On the reality of quantum states: A pedagogic survey from classical to quantum mechanics

TL;DR

The paper argues that the quantum wave function is real by.showing a seamless lineage from classical Hamilton-Jacobi theory to the Schrödinger equation, paralleling the transition from geometrical optics to wave optics. It emphasizes that introducing superposition at the classical level yields the quantum linear framework, reconciling wave and particle descriptions and demystifying quantum puzzles. By framing observables as Hermitian operators and introducing observable fields, it presents a realist interpretation of the wave function and links quantum expectations to field-based statistics. The work highlights how many quantum features—superposition, measurement, and entanglement—originate from the adoption of linear, superposable dynamics, and shows that classical mechanics harbors dormant seeds of quantum behavior. Overall, it offers a pedagogical route where quantum concepts emerge as natural extensions of classical wave theory, clarifying the reality of the quantum state.

Abstract

Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work undertakes to investigate the issue of reality, treading a more fundamental route from the Hamilton-Jacobi equation of classical mechanics to the Schrodinger equation of quantum mechanics. Motivation for this is a similar approach from the eikonal equation in geometrical optics to the wave equation in electromagnetic theory. We rewrite the classical Hamilton-Jacobi equation as a wave equation and seek to generalise de Broglie's wave particle duality by demanding that both particle and light waves have the freedom of being described by any square-integrable function. This generalisation, which allows superposition also for matter wave functions, helps us to obtain the Schrodinger equation, whose solution can be seen to be as much objective as the classical mechanics wave function. Several other equations which one writes in quantum mechanics, including the eigenvalue equations for observables, series expansion of energy states in terms of eigenstates of observables other than energy, etc., can be written in the classical case too. Absence of any collapse of the wave function, entanglement, etc. in the classical realm have their origin in the nonlinearity of the classical wave equation. These considerations indicate that many of the puzzles in quantum mechanics are present also in classical mechanics in a dormant form, which fact shall help to demystify quantum mechanics to a great extent.