A blackbody is not a blackbox

TL;DR

This paper clarifies the blackbody approximation, emphasizing its limitations and deriving the Planck spectrum without a box, thus providing a more conceptually accurate understanding of blackbody radiation.

Contribution

It presents a novel derivation of the Planck spectrum without using a box, highlighting the physical nature of blackbodies and introducing the local density of states concept.

Findings

Blackbody is a limit case of radiative transfer, not a perfect absorber.

The Planck spectrum can be derived without enclosing the field in a box.

The derivation emphasizes the continuous nature of the spectrum and the concept of local density of states.

Abstract

We discuss carefully the blackbody approximation, stressing what it is (a limit case of radiative transfer), and what it is not (the assumption that the body is perfectly absorbing, i.e. black). Furthermore, we derive the Planck spectrum without enclosing the field in a box, as is done in most textbooks. Athough convenient, this trick conceals the nature of the idealization expressed in the concept of a blackbody: first, the most obvious examples of approximate blackbodies, stars, are definitely not enclosed in boxes; second, the Planck spectrum is continuous, while the stationary modes of radiation in a box are discrete. Our derivation, although technically less elementary, is conceptually more consistent, and brings the opportunity to introduce to students the important concept of local density of states, via the resolvent formalism.