# Continuous Quantum-Classical Transitions and Measurement: A Relook

## TL;DR

This paper revisits the measurement problem in quantum mechanics, proposing a unified wave function framework that smoothly transitions between quantum and classical regimes, offering a natural solution to measurement outcomes without collapse.

## Contribution

It develops and clarifies a wave function equation that unifies quantum and classical physics, providing a realist interpretation and addressing the measurement problem.

## Key findings

- The wave function equation interpolates between quantum and classical limits.
- Classical limits of the wave function lead to definite measurement outcomes.
- Proposes experimental tests using quantum dots.

## Abstract

The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such objectivity can be achieved if a unified realist conceptual framework can be formulated in terms of wave functions and operators acting on them for both the quantum and classical domains. Such a framework was proposed and an equation for the wave function (13, 14) smoothly interpolates between the quantum and classical limits. The arguments leading to the equation are clarified in this paper, and the theory is developed further. The measurement problem in quantum mechanics is then briefly reviewed and re-examined from the point of view of this theory, and it is shown how the classical limit of the wave function of the measuring apparatus leads to a natural solution of the problem of definite measurement outcomes without the need for either collapse or pragmatic thermodynamic arguments. This is consistent with Bohr's emphasis on the primacy of classical concepts and classical measuring devices. Possible tests of the theory using low-dimensional systems such as quantum dots are indicated.