LC Oscillating Circuit as the Simple Classical Analog of the Quantum Zeno Effect

TL;DR

This paper presents a simple classical LC circuit model that demonstrates a classical analog of the quantum Zeno effect, where frequent switching prevents the circuit's oscillation, illustrating a broader concept of the Zeno effect.

Contribution

It introduces a classical LC circuit model as an analog to the quantum Zeno effect, expanding the understanding of the Zeno phenomenon beyond quantum systems.

Findings

Infinite switching halts LC oscillations

Classical Zeno effect analogous to quantum Zeno effect

Defines a general Zeno effect applicable to both quantum and classical systems

Abstract

In this work a simple classical analog of the quantum Zeno effect is suggested. As it is well known, in the quantum mechanics, in the limit of the infinite series of alternative short dynamical evolution and measurement, an unstable quantum system will never decay, that is called quantum Zeno effect. Here an ideal (without resistance), classical LC oscillating circuit with quick switch ON-OFF alternation is considered. In the limit of the infinite series of alternative short electrical current regime (switch in the ON state) and no-current regime (current breaking by quick switch ON-OFF state alternation) given LC circuit will never oscillate. Obviously, it represents a classical electro-dynamical Zeno effect deeply analogous to quantum Zeno effect. All this admits a general definition of the Zeno effect that includes both quantum and classical cases (without any classical interpretation of the quantum Zeno effect or quantum interpretation of the classical Zeno effect).