Determination of Model of the Physical Space (Time) from Quantum Mechanics

The physical world is quantum. However, our description of quantum physics still relies much on concepts in classical physics only in some cases with ‘quantized’ interpretations. The most important case example is that of spacetime. We examine the picture of the physical space as really described by simple, so-called non-relativistic, quantum mechanics instead of assuming the Newtonian model. The key perspective is that of (relativity) symmetry representation, and the idea that the physical space is to be identified as the configuration space for a free particle. The usual quantum phase space comes up as the answer, with an intuitive noncommutative geometric picture embodying the necessary notion of noncommutative values of physical quantities. Lorentz covariant version of the theory with a quantum model of the physical spacetime is also sketched. The formulations are fully group theoretically based with proper limits retrieving lower level theories including the classical ones with the corresponding spacetime models obtained from the contraction limit of the (relativity) symmetries.