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.

Article web page: