Bohmian Mechanics as a Practical Tool

TL;DR

This paper explores how Bohmian mechanics can serve as a practical computational tool for quantum systems, aiding in predictions and interpretations even without direct measurements.

Contribution

It demonstrates the utility of Bohmian mechanics in developing quantum models and extracting observable information from trajectories, bridging theory and practical applications.

Findings

Bohmian concepts assist in non-Markovian open quantum system simulations.

Bohmian trajectories can be used to derive observable operators.

Operationally measurable quantities can be obtained from Bohmian trajectories.

Abstract

In this chapter, we will take a trip around several hot-spots where Bohmian mechanics and its capacity to describe the microscopic reality, even in the absence of measurements, can be harnessed as computational tools, in order to help in the prediction of phenomenologically accessible information (also useful for the followers of the Copenhagen theory). As a first example, we will see how a Stochastic Schr\"odinger Equation, when used to compute the reduced density matrix of a non-Markovian open quantum system, necessarily seems to employ the Bohmian concept of a conditional wavefunction. We will see that by dressing these conditional wavefunctions with an interpretation, the Bohmian theory can prove to be a useful tool to build general quantum frameworks, like a high-frequency electron transport model. As a second example, we will introduce how a Copenhagen "observable operator" can be derived from numerical properties of the Bohmian trajectories, which within Bohmian mechanics, are well-defined even for an "unmeasured" system. Most importantly in practice, even if these numbers are given no ontological meaning, not only we will be able to simulate (thus, predict and talk about) them, but we will see that they can be operationally determined in a weak value experiment. Therefore, they will be practical numbers to characterize a quantum system irrespective of the followed quantum theory.