Lately, I've been searching the literature on the development of quantum mechanics and reading selected papers (and cramming to get my reading level to the required heights). It was with considerable interest, then, that I stumbled on a paper by two Norwegian historians of science, Renstrøm & Bomark (2022). The paper has been posted on the science preprint server, ArXiv (i.e. "archive"), but has not subsequently been published as far as I can see.
The authors compare what is found in physics textbooks to what the founders of atomic physics actually said in their publications. And what they found was a systematic misrepresentation of the facts. As Renstrøm & Bomark say in conclusion:
Physics is perhaps the most exact of all sciences and we pride ourselves with extremely well tested and precise laws that allows us to make firm statements about the world we live in. This should be reflected in the way we present our field to the outside world as well.
My notes and comments on their article follow. I note that the folklore in question has spread to every corner of the internet as well.
Thomson's "Plum Pudding" Model.
Joseph John "J. J." Thomson (1856–1940) won the Nobel Prize for physics in 1906 for his work on the conduction of electricity by gases. This work also led to the discovery of electrons ca 1897. Thomson was the first to demonstrate that electrons—Thomson called them corpuscles—can appear to behave like particles. It took some time for the idea to catch on, however.
Up to this point, it was assumed that electrons were waves, like light. During this period, X-rays were discovered, which led to the realisation that light, X-rays and various other forms of radiation (UV, IR, radio, microwave) were all related. Indeed, they are the same phenomenon, at different wavelengths.
Thomson was able to experimentally estimate the mass and mass-to-charge ratio of the electron, accurately noting that the electron was of the order of 0.1% of the mass of the atom. Thomson (1906) showed that the number of electrons in an atom was "of the same order as the atomic weight".
The standard narrative is that Thomson proposed an atomic model in which negatively charged electrons were distributed in a sphere of positive charge, like "plums in a[n English] pudding" or "raisins in a cake". Encyclopedia Britannica, the acme of a reliable source, repeats this spiel and provides a helpful illustration:
Renstrøm & Bomark note that this static picture with randomly distributed electrons is what physics textbooks also give. It is part of physics folklore. And if you search online for images of Thomson's model, this is what they all look like. However, when Renstrøm & Bomark went and looked at Thomson's first publication on this, they found something quite different. For example, the title of Thomson (1904: 237) is:
On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure. (emphasis added)
And in his model, the electrons are moving at high speeds. Thomson (1904: 254) says:
In this way we see that when we have a large number of corpuscles in rapid rotation, they will arrange themselves as follows: - The corpuscles form a series of rings, the corpuscles in one ring being approximately in a plane at right angles to the axis of rotation, the number of particles in the rings diminishing as the radius of the ring diminishes.
Thomson's actual model does not involve electrons evenly distributed like plums in a pudding. It involves electrons in "a series of concentric rings" (1904: 255). He does place these rings "enclosed in a sphere of uniform positive electrification" (Thomson 1904), but his actual model doesn't resemble the physics folklore version at all.
After finishing this essay, I happened to stumble upon Hon and Goldstein (2013), which confirms what Renstrøm & Bomark have said and gives more details. See also Aaserud & Kragh (2021)—an edited volume of conference papers—which contains a related article, Hon and Goldstein (2021). For more details on the history of Thomson's discovery of the electron, see Falconer (1987), and on its acceptance by the physics community, Falconer (2001).
One of the strengths of Thomson's model was that it was stable.
The problem is that the electromagnetic force is relatively strong. Two oppositely charged particles strongly attract each other. So we might expect the electron to rapidly fall down the potential well to collide with the proton. In this case, reality is somewhat counterintuitive.
An electron and a proton can fuse into a neutron (plus a neutrino), but the reaction is endothermic, meaning that it requires a considerable input of energy. A neutron is about 0.782 MeV heavier than a proton and an electron combined. In practical terms, the electron and proton would have to have on the order of 20 million times the thermal energy they typically have at room temperature and one atmosphere. Which effectively means that it never happens. It is the sort of process we expect to find in the core of a star with very high temperatures and pressures, or indeed, in neutron stars.
By far the most common occurrence when an electron and a proton meet is that they form a hydrogen atom. This process, by contrast, is exothermic, and the excess energy generated is emitted as a photon.
This highlights the role of thermodynamics in our images of matter. Just because the electron and proton have opposite charge and experience a strong attraction, does not mean that they collapse into each other. The electromagnetic force is not the only consideration.
To emphasise the importance of stability, Renstrøm & Bomark briefly discuss Hantora Nagaoka’s (長岡 半太郎) (1904) contemporary "Saturnian model", also published in Philosophical Magazine. The Nagaoka model was not stable and is seldom mentioned in standard works.
Thomson continued to speculate on how electrons are arranged in atoms. In 1905, Thomson gave a lecture in which says that mathematical investigation leads us to believe that electrons would form platonic solids with electrons at the vertices:
Thomson (1905: 2)
This is also misrepresented, on Wikipedia, for example, as part of Thomson's model. But Thomson does not endorse this theoretical picture and instead chooses, like a good scientist, to argue from experiment. And before long (1905:3), he is once again talking about arranging electrons in concentric rings. Wikipedia redeems a little itself by noting (without a citation) the first use of the term "plum pudding" in this connection.
The first known writer to compare Thomson's model to a plum pudding was an anonymous reporter in an article for the British pharmaceutical magazine The Chemist and Druggist in August 1906.
While the negative electricity is concentrated on the extremely small corpuscle, the positive electricity is distributed throughout a considerable volume. An atom would thus consist of minute specks, the negative corpuscles, swimming about in a sphere of positive electrification, like raisins in a parsimonious plum-pudding, units of negative electricity being attracted toward the centre, while at the same time repelling each other.
Thomson himself never used the term "plum pudding", and the model illustrated in textbooks and all over the internet is nothing like Thomson's rapidly revolving concentric rings (with his painstakingly calculated energies). Given the information he had, his model is a good attempt to balance the forces that were understood at the time.
However, things would very soon change because Thomson had a brilliant student by the name of Rutherford.Rutherford's Model
Ernest Rutherford (1871-1937) won the Nobel Prize in Chemistry in 1908 "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances." When I was growing up in New Zealand in the 60s and 70s, Rutherford was one of only a handful of internationally renowned New Zealanders (outside of sports). Rutherford was known to us as "the man who split the atom".
Renstrøm & Bomark once again outline the textbook story, illustrated with extensive quotes. The story goes that Rutherford proposed a new model of the atom that eclipsed Thomson's. Rutherford's model was like a tiny solar system with the positively charged nucleus at the centre and negatively charged electrons orbiting like tiny planets.
This is still the most recognisable picture of the atom down to the present. If you search online for images of atoms, what you mostly get is versions of tiny solar systems. The official emoji for atom is ⚛️, which is more or less the image we associate with Rutherford. Such a diagram does not appear in Rutherford's published works as far as I can see.
Once again, Renstrøm & Bomark (2022: 10) turn to the original source, Rutherford (1911), and once again find that his conclusions have been misrepresented. They say:
Rutherford did not suggest a planetary atom in 1911. He offered no suggestions of how the electrons were arranged or moved; the electrons’ exact distribution was not important for the experimental results.
The title of Rutherford (1911) is "The scattering of α and β Particles by Matter and the Structure of the Atom." Despite the latter phrase, I agree that the paper barely discusses "the structure of the atom" and constructs no models. What Rutherford showed is that the larger share of the mass of a gold atom is concentrated in a small volume at the centre of the atom.
Renstrøm & Bomark, add
The theory Rutherford presented in his paper was primarily a scattering theory, and it was not considered to be an atomic model. Rutherford’s model was met with indifference and scarcely considered to be a theory of the constitution of the atom. It was not mentioned in the proceedings of the 1911 Solvay Congress, nor was it widely discussed in physics journals.
Something that I picked up from Rutherford (1911: 688)
The deductions from the theory so far considered are independent of the sign of the central charge, and it has not so far been found possible to obtain definite evidence to determine whether it be positive or negative.
He notes that Hans Geiger and Ernest Marsden were attempting to determine this by experiment. Just three years later, Rutherford (1914: 488-489) says, referring specifically to his 1911 publication:
In order to account for this large angle scattering of α particles, I supposed that the atom consisted of a positively charged nucleus of small dimensions in which practically all the mass of the atom was concentrated. The nucleus was supposed to be surrounded by a distribution of electrons to make the atom electrically neutral and extending to distance from the nuclear comparable with the ordinary accepted radius of the atom.
Renstrøm & Bomark point out that even in the 1914 paper, Rutherford is still not suggesting that electrons are in "orbit" around the nucleus or moving in any way. His comments on the electron are the minimal corollaries of (1) a massive nucleus, (2) a positively charged nucleus, and (3) an electrically neutral atom.
In my previous essay, I showed by simple logic that these three facts are extremely important when proposing atomic structures, since there is only one configuration that can possibly balance a spherically symmetrical electrostatic field to make for an electrically neutral atom, i.e. a sphere.
Incidentally, Rutherford (1914: 488) also notes that Thomson was in fact developing a model first proposed by William Kelvin, which is also omitted from the folklore.
Lastly, Renstrøm & Bomark note another contemporary atomic structure model by John Nicholson. Nicholson managed to show that angular momentum is quantised. I'm not going to say much more about this.
Reflections
There are several takeaways here:
- Thomson (1904) did not propose a plum pudding model.
- Thomson's model involved concentric rings of negatively charged electrons rotating within a nebulous sphere of (free-floating) positive charge.
- Rutherford (1911) did not propose a model of the atom. And initially, no one thought that he did.
- Rutherford (1911) proved that the bulk of the mass of a gold atom was concentrated in the centre, but was initially unsure about the associated electric charge and did not comment on the arrangement of electrons (since they were irrelevant to his experiment).
- Later, Rutherford (1914) claimed to have said that the nucleus had a positive charge in 1911.
- Rutherford's (1914) picture is accurate as far as it goes: mass concentrated in the positively charged nucleus, surrounded by electrons which balance the electric charge to give an electrically neutral atom. But it's not a model in any formal sense.
The papers in question are easily obtainable. I didn't even have to leave my desk. So there is no excuse for not reading them.
Renstrøm & Bomark (2022) conclude that such systemic misrepresentation is counterproductive because it can only undermine the confidence of students (if and when they discover the lie). I agree. But I take a much dimmer view of misrepresentation.
As a historian of religious texts, I am all too familiar with systematic misrepresentation. As my studies have shown, the history and philosophy of the Heart Sutra were systematically misrepresented in ways that seemed designed to elevate perceptions of its authenticity and authority. This makes me wonder about the systematic misrepresentation of classical atom models by later (quantum) physicists. As always, with a transgression, the question is "Cui bono?", i.e. "Who benefits from this?"
As I noted in my previous essay, attempts to reify the Schrödinger equation lead to a series of incoherent, mutually exclusive metaphysics. But if we go back to the early days of quantum mechanics, there was much less in the way of pluralism. Most people accepted some form of the Copenhagen hypothesis, which required a metaphysical dualism: the world behaves in a wholly counter-intuitive manner when we don't observe it, and then, when we do observe the world, it falls into behaving intuitively. And this distinction, they say, is unavoidable.
As I showed in my last essay, the idea that probabilities all co-exist before an observation and "collapse" at the point of observation is true of every system that we describe using probabilities. It's not that profound, unless we reify the wavefunction.
The failure to produce a plausible metaphysics from the mathematical formalism is an ongoing problem that few physicists wish to think about, though most privately admit the problem exists. Indeed, physics folklore tells us that many physicists are openly hostile to questions about the foundations of quantum mechanics. "Shut up and calculate" and all that.
I'm not saying this is what happened, but it would not surprise me to learn that stories designed to make classical physics look trivially wrong were invented to help sell the "necessity" of embracing quantum mechanics. Along these lines, I note a comment by Hon and Goldstein (2021)
Bohr’s theory has roots in the theories of Ernest Rutherford and Joseph J. Thomson on the one hand, and that of John W. Nicholson on the other. We note that Bohr neither presented the theories of Rutherford and Thomson faithfully, nor did he refer to the theory of Nicholson in its own terms.
The metaphysical consequences of Schrödinger's approach, especially in the hands of Niels Bohr, were all too obviously problematic. Schrödinger himself was appalled by Born's "interpretation" of his wavefunction in probability terms. In a 1952 letter to Max Born, Schrödinger wrote:
"I don’t like it, and I’m sorry I ever had anything to do with it."
(This is widely misinterpreted/misrepresented as a comment on quantum mechanics generally.)
I suspect that the quantum crowd were partly able to assert their dominance by exaggerating the failures of classical physics and using them as a stick to beat dissenters. This is an example of "there is no alternative" gas-lighting (which is very much the zeitgeist). More on this in my next essay.
The bottom line is that there is still no coherent metaphysics associated with quantum theory. Rather, there is a growing list of incoherent metaphysics, with no overlap between any of them, and nothing like a consensus on the horizon. This confusion is reinforced by the insistence that quantum mechanics cannot be understood rationally or even imagined.
Incidentally, it is this claim of ineffability that provides leverage for mystical Buddhists to claim some kinship between their religious ideology and science. All rhetoric of "ineffability" is isomorphic. And thus, quantum mechanics becomes like a cult. And Bohr was very much like a cult leader.
But I can envisage a coherent metaphysics, the existing metaphysics of science, and I find that I can explain the foundations of quantum mechanics in a way that, while yet incomplete, is still far more intellectually satisfying than the nonsense that passes for philosophy amongst quantum physicists. In fact, there are many signs that quantum physics, with its intimate ties to the military-industrial complex, is a scam (an essay on this issue is in the pipeline).
The winners write the history. And even in the field of science, the winners are human beings who try to eclipse their antecedents and present their own view as the culmination of a telos.
~~Φ~~
Bibliography
Aaserud, F. and Kragh, H. (eds). (2021). One hundred years of the Bohr atom: Proceedings from a conference. Scientia Danica. Series M: Mathematica et physica, vol. 1. 2015.
Falconer, I. (1987) "Corpuscles, Electrons and Cathode Rays: J J Thomson and the ‘Discovery of the Electron.” British Journal for the History of Science 20: 241-276.
Falconer, I. (2001), "Corpuscles to Electrons". In Histories of the Electron, edited by J Buchwald and A Warwick, 77-100. Cambridge, Mass: MIT Press.
Hon, G. and Goldstein B. R. (2013). "J. J. Thomson's plum-pudding atomic model: The making of a scientific myth." Annalen der physik https://doi.org/10.1002/andp.201300732
———. (2021). "Constitution and Model: Bohr’s Quantum Theory and Imagining the Atom." In One hundred years of the Bohr atom: Proceedings from a conference, 347-359. Scientia Danica. Series M: Mathematica et physica, vol. 1., 2015 (2021).
Renstrøm, Reidun and Bomark, Nils-Erik (2022). "Textbook myths about early atomic models." October 2022. DOI:10.48550/arXiv.2212.08572. [12 unnumbered pages]
———. (2024) "The Ultraviolet myth." 2024. The European Physical Society Conference on High Energy Physics. https://doi.org/10.48550/arXiv.2402.03405
Rutherford, Ernest. (1911). "The scattering of α and β Particles by Matter and the Structure of the Atom." Philosophical Magazine. Series 6. 21 (125): 669–688. doi:10.1080/14786440508637080.
Rutherford, Ernest. (1914). "The Structure of the Atom." Philosophical Magazine. Series 6, 27: 488 - 498
Thomson, J. J. (1904) "On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure." Philosophical Magazine, Series 6, 7(39): 237 - 265. http://dx.doi.org/10.1080/14786440409463107
Thomson, J. J. (1905). “The Structure of the Atom” A Lecture Delivered at the Royal Institution. (Weekly Evening Meeting, Friday, March 10, 1905): 1-15. http://www.ub.edu/hcub/hfq/sites/default/files/Thomson_model(6).pdf
Thomson, J.J. (1906) "On the number of corpuscles in an atom." Philosophical Magazine Series 6. 11(66): 769-781, DOI: 10.1080/14786440609463496
