Quantum decoherence in a pragmatist view: Part I

The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum probabilities as a guide to their truth. The content of a claim is to be understood in terms of its role in inferences. This promises a better treatment of meaning than that of Bohr. Quantum theory models physical systems with no mention of measurement: it is decoherence, not measurement, that licenses application of Born’s probability rule. So quantum theory also offers advice on its own application. I show how this works in a simple model of decoherence, and then in applications to both laboratory experiments and natural systems. Applications to quantum field theory and the measurement problem will be discussed elsewhere.

💡 Research Summary

The paper presents a pragmatist interpretation of quantum theory in which quantum decoherence, rather than measurement, supplies the normative content for claims about physical magnitudes and determines when the Born rule may be applied. The author begins by contrasting the traditional Copenhagen view—where meaning and probability are tied to an external act of measurement—with a pragmatist stance that defines the “content” of a claim in terms of its role in inferences. In this framework a statement such as “the spin‑z component is +½” acquires meaning only insofar as it participates in a network of inferential relations that become stable once decoherence has singled out a preferred basis.

A concrete model is introduced to illustrate the idea. Two spin‑½ particles interact with a large bath of harmonic oscillators via a Hamiltonian of the form
(H = H_S + H_E + g,\sigma_z\otimes\sum_k(a_k + a_k^\dagger)).
Starting from a pure product state, the reduced density matrix of the system is computed. For times longer than the decoherence time (\tau_D) the off‑diagonal elements decay exponentially, leaving a diagonal matrix in the (\sigma_z) eigenbasis. This “pointer basis” is the result of the environment continuously recording the σz value; consequently the two mutually exclusive claims “σz = +½” and “σz = –½” become inferentially independent and can be treated with classical logic.

The crucial move is to show that decoherence itself supplies a meta‑rule for the use of the Born rule. When the system‑environment interaction has proceeded for at least (\tau_D), the probability (p(+½)=\mathrm{Tr}