Monday, August 22, 2022

My black body story (it's physics).

 I studied physics in university, and at one point asked a professor if I should learn German, because it seemed all the key texts of early 20th century physics were written by German-speaking physicists in German journals such as Annalen der Physik. But my prof assured me that was not needed, insisting that my own native language would serve me well. And he knew German, so his advice seemed sincere.

In the end he was right, but I still have an occasional pang of regret about never learning another language well enough. Wouldn't it be nice to read Einstein in the original? The E=mc² paper is astonishing in its precision and brevity even in translation. (Although later physicists have criticisms of it, it remains a marvel). I did eventually pick up a bit of German, but not enough for Einstein.

Which brings me to Max Planck, who first quantized light, or so I was told.

By the third year of undergraduate physics, I had been taught the same derivation of the resolution of the "ultraviolet catastrophe" at least three times. The classical (19th century) physics theory of a black body was clearly incomplete because the energy emitted was unbounded: higher and higher frequencies of light (the "ultraviolet")  contributed ever more energy to the solution, leading to infinite energy regardless of the temperature (the "catastrophe"). By quantizing the light, Planck tamped down the runaway energy because as the frequency increased, the energy required to fill the quantized slots (photons) was no longer available, and the spectrum died down, as it does in the real world.

By the third or maybe fourth or fifth rendering of this story in class, I began to wonder: Why is the story always told this way? Why is the derivation always exactly the same? It almost seemed like a "just so" story, with the conclusion leading the analysis rather than the other way around. (But read on.) Or perhaps some pedagogue found a nice way to explain the theory to students, and that story was copied from textbook to textbook ad infinitum, eventually to become the story of the invention of quantum mechanics. In short, I was being taught a way to understand the physics, which is fine, but not how the ideas came to life, which left me wanting.

I wanted to investigate by going back to the original paper by Planck. But I couldn't read German, and as far as I knew there was no English translation of the original.

I visited my prof after class and asked him if he would help. He enthusiastically agreed, and we went off to the library to find the appropriate issue of Annalen der Physik. Fittingly, the paper was published in 1900.

Slowly, we—mostly he—worked our way through the paper. It was delightfully, completely, and utterly a 19th-century answer, not the 20th century one that was taught. Planck used thermodynamics, the jewel in the crown of 19th century physics, to derive the black body formula and create the 20th century. The argument was based on entropy, not energy. It had nothing to do, explicitly at least, with photons. But by focusing on the entropy of a set of indistinguishable oscillators at distinct frequencies, he could derive the correct formula in just a few pages. It was a tour de force of thermodynamic reasoning.

Why not teach us the historical derivation? The answer was now clear: This was a deep argument by a towering figure of 19th century physics, one that was beautiful but not a good fit for a 20th century, quantum-capable mind. Yes, Planck quantized the energy, but he did it as a mathematical trick, not a physics one. It was Einstein 5 years later, in his paper on the photoelectric effect, who made photons real by asserting that the quantization was not mere mathematics but due to a real, physical particle (or wave!). Us lowly students were being taught in a world that had photons already in place. Planck had no such luxury.

Another point I learned later, through the books of Abraham Païs, was that Planck knew the formula before he started. Using brilliantly precise experimental work by people in his laboratory, he recognized that the black body spectrum had a shape that he could explain mathematically. It required what we would now call quantization, a distribution over distinct states. In one evening, he found a way to derive that formula from the physics. It was not a matter of quantizing and finding it worked; quite the reverse. The analysis did in fact start from the conclusion, but not as we had been taught.

It's a lovely side detail that Einstein's Nobel Prize was for the photoelectric effect, not relativity as many assumed it would be at the time. The old guard that decided the prizes thought it was safe to give it to Einstein for his explanation, based on ideas by Planck, of a different vexing physics problem. That relativity stuff was too risqué just yet. In retrospect, making the photon real was probably Einstein's greatest leap, even though Planck and others of his generation were never comfortable with it. The Nobel committee got it right by accident.

To put all this together, what we learn through our education has always been filtered by those who came after the events. It can be easier to explain things using current ideas, but it's easy to forget that those who invented the ideas didn't have them yet. The act of creating them may only be well understood by stepping back to the time they were working.

I'm sorry I don't remember the professor's name. Our unpicking of the black body story was one of the most memorable and informative days of my schooling, and I will be forever grateful for it.

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