The Topological Origin of Quantum Randomness

What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the '4 pi-realm') lead to a probabilistic behaviour of observables in space-time (the '2 pi-realm')? We propose a simple topological model for quantum randomness. Following Kauffmann, we elaborate the mathematical structures that follow from a distinction (A,B) using group theory and topology. Crucially, the 2:1-mapping from SL(2,C) to the Lorentz group SO(3,1) turns out to be responsible for the stochastic nature of observables in quantum physics, as this 2:1-mapping breaks down during interactions. Entanglement leads to a change of topology, such that a distinction between A and B becomes impossible. In this sense, entanglement is the counterpart of a distinction (A,B). While the mathematical formalism involved in our argument based on virtual Dehn twists and torus splitting is non-trivial, the resulting haptic model is so simple that we think it might be suitable for undergraduate courses and maybe even for High school classes.

Automated summary

The study proposes a topological model to explain the origin of quantum randomness, elaborates on the mathematical structures behind quantum randomness using group theory and topology, and points out that the 2:1-mapping from SL(2,C) to SO(3,1) plays a crucial role in the observable aspects of quantum physics. Additionally, entanglement leads to a change in topology that makes the distinction between A and B impossible.