a good model of reality. This comment box is too small to state it. People are currently in the process of determining if this probabilistic description is a good one outside of the mathematical framework of QM. See http://www.nature.com/news/quantum-physics-what-is-really-re...
This is a very simplified colloquial way of stating a concept that also makes it seem mysterious. The state of an electron is described by a vector 'v' in a 2D complex vector space. Now, to actually talk about the vector concretely you should choose a basis. Suppose your basis is one in which the vector 'v' is not parallel to any of the basis vectors. Then you can say the vector v is "somewhere in between basis vectors e1 and e2". No magic in the way I have stated it. There is a little bit of fake magic when you start thinking about the random measurement results you get when you measure the electron in state 'v'. But these effects can be simulated in a classical deterministic universe.
The real magic of quantum mechanics is in entanglement which can't be simulated in a classical deterministic universe. But that is a much longer story.
Now to answer your question, yes there is lots of physical evidence that this non-deterministic description of systems is a good model of reality. This comment box is too small to state it. People are currently in the process of determining if this probabilistic description is a good one outside of the mathematical framework of QM. See http://www.nature.com/news/quantum-physics-what-is-really-re...