Conservation Laws in the Quantum Mechanics of Closed Systems

TL;DR

This paper explores how conservation laws in quantum mechanics of closed systems are affected by decoherence, showing that certain quantities are exactly conserved when they decohere, especially when coupled to long-range fields.

Contribution

It demonstrates that decoherence enforces exact conservation of quantities like charge and mass in realistic quantum systems with long-range interactions.

Findings

Exact decoherence implies conservation of commuting quantities.

Decoherence limits the set of histories for non-coupled quantities.

Long-range field couplings ensure exact conservation when decoherence occurs.

Abstract

We investigate conservation laws in the quantum mechanics of closed systems. We review an argument showing that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian including the total energy and total electric charge. However, we also show that decoherence severely limits the alternatives which can be included in sets of histories which assess the conservation of these quantities when they are not coupled to a long-range field arising from a fundamental symmetry principle. We then examine the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature and show that when alternative values of charge and mass decohere, they always decohere exactly and are exactly conserved as a consequence of their couplings to long-range fields. Further, while decohering histories that describe fluctuations in total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict {\it physical} alternatives and are therefore not really limitations at all.