The Ultra-Violet Catastrophe or a Storm in a Teacup

The first of six podcasts in the search of the true identity of the quantum: is it a particle or a wave or both; or a mathematical entity which has some utility in solving equations. The remaining podcasts in this series are:

2. Einstein's Other Blunder – the photo-electric effect misinterpretation

3. Heisenberg, the Salieri of Physics – how Heisenberg sabotaged his rival Schrödinger

4. Quantum Circus: Jumps and Spins – questions the Bohr model of the atom

5. Magic Particles – examines the concept of entanglement or 'spooky action at a distance'

6. The Quantum Cat meets the Quantum Computer – how both are chimeras

More detailed analysis, booklists, additional material and scientific papers can be found at www.quantumid.science

Transcript

The Ultra-Violet Catastrophe or a Storm in a Teacup

Hello, I'm Kay Strang. You can check me out at my website quantumid.science, where you can find more detailed analysis and material on my series of six podcasts, hunting down the identity of the quantum. 

   It's important to distinguish the development of two branches of quantum mechanics. The first is the pursuit of more particles, and the second the development of technology, chemistry, and biology. I have nothing but admiration for the second, but am critical of the first. 

   In these six podcasts, I've tried to unravel the accepted historical account of quantum mechanics to demonstrate where, how, and why the first branch of it veered off in the wrong direction down a rabbit hole of nonsense. You may have come across the view that quantum mechanics is so crazy and complicated that no one, not even experienced physicists, can actually understand what is really happening. Richard Feynman's admonition to those who question quantum mechanics was 'shut up and calculate'. My view is that there should be no sacred cows and that it is philosophically legitimate to examine the logical foundations of this particular branch of physics. 

   The titles of the six podcasts are, one, The Ultraviolet Catastrophe or a Storm in a Teacup, which shows how the catastrophe was caused by the use of out of date mathematics. Two, Einstein's other blunder examines the photoelectric effect. Three, Heisenberg The Salieri of Physics, how Heisenberg sabotaged his rival Schrödinger. Four, Atomic circus: jumps and spins, questions the Bohr model of the atom. Magic Particles, number five, examines the concept of entanglement or spooky action at a distance, as Einstein called it. Six, the quantum cat meets the quantum computer, how both are chimeras. 

   So let's start with one, the ultraviolet catastrophe or a storm and a teacup. The accepted history of the ultraviolet catastrophe is well documented, and the conclusion drawn is that classical physics was not up to the task of describing the absorption and emission of radiation. Planck's constant, h, which divided the wave of radiation into discrete packets of energy, solved the problem and heralded in the quantum era. I'm going to concentrate on the flaws in the standard historical account. First, when Rayleigh and Jeans attempted to theoretically describe the results of experiments of blackbody radiation, they used the mathematics of statistical mechanics developed to describe a finite number of molecules of gas in an enclosed volume. This was the incorrect approach, and they should have used vector calculus. This is the established method of describing continuous phenomena. In their attempt to count the number of waves in the cavity of the Jeans cube, which is a metal box with a hole designed as an approximation to an ideal black body, they encountered the infinite divisibility of space, known since at least the time of Zeno from his account of Achilles and the Tortoise. Naturally, they counted an infinite number of waves which led unsurprisingly to an infinite amount of energy. This is the catastrophe. 

   According to Thomas Kuhn in his book Blackbody Theory and the Quantum Discontinuity, many other scientists could have refuted their proof at the time, but were tied up in other scientific inquiries. Secondly, I mentioned vector calculus because I had mistakenly thought it was well understood around the end of the nineteenth century. Maxwell's equations had been around since 1865 after all. However, this was chronologically incorrect, and Maxwell in his paper, A Dynamical Theory of the Electromagnetic Field, had written twenty equations in co-ordinate form, which were later compressed into the four recognised today by a remarkable physicist and engineer, Oliver Heaviside, who jointly invented vector calculus with the American W. J. Gibbs. 

   Oliver Heaviside seems to have been written out of most history of physics texts, and the question is why? Like Faraday, he was not university educated, and like Einstein he had a mundane day job, but he contributed a huge amount to science. There is a brilliant biography of Heaviside by Paul J. Nahan, which I recommend. Gibbs brought out his book Vector Analysis in the early 1880s and sent copies to all the major scientists of the day. There was much resistance from the physicist and friend of Maxwell, Peter Tait, who preferred the use of quaternions introduced by the Irish physicist William Hamilton. Even assuming Planck was unaware or unfamiliar with vector calculus in 1901 when he solved the ultraviolet catastrophe, why has no one, to my knowledge, produced a proof of blackbody radiation using vector calculus? 

   Lastly, the methodology used by Planck in determining his constant h was taken from an 1872 paper by Boltzmann. Boltzmann used his discrete energy elements as a mathematical device which could be synthesised later into a continuous quantity. So even if vector calculus was not the go-to mathematics of the day, why not use the idea of a convergent series to arrive at the correct conclusion that the radiation is continuous? 

  There is a further argument Planck could have used to avoid discontinuity, which is offered in Volume 1 of Constructing Quantum Mechanics by A. Duncan and M. Jansen at pages 78 and 79. Notwithstanding this, Planck's h took on a life of its own, and Planck gained the title ‘The Father of Quantum Physics’. It took some time into the 1920s for this to happen, as most physicists were reluctant to qualify Maxwell's wave theory of radiation. 

  The conclusion that classical physics could not explain blackbody radiation overstated the position. It was really just a branch of classical physics, namely statistical mechanics that was flawed. The irony is that Planck was never 100% on board with statistical mechanics, nor the particle theory of matter, as they conflicted with the second law of thermodynamics. He believed that atomic theory, productive though it was, would eventually give way to a mechanical theory of the continuum. 

  If you want to find out more, please visit my website at quantumid.science, where you will find more in-depth downloadable essays, book lists, and original papers by some 19th and 20th century physicists. The next podcast is titled Einstein's Other Blunder, which analyses the conclusions drawn from the photoelectric effect. I hope you can join me again in tracking down the true identity of the quantum. 

© K. Strang 2025