Towards noncommutative quantum reality

The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and 'interpretation' of the theory remains controversial. Through a careful analysis of the theoretical notions with the help of modern mathematical perspectives, we give here a picture of quantum mechanics, as the basic theory for 'nonrelativistic' particle dynamics, that can be seen as being as much about the physical reality as classical mechanics itself. The key is to fully embrace the noncommutativity of the theory and see it as a notion about the reality of physical quantities. Quantum reality is then just a noncommutative version of the classical reality.