On the Law of Distribution of Energy in the Normal Spectrum

These are my notes on a paper by Max Planck. I am reading the translation in Hawking's book, The Dreams that Stuff is Made Of.

Background

I'm not completely clear on what a blackbody is. One definition: a blackbody is a body that can absorb or emit any frequency of wavelength. Another definition (Hawking's): a blackbody is the light produced by a glowing hot object. I think that the latter definition is better than the former, because it's clearer what it refers to in reality. Coal, metal, the sun, etc. For the former definition, it seems like you would have to know something more theoretical about the object in question.

[TODO say something about Rayleigh-Jeans law, which preceded Wien's law (and Planck-Wien law, and Planck's law). Rayleigh-Jeans was inaccurate at high frequencies. Though from what I'm reading, the importance of this thing is overstated, and it wasn't even formulated until 1905.]

Wien's law describes the peak of the spectrum of light emitted by a blackbody, as a function of its temperature. The law simply says that the frequency of this peak is proportional to the temperature. This law was empirically justified, and it also had a theoretical justification from statistical mechanics, due to Wien "from molecular-kinetic considerations" and due to Planck himself "from the theory of electromagnetic radiation." However, the law disagreed with experiment at low frequencies.

Wien's original paper

Possible misconceptions

The opening paragraph of GSW says something about Planck's law:

In 1900, in the course of trying to fit experimental data, Planck wrote down his celebrated formula for black body radiation. It does not usually happen in physics that an experimental curve is directly related to the fundamentals of a theory; normally they are related by a more or less intricate chain of calculations. But black body radiation was a lucky exception to this rule. In fitting to experimental curves, Planck wrote down a formula that directly led, as we all know, to the concept of the quantum.

I think this is completely wrong, based on my reading of the history. Hawking says in the same damn book that I'm reading, that

Wilhelm Wien found an empirical relationship that described the spectrum at high frequencies. However, he was not able to derive this relationship from previously discovered physical laws, so it was not grounded well conceptually. In other words, the Wien law worked, but no one knew why.

According to this source, Planck thought Wien's formula was right, but his derivation of the formula was not. Planck set out to give a satisfactory derivation in his first paper Ann. d. Phys. 1 (1900) p. 719. Then somehow in his later paper (the one appearing in Hawking), he modified his derivation to give the now-famous one.