# A Quantum Space Behind Simple Quantum Mechanics. (arXiv:1603.05371v4 [quant-ph] UPDATED)

In physics, experiments ultimately inform us as to what constitutes a good

theoretical model of any physical concept: physical space should be no

exception. The best picture of physical space in Newtonian physics is given by

the configuration space of a free particle (or the center of mass of a closed

system of particles). This configuration space (as well as phase space), can be

constructed as a representation space for the relativity symmetry. From the

corresponding quantum symmetry, we illustrate the construction of a quantum

configuration space, similar to that of quantum phase space, and recover the

classical picture as an approximation through a contraction of the (relativity)

symmetry and its representations. The quantum Hilbert space reduces into a sum

of one-dimensional representations for the observable algebra, with the only

admissible states given by coherent states and position eigenstates for the

phase and configuration space pictures, respectively. This analysis, founded

firmly on known physics, provides a quantum picture of physical space beyond

that of a finite-dimensional manifold, and provides a crucial first link for

any theoretical model of quantum spacetime at levels beyond simple quantum

mechanics. It also suggests looking at quantum physics from a different

perspective.