How does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?

TL;DR

This paper explores how quantum uncertainty naturally arises within the deterministic framework of Bohmian mechanics, emphasizing the role of measurement constraints and the wave function in producing observable quantum randomness.

Contribution

It clarifies the emergence of quantum uncertainty in Bohmian mechanics by analyzing measurement limitations and the non-measurability of the wave function.

Findings

Quantum uncertainty arises from measurement constraints in Bohmian mechanics.

The wave function cannot be directly measured, influencing particle position measurements.

Deterministic Bohmian mechanics can still account for quantum randomness.

Abstract

Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state -the positions of the particles- must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.