Hello everyone,
I originally intended to write an essay on Quantum Geometry for an undergraduate Geometry class, but I ran into some problems. Although there is plenty of information available on thebasics of the Heisenberg Uncertainty Principle and Planck's Constant, there doesn't seem to be any information available on how this affects the behavior of points, lines, plains, and half planes (the undefined terms of neutral geometry) on a quantum scale. Would it even be possible to use the basic theorems of Neutral Geometry? Does a Euclidean model fit Quantum Geometry? Is a completely different set of axioms required to work with Quantum Geometry? Do I need a good understanding of calculus even to work with Quantum Geometry? I tried asking my professor, but this seems to require knowledge of both theoretical particle physics and Geometry.
