Excited-state decay in strictly Everett-like interpretations of quantum mechanics

TL;DR

This paper investigates excited-state decay within strictly Everett-like interpretations of quantum mechanics, revealing limitations in parameter determination and providing bounds on the probability epsilon, thus challenging the completeness of SEL formulations.

Contribution

It demonstrates that SEL formulations require additional parameters and cannot fully specify excited-state decay without external assumptions, contrasting with Everett's original superposition approach.

Findings

Wave function branch topology is consistent across SEL formulations.

The decay rate parameter lambda_A relates to lambda_B and epsilon as lambda_A = (1-epsilon) lambda_B.

An upper limit of 0.1% is established for epsilon based on current experimental data.

Abstract

Excited state decay is examined within the framework of strictly Everett-like (SEL) formulations of quantum mechanics. Even though these formulations were developed for systems of particles as part of a larger system that includes a measurement apparatus, the analysis is carried out in terms of isolated particles because excited state decay measurements are performed under conditions that approximate isolation. It is shown that the time evolution of the wave function describing each particle in a sample of well-isolated identical particles in their lowest excited state must satisfy the same branch topology for all strictly SEL formulations. This topology describes a countably infinite sequence of random branching events that occur at a rate lambda_B for each particle in the sample. Two more parameters are required: lambda_A, the expectation value of the excited-state decay rate determined by an observer state measuring the lifetime of the particles, and epsilon, the probability that an observer state that branches off an observer state associated with the excited state is associated with the excited state following the branching event. There does not appear to be any way to determine the value of epsilon within the framework of SEL formulations. Therefore, contrary to Everett's goal, SEL interpretations do not provide a complete description of every system. However, it is possible to show that lambda_A = (1-epsilon) lambda_B, which with the agreement between theoretical and experimental lifetime determinations provides a conservative upper limit of 0.1% for epsilon at the current state of the art. This result is very different from the example of a superposition of states originally considered by Everett wherein the probability of each final state is given by the conventional Born's rule and no new parameters are required.