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Landscape of the Pre-relativistic, Pre-quantum Electron

In 1902, Pieter Zeeman and H. Lorentz received the Noble Prize in Physics for their work on the Zeeman Effect and the Electron.  Abraham Pais in Inward Bound – alongside his discussion of the pitfalls of simplicity – says that the period from 1895 to 1905 shows an extraordinary variety of discoveries: X-rays, radioactivity, the Zeeman Effect and the electron.  The phenomenological understanding of these – which should probably include the full spectrum of blackbody radiation – was unclear, even (or especially) in the case where the phenomenological explanation itself amounted to a fundamental discovery as was the case with Planck’s constant in 1900.

As we have seen in the case of Drude’s work in optics, it was difficult to align the various phenomenological models with the theoretical and experimentally-derived entities.  Drude, for example, uses the Lorentz transformations, but can’t get them to derive the relative motions involved in the optical Doppler effect in the context of the aether.  So even when the effect was understood and the methods were available, it was still impossible to assemble them in a way that made complete sense – mostly because the purely theoretical (or was it observable?) framework (almost literally) in terms of the framework of the aether added a whole layer of unworkable complexities such as the use of an absolute (aetherial) time scale alongside other timescales defined by relative motion.

Also, early in 1902, Michelson wrote his foreword to Millikan and Mann’s translation of Drude’s Optics.  Michelson had by then already gotten more exact measurements of the Zeeman effect using his own interferometer set up.  Zeeman had originally used a Rowland Diffraction Grating.

The year 1902 brings us to the edge of another set of discontinuities.  Thomas Kuhn notes in his book on black-body theory that in 1902 J. W. Gibbs completed his book on statistical thermodynamics,  
 Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics — and (notably), The only other person publishing in the area of statistical thermodynamics in 1902 was Albert Einstein.  Kuhn notes that, other than, Gibbs, Einstein, Maxwell and Boltzman, nobody else at the time (including Planck) seems to have grasped how to use ensembles rather than idealized “molecules.”   Einstein’s statistical approaches will come up later in discussing the quantum theory of heat as well as Einstein’s elucidation of light quanta and Planck’s constant.  However, in the landscape of the early electron, it is the Einstein-Lorentz model of the electron that will be a major pre-occupation of experimentalists.

Was there an Einstein-Lorentz model?  Apparently, not exactly, or rather only in a reading of Einstein’s relativity as a more conservative, minimalist electromagnetic model featuring an electron with a simple, point-like, basic, inherent mass, but no structure or internal charge distribution.  The notion of a “relativistic rest mass” was not seriously considered since that seemed to be fictive and well outside the realm of the only known ultimate reality: electromagnetism.  The Lorentz part of the supposed Einstein-Lorentz theory included a deformable (obviously not point-like) electron  This was in contrast to the more complex and advanced model of the electron put forward by Abraham which featured a stoutly rigid, spherical electron with a transverse electromagnetic mass as well as a longitudinal electromagnetic mass or the electron models of Bucherer and Langevin with a deformable electron of constant volume.  All of these models of the electron – except for Einstein’s minimal model – aimed at describing an electron that could be the basis of a purely electromagnetic universe.

Which brings us again to how to follow all the strands of Einstein’s contributions to quantum, relativistic and statistical physics.  My plan is to first, follow the path of the electron in relativistic terms, second, the quantum in terms of elucidating Planck’s work (and then on to radiative processes, the photoelectric effect and early quantum theory) and then statistics for specific heat and circling back to radiative processes and quantum theory.  So, first: the electron on its way to becoming relativistic – but not for at least a decade after 1905.  

But let’s stop and look at the thermodynamic surface that Maxwell made in 1873 as inspired by Gibbs’ early work:

First from one of Maxwell’s letters:

And second — a different image of the same surface:

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Ideal, Simple Molecule

In 1890, Pieter Zeeman started a series of magneto-optic experiments that eventually showed that the application of a magnetic field caused emission lines to split.  Given the resolution available with his apparatus in 1896, the splitting looked like a widening of the emission lines in the spectrum.  In any case there was a shift in the wavelength (or “frequency”) of the emission.

Theodore Arabatizis, “The Zeeman Effect and the Discovery of the Electron” inHistories of the Electron, says:

In the same paper that contained Lorentz’s analysis, Zeeman confirmed that the polarization of the edges of the broadened lines followed the theoretical predictions. Lorentz considered the confirmation of his predictions as “direct proof for the existence of ions.” Furthermore, Zeeman estimated the order of magnitude of the ratio e/m. As we saw, the change in the period of vibration of an ‘ion’ due to the influence of a magnetic field depends on e/m. Thus, the widening of spectral lines, which is a reflection of the alteration in the mode of vibration of an ‘ion,’ is proportional to the ‘ionic’ charge to mass ratio. According to Zeeman’s approximate measurements a magnetic field of 10000 Gauss produced a widening of the D-lines equal to 2.5 percent of their distance. From the observed widening of the spectral lines, Zeeman calculated e/m, which turned out to be unexpectedly large. As he recalled, when he announced the result of his calculation to Lorentz, the latter’s response was: “That looks really bad; it does not agree at all with what is to be expected.” It should be noted that this was the first estimate of the charge to mass ratio of the ‘ions’ that indicated that the ‘ions’ did not refer to the well-known ions of electrolysis, but corresponded instead to extremely minute subatomic particles. J. J. Thomson’s measurement of the mass-to-charge ratio of the particles that constituted cathode rays was announced several months later and was in close agreement with Zeeman’s result.

I should note that what was surprising about the e/m ratio was that the mass was extremely small compared to the charge.  A mass close to the mass of an atom (“the well-known ions of electrolysis”) was what was expected and an electron’s mass is much smaller than that.  Both Larmor and Lorentz noted that if you knew how much the magnetic field of a given strength shifted the emissions, then you could derive the mass and electrical charge of the emitter.  Lorentz called this emitter the “ion” as did Larmor in 1897, though he noted it might be the same object as J.J. Thomson’s “electron”.  Lorentz assumed the emitter was “oscillating” in response to the magnetic field while Larmor described a more elaborate set of possibilities including rotations.

Earlier (December 1896), Larmor had reflected in a letter to Lodge before he undertook his more elaborate aetherial analyses:

in an ideal simple molecule consisting of one positive and one negative  electron revolving round each other, the inertia of the molecule would  have to be considerably less than the chemical masses of ordinary molecules, in order to lead to an influence on the period, of the order observed  by Dr. Zeeman.

This simple picture, of course, anticipates many aspects of Bohr’s model of the hydrogen atom, which would not see the light of day until almost 20 years later.  What were the problems that hindered looking at an ideal, simple model in 1896?  Several basic problems, I think:

  1. The need to relate every electromagnetic event to elaborate aether models
  2. The lack of a definite notion of a nucleus differing in mass (maybe or just being aetherial) and charge from the electron (Rutherford would eventually work that out – removing even the positive charge from the among the plum puddings of the aether)
  3. Related to problem 1 – no possibility of using quantum structures (in 1896 Planck’s constant had not yet been glimpsed and it would be almost two decades before the Bohr model of electrons at quantum energy levels and emitting as they made transitions between levels) so the aether models provided the only basis for any phenomenological descriptions of what was happening.

But what happened with the electron in the pre-quantum world?  Say from 1896 to 1913?  Again, several things, I think:

  1. A change in how the Maxwell equations were modelled as interacting with the aether
  2. A new type of models, where the electron formed material objects (“Atoms” and “molecules” and “corpuscles”)
  3. New dynamic models where the electromagnetic field formed the apparent mass of the electron (I’ll note again that for a time these models were seen as being better supported by experiment than models that used what was assumed to be the Einstein-Lorentz models using relativistic mass for the electron)
  4. Models of the electron itself (in terms of shape, self-energy, mass, size and deformability)

Meanwhile what about Larmor’s electron?  It changes the interaction of aether and matter and it solves aether-dragging by undergoing FitzGeraldian contraction:

Theodore Arabatizis, “The Zeeman Effect and the Discovery of the Electron” in Histories of the Electron, says:

Furthermore, he [Larmor] suggested that they were universal constituents of matter.  He had two arguments to that effect. First, spectroscopic observations in astronomy indicated that matter “is most probably always made up of the same limited number of elements.” This would receive a straightforward explanation if “the atoms of all the chemical elements [were] to be built up of combinations of a single type of primordial atom.” Second, the fact that the gravitational constant was the same in all interactions between the chemical elements indicated that “they have somehow a common underlying origin, and are not merely independent self-subsisting systems.” Larmor’s electronic theory of matter received strong support from experimental evidence. First, it could explain the Michelson-Morley experiment. Inspired by Lorentz, Larmor managed to derive the so-called FitzGerald contraction hypothesis, which had been put forward to accommodate the null result of that experiment. As he mentioned in a letter to  Lodge, “I have just found, developing a suggestion that I found in Lorentz,  that if there is nothing else than electrons—i.e., pure singular points of  simple definite type, the only one possible, in the aether—then movement  of a body, transparent or opaque, through the aether does actually change its dimensions, just in such way as to verify Michelson’s second order experiment.” Second, Fresnel had suggested that the ether was dragged by moving matter and had derived from this hypothesis a formula for the velocity of light in moving media. Larmor’s theory was able to reproduce Fresnel’s result: “The application [of electrons] to the optical properties of moving media leads to Fresnel’s well-known formula.” The introduction of the electron initiated a revolution that resulted in the abandonment of central features of Maxwellian electrodynamics.

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Entwining Theories and Experiments with the Electron

The emergence of the electron as an object with measurable characteristics is a fairly twisted tale, but it all does sort of come together in 1896-7 as Larmor and Lorentz use their ideas about the electron to explain what Zeeman observes in emission spectra where the application of a magnetic field multiplies the emission lines.  And, at the same time, Thomson measures the charge to mass ratio of what was most laboriously supposed to be the same object – the electron.

About Thomson in 1897, Graeme Gooday says (in a paper in Histories of the Electron right after Falconer’s “From Corpuscles to Electrons”):

Thomson appears at this stage to have had no comparable interest in the Zeeman effect. As Isobel Falconer has pointed out, however, by this time Thomson had, like many other physicists, taken a keen interest in another, earlier unexpected result from experiments on radiation: the phenomenon of x-rays. And it was the publicity surrounding the extraordinary properties of x-rays that emerged in 1895–96 which turned Thomson’s attention for the first time to the constitution of cathode rays.

George E. Smith “J.J,Thomson and the Electron, 1897-1899” on Thomson’s work :

 Modern atomic physics appears to derive far more from Rutherford’s 1911 and Bohr’s 1913 papers than from Thomson’s 1897 paper. This is true. What made Thomson’s paper a watershed is not that it initiated modern atomic and elementary particle physics. It was a watershed because, together with the papers of the next two years, it freed the investigation of phenomena of electrical conduction, in metals and liquids as well as in gases, from aether theory and questions about the fundamental character of electricity. As such, it marked the end of the period Jed Buchwald describes in From Maxwell to Microphysics and the start of a new era in electrical science.

And I quote Falconer again:

The story I have been telling traces two parallel and apparently quite similar theoretical developments by Lorentz and Larmor, although Larmor’s is now largely submerged. Yet they were based on fundamentally different concepts of nature. Intertwined was a series of experiments that were ultimately successful largely because they got hijacked by both theoretical camps. The existence of the phenomena demonstrated by Thomson was sufficient evidence for Lorentz and especially Larmor, but the quality of the experiments was not sufficient to establish Thomson’s own corpuscular theory in opposition to the electron theories. The potential unifying power of the electromagnetic view of nature concentrated attention on the electron’s charge and mass, and these became its defining characteristics.  The one respect in which Thomson does seem to have been before others is in deflecting cathode rays electrostatically. His cross-field e/m method, said to involve fewer assumptions than Wiechert’s or Kaufmann’s original measurements, came to exemplify the new physics.  In this process, a significant historical contingency is that Lodge’s account (in Electrons, 1906 — I note), which set the tone for many later histories, was delivered to the Institution of Electrical Engineers. As Gooday points out, electrical engineers were a far larger community than academic physicists and were also intimately familiar with the history and potential of vacuum tube technology.  Lodge’s decision to present the electron development through a familiar technology rather than a more abstruse theoretical path was well received and was perpetuated by a wide audience. Thus, even “acceptance” begins to look more complex than it at first appeared for, as well as the background concepts of the author, we have to take into account the potential influence of the intended audience.  Both accounts agree that cathode rays were particularly compelling evidence for the existence of electrons. Even Kaufmann, who placed the reality of electrons prior to 1897, considered that “[w]e have in the cathode rays the electrons—which in optical phenomena lead a somewhat obscure existence—bodily before us so to speak.” In Britain, Thomson was the first to produce this evidence, while in Germany, Wiechert performed a similar role.  That Wiechert is now largely forgotten while Thomson is remembered as “the discover of the electron” is due to more than the contingency that Thomson had a large and increasingly powerful group of former research students who extolled his work. It is due in part to the nature of Thomson’s corpuscle suggestion. In speculating about the role of the corpuscle in the structure of the chemical atom, Thomson initiated a research program in subatomic physics among these students that was to dominate British physics in the first half of the twentieth century. By the 1920s the ethereal concepts in which Thomson’s work was founded were outmoded, yet his ideas underpinned subatomic physics and his successors needed to justify their belief in them. His students, unable to accept his concepts, transformed his experiments into a paradigm of pure physics research. They thus used his cathode ray work to make their own enterprise acceptable (and fundable).

I would add (or note) a couple of things: 1) while Thomson did go on to work on aethereal theories into the 1920s, his concern with the “electron” as a “corpuscle” was to distinguish it from the aether, I think and 2) as George Smith points out in his paper in Histories of the Electron, it is hard for people after the crucial changes around 1900, to remember just how confused things were before.  For example, until the definition of the electron as a negatively charged particle, positive and negative electricity was assumed to be symmetrical at the atomic level and separating the atom into a positive nucleus or “pudding” and a negative outer or free component was a step so fundamental as to be difficult for us to imagine.  The aether problems are similar in that – although Thomson continued to use aethereal theoretical constructs, I do think his extraction of a negative particle from the aethereal continuum was a crucial step and part of the reason for the later emphasis on his experimental techniques rather than his theoretical aims has to do with a later need to forget about the aether as much as possible since by the 1920s, aethereal concepts were not just fading, but becoming painfully unproductive compared to working within the new relativistic and quantum frameworks — at least for physicists if not for electrical engineers — which I guess adds another complex twist to our journey to the realm of the mesons.

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Histories of the Electron

Turning to the electron, a lot happens from around 1891 to 1910 or so that centers on the electron: it gets described in theoretical terms from 1891 on.  Its effects are systematically detected and it is itself measured from 1896 on.  It is incorporated in theories of atoms and aethers and a “failed revolution” (as Kragh calls it) is centered on it – the “revolutionary” theories of a purely electromagnetic world where all things are constituted only of aether and electrons.  As quantum theory and relativity take off, the aetherial electromagnetic revolution gets sidelined pretty quickly, but from 1905 to 1910, it was seen as having a better basis in experimental results than relativity.

First, some books.  Most importantly:

Buchwald, Jed Z, and Andrew Warwick, eds. Histories of the Electron (Dibner Institute Studies in the History of Science and Technology) The MIT Press.

  • But also: Mehra and Rechenberg. The Historical Development of Quantum Theory, Volume 1 Part 1 – yes, at the very beginning – there’s Larmor, Zeeman and Lorentz in 1896 elucidating the dynamics of the spectral lines from electrons radiating in a magnetic field.  Something that will be crucial for the next 30 years in the development of quantum theory.
  • And (because we are going to go back over stellar aberration, Fresnel and Fizeau again): Riccardo D’Auria and Mario Trigiante From Special Relativity to Feynman Diagrams – Where we will see that stellar aberration can be described to some degree with pre-relativistic models

and no need to invoke any aethereal effects EXCEPT to explain why all celestial sources emit light at the same speed relative to the telescope, which, of course special relativity explains in its own way (ie the speed of light is the same in all reference frames no matter what the relative speed of the emitter is).

  • Also, the usual Miller on Einstein and Resnick and Halliday Basic Concepts in Relativity and Early Quantum Theory
  • And, Kragh’s Quantum Generations
  • And Buchwald ed. Scientific Practice – Giora Hon’s article about Kaufmann’s experimental quest to evaluate different theories of electron structure and the interpretation of Kaufmann’s results.

So, for now, let’s summarize what Isobel Falconer says about electrons with reference to Larmor in “Corpuscles to Electrons” in Buchwald and Warwick’s Histories of the Electron.

Quoting Falconer :

“Electron” — This was a term invented by Irishman George Johnstone Stoney in 1891 to account for the double lines in gas spectra, postulating a tiny charged particle that emitted electromagnetic radiation as it rotated around an atom to which it was inseparably bound. Soon afterward the “electron” was appropriated and recontextualized by theorists of the electromagnetic ether:  the “Maxwellian” Joseph Larmor in Cambridge used it to label the little vortex “knots” of ether by which he sought to explain interactions between ether and matter.

And, for “Maxwellians” Falconer writes:

 matter is merely a structure of the ether, often a vortex ring or center of strain. By 1894 Joseph Larmor had independently arrived at a theory of electric particles that addressed the same problems as Lorentz’s theory. Following FitzGerald’s suggestion, Larmor named his particles “electrons,” defining them as centers of radial strain in a rotationally elastic ether.  Larmor was the first to suggest that matter might  be purely electromagnetic in origin, writing in the spring of 1895 that “material systems are built up solely out of singular points in the aether which  we have called electrons and that atoms are simply very stable collocations  of revolving electrons,” although he constantly hedged his bets on this subject.  He had previously shown that if the mass was purely electromagnetic, then electrons must be capable of moving near the speed of light, and he had noted their possible connection with cathode rays. Until the discovery of the Zeeman effect, Larmor assumed that his electron was associated with a mass at least as massive as the hydrogen atom. In 1897 he revised this assumption and identified his electron with the small oscillating charges postulated by Zeeman and Lorentz.

Note that Falconer is careful and correct to say “associated with a mass,” because from around 1895 to well into the first two decades of the 20th century, there was a strong current of opinion and plenty of experimental evidence (as we will see) that the “real” mass of the electron was zero and that all of its mass emerged from either its interactions with its own field or the “inertia” of its interactions with fields as it moved through them (including “through” its self-interactive field).  The problem of “self-energy” has persisted, but the electron these days is considered to have a mass even without taking its relativistic motion and field interactions into account.

But to return to what was going on with cathode rays and the electron, here’s a review of the basic phenomenological chronology:

  1. Zeeman finds the splitting of emission spectra when a magnetic field is applied (1896)
  2. Lorentz and Larmor interpret this effect as an indication of the characteristics of the electron (1897)
  3. Thomson measures the charge-to-mass ratio of the “corpuscles” in cathode rays (1897).  Now what is interesting here is that Thomson’s measurement is the first “direct” measurement of the electron itself.  Not only that, but it is done in a much simpler experimental set-up than what Kaufmann was going to be doing slightly later with beta-rays (fast electrons).

Here is a diagram of Thomson’s experimental set-up of 1897: