max planck -- 9/27/23

Today's selection -- from The Rigor of Angels by William Egginton. Max Planck unleashed a revolution in physics:

“The age of quantum physics began in December 1900. The man who launched the most significant scientific revolution since Galileo did not come across as much of a rebel. Indeed, he was a hardworking, somewhat conservative man of science. It would be many years before he would accept the truth of what he had discovered, and he sought for the rest of his life to avoid its implications.

“Already a well-established scientist, Max Planck made his most important mark at the relatively advanced age of forty-two, when he had held the chair in theoretical physics in Berlin for the previous eight years. He spent the previous half decade working on a problem that had bedeviled physicists for some time. If a receptacle, say a metal tube, is entirely closed off at both ends save for a tiny hole and then heated up, small amounts of electromagnetic energy will escape through the hole. This so-called black-body radiation can be analyzed by a spectrograph. Depending on the temperature of the tube, it will release small amounts of low-frequency waves and a much larger proportion of medium-frequency waves and then taper off again at the high end of the wavelength spectrum.

“Curiously, these findings contradicted what scientists predicted should happen. If light were transmitted as a wave, as experts thought they had established, the amount of radiation should increase in proportion to the frequency of its wavelength. This makes sense. The smaller the waves spreading across a given surface, the more of them there are: think of the tiny ripples on a pond compared with the relatively scarce swells that big-wave surfers wait for off the coasts of California or Portugal. This is true of all sorts of waves. The smaller the magnitude, the higher the frequency--much as a guitar string being tightened produces a higher pitch as its vibrations stir up smaller and faster air waves--and hence the higher the number of waves. And yet, for some reason, light bucks that trend. It's a good thing it does, too. If it did not, everyday lightbulbs would bathe us in deadly high-frequency radiation every time we turned them on--a theoretical expectation that scientists call, somewhat melodramatically, the ultraviolet catastrophe. That this catastrophe didn't occur in reality was certainly comforting, but it didn't make sense. And Max Planck wanted to know why.

“In the summer of 1900, Planck tried something new. He turned from the theory of electrodynamics to thermodynamics, specifically to that theory's second law, which states that the entropy of a dosed system increases over time. Entropy indicates a system's disorder. An egg is highly ordered. An omelet less so. An omelet you have just chewed, swallowed, and digested, even less so. While it is relatively easy to turn that egg into a meal, it is far more difficult to reverse the process. That, in a nutshell, is entropy.

“Planck, ever the old-school physicist, believed strongly that laws were laws, and that when they apply, they must apply without exception. If entropy is a law, that means that eggs always become more disordered, but the reverse never happens. This conviction led him to some rigorous debates with a dour Viennese physicist by the name of Ludwig Boltzmann. Boltzmann interpreted the second law of thermodynamics to mean that the entropy of any closed system would tend to increase, but that didn't mean that it couldn't decrease in individual cases. Gas molecules will indeed tend to evenly fill a room; however, it is possible that at any given moment they could all cluster together in one part of the room. Possible, but just very unlikely. Ironically, it was by borrowing his scientific opponent's probabilistic model that Planck stumbled upon a solution to the riddle of black-body radiation.

From left to right: W. Nernst, A. Einstein, Planck, R.A. Millikan and von Laue at a dinner given by von Laue in Berlin on 11 November 1931

“For Boltzmann's math to work, Planck had to provisionally break smooth quantities of whatever stuff he was measuring into chunks and then subject the movements of those chunks to statistical analysis. When Planck treated light frequencies as discrete, albeit very tiny, chunks, as opposed to smoothly diminishing wave sizes, he found that the expected distribution of wavelengths reverted to what was found in the laboratory. In other words, by assuming electromagnetic waves had a kind of internal limit keeping them above a minimal size and hence below a maximal frequency, one avoided the ultraviolet catastrophe, and the number of high-frequency waves tapered off. He also managed to derive a specific value that determined the cutoff point at which the theory would conform to the experimental data. This value became known as Planck's constant. Just as the speed of light is a constant with the notation c, this constant has its own notation as well, h. As we will soon see, it would become one of the most important numbers in modern physics and a key element of the quantum revolution to follow.

“Planck, who continued to believe that light was propagated exclusively as waves, accepted this limitation as a kind of mathematical heuristic, but he didn't believe it corresponded to a physical aspect of the light waves themselves. Instead, he thought this chunkiness might be a signature of the atoms emitting the light, that they could vibrate only at certain frequencies and hence admit or absorb light in specifically sized chunks, which he called ‘quanta.’ In 1918, Planck won the Nobel Prize for his discovery and is still regarded as one of the most important figures in twentieth-century science. Nonetheless, as he would later reflect, ‘I can characterize the whole procedure as an act of despair’; ‘a theoretical interpretation had to be found at any price, however high it might be?’ Yet, as unpalatable as it might have been for him, Planck seems to have known he had landed on something remarkable. That very December, he told his son about his discovery while on a walk in the Grunewald forest in Berlin. He described it as ‘a discovery of the first rank, comparable perhaps only to the discoveries of Newton.’

“That it certainly was. But it would take another scientist, arguably the greatest since Newton, to fully grasp what Planck had unearthed.”



William Egginton


The Rigor of Angels




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