A Classical and Quantum Mechanical Analog of Two Capacitors Paradox

TL;DR

This paper presents a classical and quantum mechanical analogy of the two capacitors paradox using elastic devices, providing a straightforward explanation for the energy discrepancy through elastic work, linking it to foundational quantum discussions.

Contribution

It introduces a novel analogy between the two capacitors paradox and elastic devices, offering a simple resolution rooted in classical and quantum mechanics.

Findings

Energy difference explained by elastic work

Analogy clarifies the paradox's conceptual basis

Links to foundational quantum mechanics discussions

Abstract

As it is well-known one of the most fascinating examples in remarkable discussion between Einstein and Bohr on the conceptual foundation of the quantum mechanics (Heisenberg energy-time uncertainty relation especially) was an experimental device representing a box hanged on an elastic spring. The pair of similar devices is used in this work for formulation of a classical and (implicitly) quantum mechanical analog of the famous two capacitors paradox. It admits a simple solution of the paradox since energy difference or seeming paradoxical "loss" can be explained by work of the elastic force for moving of the boxes in the gravitational field. (Obviously, original two capacitors paradox can be explained in the analogous way.)