Quantum Mechanics of Large Systems

Theory

Quantum mechanics is a statistical theory (see, e.g., Margenau [239, 240], Ballentine [25, 26], Klyshko [216], Holevo [115, 116], Khrennikov [192]). It cannot tell us anything about an individual quantum system, e.g., an electron or a photon. It predicts only probabilities for results of measurements for large ensembles of quantum systems. Classical statistical mechanics (CSM) does the same.Why are QM and CSM based on different probabilistic models?

Luca Salasnich

Vyacheslav Lysov, Yasha Neiman

In the mid-19th century, both the laws of mechanics and thermodynamics were known, and both appeared fundamental. This was changed by Boltzmann and Gibbs, who showed that thermodynamics can be *derived*, by applying mechanics to very large systems, and making simple statistical assumptions about their behavior. Similarly, when Quantum Mechanics (QM) was first discovered, it appeared to require two sets of postulates: one about the deterministic evolution of wavefunctions, and another about the probabilistic measurement process. Here again, the latter is derivable from the former: by applying unitary evolution to large systems (apparatuses, observers and environment), and making simple assumptions about their behavior, one can derive all the features of quantum measurement. We set out to demonstrate this claim, using a simple and explicit model of a quantum experiment, which we hope will be clear and compelling to the average physicist.

Jürg Fröhlich, Alessandro Pizzo

This note starts with a recapitulation of what people call the ``Measurement Problem'' of Quantum Mechanics (QM). The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical isolated systems consisting of matter interacting with the radiation field is discussed and shown to correspond to a stochastic time-evolution of states of individual systems. The importance of dissipation for the successful completion of measurements is highlighted. To conclude, a solution of the ``Measurement Problem'' is sketched in an idealized model of a double-slit experiment.

Akakii Melikidze

Hannah Troger, Ofek Bengyat, Thomas D. Galley +1 more

The standard description of the state of a spin in quantum mechanics presupposes externally fixed directions -- a classical background. Can a spin be fully described instead in relation to other quantum mechanical systems? Poulin suggested twenty years ago group averaging over rotations the joint state of a fundamental spin and a reference spin with large angular momentum which, however, yields a classical bit in a probabilistic mixture. We revisit this idea and show that when the quantum reference system is augmented to \emph{two} large spins, the standard quantum mechanical description of a spin is recovered in the limit of large quantum numbers for the reference system.