Zero-point term and quantum effects in the Johnson noise of resistors: A critical appraisal

TL;DR

This paper critically examines the existence of the zero-point term in Johnson noise, questioning its quantum origin and implications for quantum theory, measurement, and nanotechnology.

Contribution

It provides a detailed analysis of the zero-point term in Johnson noise, challenging its assumed quantum origin and highlighting the importance of measurement systems in quantum noise theories.

Findings

Zero-point term may be an experimental artefact or require renormalization.

Measurement of mean energy and force can verify the zero-point term.

Quantum Johnson-Nyquist formula may be invalid in the quantum limit.

Abstract

There is a longstanding debate about the zero-point term in the Johnson noise voltage of a resistor. This term originates from a quantum-theoretical treatment of the Fluctuation-Dissipation Theorem (FDT). Is the zero-point term really there, or is it only an experimental artefact, due to the uncertainty principle, for phase-sensitive amplifiers? Could it be removed by renormalization of theories? We discuss some historical measurement schemes that do not lead to the effect predicted by the FDT, and we analyse new features that emerge when the consequences of the zero-point term are measured via the mean energy and force in a capacitor shunting the resistor. If these measurements verify the existence of a zero-point term in the noise, then two types of perpetual motion machines can be constructed. Further investigation with the same approach shows that, in the quantum limit, the Johnson-Nyquist formula is also invalid under general conditions even though it is valid for a resistor-antenna system. Therefore we conclude that and a satisfactory quantum theory of the Johnson noise, the Fluctuation-Dissipation Theorem, must, as a minimum, include also the measurement system used to evaluate the observed quantities. Issues concerning the zero-point term may also have implications for phenomena in advanced nanotechnology.