Abstract
What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the ‘4π-realm’) lead to a probabilistic behaviour of observables in space-time (the ‘2π-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.
Highlights
The stochastic nature of quantum physics is an experimental fact beyond any doubt.The debate on the interpretation and the origin of quantum randomness is as old as quantum physics itself
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
While there are many complex and interesting questions waiting for future research, we advocate the striking simplicity of the haptic model for quantum randomness as proposed in Figure 1, which might be of merit for didactical approaches to quantum and to particle physics
Summary
The stochastic nature of quantum physics is an experimental fact beyond any doubt. The debate on the interpretation and the origin of quantum randomness is as old as quantum physics itself. Of central importance in that context is the fact that measurable properties of a quantum system, which are considered part of our accessible physical reality, seem to be inherently random in nature, while their mathematical representations are at all times welldefined. The recognition of this gap between well-defined mathematical representation and observable reality gives rise to several questions, which are closely related to each other. The simple and intuitive haptic model for quantum randomness as shown, seems to have its deeper origin in the fact that this 2:1-mapping from quantum states into space-time is impossible during interactions, that is, while the topology of the quantum states is changed. While there are many complex and interesting questions waiting for future research, we advocate the striking simplicity of the haptic model for quantum randomness as proposed in Figure 1, which might be of merit for didactical approaches to quantum and to particle physics
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