2023-04-11 - 2023-04-14
Christof Wetterich
Heidelberg University
Quantum mechanics and quantum field theory can be understood as part of classical statistics.
Classical statistical systems are characterized by a positive probability distribution. The axioms of quantum mechanics follow from the simple standard laws for probabilities.
Wave functions and operators are useful concepts for general classical statistical systems, not only for quantum mechanics. We explain the quantum formalism for general probabilistic systems. „Classical wave functions" correspond to the Schrödinger picture, while the Heisenberg picture is given by the well known transfer matrix formalism. The particularity of quantum systems is the unitary time evolution which is not shared by general classical statistical systems.
We develop probabilistic cellular automata as simple examples for classical statistical systems with a unitary time evolution. While the updating steps are deterministic, similar to the treatment of bit configurations for classical computers, the probabilistic aspects enter by a probability distribution for the very large number of initial bit configurations. We describe automata that correspond to discrete quantum field theories for fermions. This uses the direct correspondence between fermionic occupation numbers and bits. In particular, we propose an automaton with randomly distributed scattering points whose continuum limit describes a quantum particle in a potential in one space dimension.
