Higher Speculations

Some commenters here a while ago made the excellent suggestion that I should take a look at a book published this spring, Helge Kragh’s Higher Speculations: Grand Theories and Failed Revolutions in Physics and Cosmology. I’ve always wondered what historians of science would make of the increasing dominance of research in fundamental physics by unsuccessful highly speculative research programs, and have also often wondered if there are any relevant historical parallels to this situation. This book does a great job of addressing those questions, and it’s pretty much unique in doing so.

Kragh spends the first half of the book on history, the second half on currently popular (of varying degrees of popularity…) topics including varying constants of nature, cyclic cosmological models, anthropics, the multiverse and string theory. He doesn’t explicitly make any attempt to evaluate how successful these current efforts are, but they are discussed in the context of previous failures and parallels are drawn. I didn’t know much about the history of “vortex theory” in nineteenth century physics, and this turns out to be possibly the best historical parallel to the story of string theory. Here’s an extract from the extensive and enlightening discussion of that bit of scientific history:

From its beginnings in 1867 to its end at about 1900, the [vortex] theory was frequently justified on methodological and aesthetic grounds rather than its ability to explain and predict physical phenomena. In an 1883 review of ether physics, Lodge described the vortex atom theory as ‘beautiful’ and ‘the simplest conception of the material universe which has yet occurred to man’. He added, just as Michelson would do twenty years later, that it was a ‘theory about which one many almost dare to say that it deserves to be true’.

The audience listening to William Hicks’ address at the 1895 meeting of the British Association for the Advancement of Science would not suspect that the vortex theory of atoms was dying. Without paying much attention to the theory’s disappointing record with regard to empirical physics, Hicks reviewed in an optimistic tone the theory of various vortex objects such as rings, spheres and sponges. He realized that relatively little progress had been made over the years in the mathematical development of the theory, and that progress was even more lacking in the theory’s contact with experiments. However, these problems he deftly turned into a defence of the theory, for the undeveloped mathematical framework meant that the theory could not be rigorously tested. Hicks was convinced that the road towards progress would be to develop still more advanced mathematical models. The vortex theory, he said ‘is at present a subject in which the mathematicians must lead the attack’.

Surely many physicists of the day would have described vortex theory as “our best hope for a unified theory”, and one wonders if any of them thought of it as a “part of 20th century physics that fell by chance into the 19th century.”

Kragh’s book does something really remarkable and valuable: it starts to put some aspects of the last 30 years of fundamental physical theory into a plausible historical context. The future of the subject remains a mystery though, but one can hope that on the vortex theory timeline we’re about to hit the analog of 1900, with successful rather than failed revolutions ahead of us.

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29 Responses to Higher Speculations

  1. wolfgang says:

    Vortex theory was a major motivation to study knot theory – a topic advanced much later by Ed Witten.

  2. Chris Oakley says:

    From the Wikipedia article “History of knot theory”:

    In 1867 after observing Scottish physicist Peter Tait’s experiments involving smoke rings, Thomson came to the idea that atoms were knots of swirling vortices in the æther. Chemical elements would thus correspond to knots and links. Tait’s experiments were inspired by a paper of Helmholtz’s on vortex-rings in incompressible fluids. Thomson and Tait believed that an understanding and classification of all possible knots would explain why atoms absorb and emit light at only the discrete wavelengths that they do. For example, Thomson thought that sodium could be the Hopf link due to its two lines of spectra. (Sossinsky 2002, p. 3–10)

    When the luminiferous æther was not detected in the Michelson–Morley experiment, vortex theory became completely obsolete, and knot theory ceased to be of great scientific interest.

    It is just me, or does the first sentence sound a bit like “all matter is comprised of tiny vibrating strings”.

  3. Daniel says:

    History repeating itself? But doesn’t the book discuss the human aspects of the debacle of the vortex theory? I’m curious to know how the vortex theorists reacted and/or adapted.

  4. Peter Woit says:


    The book doesn’t have much on the topic of vortex theorists admitting the idea didn’t work and moving on. Perhaps this was something that Max Planck had in mind in his famous quote: “science advances one funeral at a time”.

  5. Roger says:

    The vortex theory was not so stupid. It was before the discovery of electrons, and when so little was known about atoms that some people could still doubt them. The vortex theory was not any worse than other theories. The 1902 Encyclopedia Britannica explained:

    These properties of vortex rings suggested to Sir William Thomson[5] the possibility of founding on them a new form of the atomic theory. The conditions which must be satisfied by an atom are permanence in magnitude, capability of internal motion or vibration, and a sufficient amount of possible characteristics to account for the difference between atoms of different kinds.

    The small hard body imagined by Lucretius, and adopted by Newton, was invented for the express purpose of ac counting for the permanence of the properties of bodies. But it fails to account for the vibrations of a molecule as revealed by the spectroscope. We may indeed suppose the atom elastic, but this is to endow it with the very property for the explanation of which, as exhibited in aggregate bodies, the atomic constitution was originally assumed. …

    On the other hand, the vortex ring of Helmholtz, imagined as the true form of the atom by Thomson, satisfies more of the conditions than any atom hitherto imagined. In the first place, it is quantitatively permanent, as regards its volume and its strength, two independent quantities. It is also qualitatively permanent as regards its degree of implication, whether “knottedness” on itself or “linkedness” with other vortex rings. At the same time, it is capable of infinite changes of form, and may execute vibrations of different periods, as we know that molecules do. And the number of essentially different implications of vortex rings may be very great without supposing the degree of implication of any of them very high.

    But then it goes on to give an argument that sounds a lot like the string theorists of today:

    But the greatest recommendation of this theory, from a philosophical point of view, is that its success in explaining phenomena does not depend on the ingenuity with which its contrivers “save appearances,” by introducing first one hypothetical force and then another. When the vortex atom is once set in motion, all its properties are absolutely fixed and determined by the laws of motion of the primitive fluid, which are fully expressed in the fundamental equations. The disciple of Lucretius may cut and carve his solid atoms in the hope of getting them to combine into worlds; the follower of Boscovich may imagine new laws of force to meet the requirements of each new phenomenon; but he who dares to plant his feet in the path opened up by Helmholtz and Thomson has no such resources. His primitive fluid has no other properties than inertia, invariable density, and perfect mobility, and the method by which the motion of this fluid is to be traced is pure mathematical analysis. The difficulties of this method are enormous, but the glory of surmounting them would be unique.

    In other words, it aimed to derive all of atomic theory from a few numbers and mathematical principles, without need for experiment.

  6. Wolfgang says:

    Aside from Lord Kelvin, James Clerk Maxwell, J.J. Thompson and Peter Tait, all of whom seem to have survived with their reputations intact, who else worked on “vortex theory”?

  7. Peter Woit says:


    Kragh discusses many others who made the case for “vortex theory”, including

    Gerald Francis Fitzgerald (Irish physicist)
    George Johnstone Stoney (Irish physicist)
    William M. Hicks (British physicist)
    Donald MacAlister (British physicist)
    Balfour Stewart (British physicist)
    Francis Venable (American chemist)
    Joseph Larmor (British physicist)
    Silas Holman (American physicist)

    So, proponents of the theory include the long-forgotten, as well as physicists who did important work on other subjects.

    There were also skeptics (including mathematician William Clifford), and non-scientist fans (Madame Blavatsky and the Theosophists)

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  9. Vortex theory inspired the theory of knots and braid theory is applied in quantum context to topological quantum computation. For the physical space-time dimension D=4 the orbits of space-like 1-knots are 2-knots-knotted string world sheets. If one accepts holography and the space-time correlate for finite measurement resolution as a discretization replacing 3-D space-time hologram with braids, one ends up with 2-knotted string world sheets as basic objects and we have string theory like structure in D=4. Maybe the intersection of string theory and vortex theory- actually developed by Witten- could give us the long waited physics.

  10. Bee says:

    Interesting. Can you say a few words on whether the book is well written and worth spending the time on?

  11. Peter Woit says:


    The book is well written, and definitely worth the time for anyone interested in these issues. It’s more of an intellectually serious, scholarly work, with a lot of research behind it, rather than something aimed purely at a popular audience (the publisher is Oxford University Press, not a trade publisher). From my point of view that’s a plus. It’s not full of pictures, gee-whiz language, or heavily over-simplified attempts to explain physics by analogy.

  12. Martin Ouwehand says:

    one can hope that on the vortex theory timeline we’re about to hit the analog of 1900

    I’m not sure that this is what you want, because that’s when the next unsuccessful highly speculative research program started, viz. the “electromagnetic view of Nature”…

  13. model and sim says:

    I would agree with Peter that there are some items shared by theories that make the differences between the theories more a matter of semantics. Whether we label solutions as vortexes or strings I think is purely semanitics. The question is more about the governing equations, and the nature of the thing that characterized by those equations. From that point of view, equations in string theory are much more nuanced, for better or for worse. Modern understandings of algebras are much more advanced than at any other time in history, and those algebras are fairly immune from the objects representing them. It is just disheartening that the last decade was more focused on semantics than substance. I just hope that we see something this summer that will finally move us forward.

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  15. Wolfgang says:

    Maybe I’m too literal-minded, but this seems apropos of any discussion of “vortex theory.”

  16. FrankH says:

    My response is so what? Vortex theory was a reasonable approach to try. It was very difficult to do the calculations and it turned out not to work, or rather a better more calculable theory was developed, but I hold nothing against the physicists who advocated vortex theory. Similarly, string theory is a reasonable approach to try. It is very difficult to do the calculations, but they have been able to calculate a lot more than vortex theory ever did. String theory may or may not be the appropriate theory to explain the elementary particle zoo that we have discovered, but until a better theory comes along, there is nothing wrong with getting as much as we can out of string theory, in my humble opinion…

  17. Peter Woit says:


    One can point to lots of ideas that a small number of people have tried to pursue that haven’t been any more successful than vortex theory. String theory is different though: it’s an example of an idea that dominated the whole field, including getting the attention of the major figures in the subject, for several decades, while not going anywhere.

    Actually, back in 1984/85, string theory was a much more specific proposal than vortex theory, with a much more highly developed and detailed structure. As things haven’t worked out, it has migrated towards vaguer and vaguer proposals. The latest hot topics, the multiverse and Verlinde’s entropic gravity, are even more content-free than vortex theory ever was.

  18. Wolfgang says:

    “The latest hot topics, the multiverse and Verlinde’s entropic gravity …”

    From the complete absence of multiverse-related talks at Strings 2011, and from the frosty reception that Erik Verlinde’s talk received there, one might question how “hot” those topics are.

  19. N. Nakanishi says:

    The vortex model of atom was discussed in comparison with superstring by the famous science writer, Martin Gardner in “The New Ambidextrous Universe” , 3rd ed. (1990).

  20. plum says:

    The vortex theory failed to explain atoms, but let’s not jump to conclusions that the “electromagnetic theory” of atoms got it right from the beginning. J J Thomson discovered the electron in 1897, but he was of the opinion that the positive charge in an atom was smeared out — the so-called `plum pudding’ model of the atom — the electrons were like raisins, points of negative charge, in a background mush of positive charge. In 1909 Ernest Rutherford discovered the atomic nucleus and proposed the `solar system’ model of the atom. But Rutherford’s model had immediate problems, which the plum pudding model did NOT have. It was known by 1909 that a point charge moving in a circle will radiate, which meant that Rutherford’s proposed solar-system model of the atom was unstable. In 1913 Neils Bohr proposed a solution (the Bohr model of the atom), but it was hardly a rigorously formulated theory. The Bohr theory was really a suspension of belief, with ad hoc postulates to fit the observed data. The Bohr-Sommerfeld quantization just slapped on ad hoc `quantization rules’ on top of classical physics, the “old quantum theory”. It was hardly a rigorous theory. So who is to say that the vortex theory of atoms was a ridiculous idea to pursue, circa 1900?

  21. Arun says:

    If I remember correctly, there is a lot about vortex theory in Sir Edmund Whittaker’s A History of the theories of aether and electricity, specifically the first volume. It would be interesting to collide Helge Kragh’s work against it.

  22. D R Lunsford says:

    Focusing of vortex theory in particular is barking down the wrong whirlpool. The point was that the idea of matter in the vacuum, in the light (haha) of Ampere, Faraday, and Maxwell, had become extremely complicated when compared to the sane world of Newtonian continuum mechanics. Vorticity in continuum mechanics itself obeys a sort of conservation law and so naturally, people who were attempting to construct fundamental mechanical models of matter in the vacuum fell back on this fact. The main issue was a wrong-headed and premature attempt to model the vacuum when too little was known about the actual state of matter.


  23. Nige Cook says:

    The analogy to string theory is deep. The toroidal vortex or smoke ring in an ideal fluid doesn’t disperse, so it seemed like a good model for the Greek concept of the atom. It represented atoms of matter as just a disturbance in the Maxwell model of space, a vortex in a fluid in which “displacement current” can flow (his addition to Ampere’s current, to make his equations postdict light). When Michelson and Morley failed to detect Maxwell’s postulated light-carrying vacuum medium, and when radioactivity was discovered, Lord Kelvin simply dismissed the MM experiment and radioactivity as experimentally bogus because they conflicted with his beautiful model of stable vortex atoms. You can expect the same denialist reaction to the failure of experimentalists to find supersymmetric particles, etc. Einstein is famous for saying (when light deflection was observed in 1919) that general relativity didn’t need testing because it is a beautiful theory, so it must be right. (It then turned out he was confused about the role of the cosmological constant in his “beautiful” theory.)

  24. aelight says:

    Einstein – is that so? Einstein wrote to Edwin Hubble to ask his opinion if the deflection of light could be measured by observations of stellar positions **in daylight** (emphasis by Einstein ~ I read this maybe in Physics Today ~ maybe in 2005 celebrations of Einstein annus mirabilis). Hubble replied that there was no hope of doing so, but that measurements during a total solar eclipse might be possible. A suitable solar eclipse took place in 1919, Eddington made the observations, and the rest is history. So possibly Einstein said different things before and after the test of GR proved successful. Dear Uncle Albert was only human?

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  26. John Duffield says:

    Pay careful attention to “vortex theory”. There are hands-on experimentalists doing work in this area, see for example http://www.physorg.com/news182957628.html, as Roger said the people involved in vortex theory during the 19th Century didn’t know about the electron, and it was Thomson and Tait who gave us “spherical harmonics”.

  27. CPV says:

    It’s obviously not clear which ideas will be successful ahead of time, so Monday morning quarterbacking of failed ideas is not a particularly noble or useful enterprise. I suspect the main point of this blog is the percentage of resources devoted to any one idea, not the concept that there shouldn’t or won’t be failed ideas, or that people shouldn’t be encouraged to work on wildly speculative ideas. Usually experimental evidence will break logjams and sort things out. We just don’t have any interesting evidence right now.

  28. Peter Woit says:


    In the case of string theory unification, the difference with “Monday morning quarterbacking” is that in the football case, the team that lost on Sunday had to acknowledge it. The problem with string theory unification research has in recent years evolved from a problem about relative allocation of resources into a more disturbing one of pseudo-science being promoted in order to allow failure to not be acknowledged.

    In this circumstance, a comparison of the current situation to previous ones where the failure is now clear to everyone may very well be enlightening.

  29. cormac says:

    Peter and Bee: of course it’s well-written!
    Helge Kragh is the author of Cosmology and Controversy, a highly regarded book on 20th century cosmology that focuses on the debate between the steady-state and BB models. It is a most unusual book in that it is considered historically accurate, scientifically accurate and highly readable. It is cited in almost every major cosmology book I have, whether textbook, popular book or historical analysis!

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