Gauge is quantum?

TL;DR

This paper proposes that quantum mechanics can be understood as a gauge symmetry emerging from the Madelung equations, clarifying the role of rotational invariance and gauge conditions in quantum theory.

Contribution

It introduces the idea that quantum phenomena arise from a gauge symmetry in the Madelung equations, providing a new perspective on the quantum-classical relationship.

Findings

Madelung equations require rotational invariance for quantum vortices.

Quantum gauge symmetry explains the additional conditions in Madelung equations.

Supports the view that quantum phase is a gauge component.

Abstract

An interesting phenomenon is happening in the construction of the Madelung equations from the Schrodinger equation. It seems like the Madelung equations require a rotational invariance symmetry to properly account for quantum vortices, and that Madelung equations are not fully determining the dynamics. The relation between Schrodinger's equations and Madelung equations are often debated with the observation that no clear understanding exists for why the additional rotational discretisation condition is required. Here I explain it as an additional gauge symmetry that speaks in favour of the recent idea that quantum is gauge (Q=G). Indeed, this additional symmetry seems to emerge as a gauge symmetry condition that needs to be incorporated in the Madelung equations in order to properly describe quantum mechanics. In that sense "Madelung Equation + Gauge symmetry = Quantum mechanics". Arguments in favour of understanding the quantum phase as a gauge symmetry component of the solution of Schrodinger's equations are also introduced.