From dynamics of quantum measurement to the interpretation of quantum mechanics

by Theo M. Nieuwenhuizen (Institute for Theoretical Physics University of Amsterdam)

Tuesday 10 May 2022, 12:00 → 14:00 Europe/Rome

Aula 5 (Dipartimento di Fisica - Ed Fermi)

Since the only point of contact between the quantum formalism and the reality in a laboratory lies in quantum measurement, the interpretation of quantum mechanics should be based on the analysis of this process. The ``Curie-Wesis model for quantum measurement'' is rich enough for this task.It models the measurement of the $z$-component of a spin $\frac{1}{2}$ by an apparatus which is an Ising magnetconsisting of $N \gg1$ spins $\frac{1}{2}$, coupled to a thermal bath. The Born rule follows because $s_z$ is conserved in the dynamics; the disappearance of $\langle s_x\rangle$ and $\langle s_y\rangle$(truncation of the off-diagonal elements of the density matrix) is a dynamical effect, akin to $T_2$ relaxation in quantum optics.On a longer timescale, the measurement gets registered when the apparatus goes from its initial metastable paramagnetic stateto its stable up or down ferromagnetic state, correlated to $s_z$ being up or down. The bath is essential for this dynamics, including the dumping of excess free energy. In this approach, the density matrix is an abstract quantity which codes our best information about the ensemble of systems (here: spins) on which an ensemble of measurements is performed. Postulates are needed after solving the dynamics; they are weaker than the usual Copenhagen postulates. In particular, the Born rule is related to the pointer indications of the apparatus, while the frequency interpretation of probabilities is encountered along the way. In the ensuing version of the statistical interpretation, there is no need for notions such as ``many worlds’’ or ``the wave function of the system’'.