The Emergence of Classical Properties from Quantum Mechanics

L. E. Ballentine

Ricardo Gallego Torromé

We argue that in a framework for emergent quantum mechanics, the weak equivalence principle is a consequence of concentration of measure in large-dimensional spaces of [Formula: see text]-Lipshitz functions. Furthermore, as a consequence of the emergent framework and the properties that we assume for the fundamental dynamics, it is argued that gravity must be a classical, emergent interaction.

Alberto Cordero

CHRISTOF WETTERICH

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables "measure" properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics – the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditiona probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

Hanns Sommer

Roger A. Hegstrom, Alexandra J. MacDermott

Several recent studies have suggested that incompatible variables, which play an essential role in quantum mechanics (QM), are, somewhat surprisingly, not necessarily unique to QM. To investigate this possibility and obtain a better understanding of two central postulates of QM, namely the commutator postulate and the Born postulate, we introduce a classical probabilistic theoretical framework which is more general than QM and contains QM as a special case. We call this framework the General Incompatible Variables (GIV) theory, and we show that not only QM systems but also any probabilistic systems (classical or quantal) that possess incompatible variables will exhibit the quantal properties of uncertainty and interference, and we illustrate this with a roulette-like classical system (which we call the Arrow) that shows precisely these properties. We show that QM emerges naturally from the GIV framework when the fundamental variables are taken to be symmetries, so that the incompatibility of the QM variables is actually just the incompatibility of the corresponding symmetries (or their generators). Specifically, when the variables are taken to be the elements of the Poincare group (the symmetry of spacetime) we find that the commutator postulate and the Born postulate follow automatically, and are therefore no longer postulates. QM thus emerges as a special case of GIV theories for which the variables are symmetries.