The Net Advance of Physics RETRO:

2013 April 8 - May 27
A New Approach to Experimental History of Science
Part 7: Conclusion

Image from NASA; artist not identified

2013 May 20

Having devoted so much of this series to Galileo and the equivalence principle, I wish that I could close with a discussion of F. A. Kaempffer's article "If Galileo Had Known Quantum Mechanics", published as an appendix to his regrettably little-used -- and very Twentieth-Century, in a positive sense -- textbook Concepts in Quantum Mechanics [New York: Academic, 1965, p. 347]. Unfortunately, the essay does not quite live up to its catchy title: Kaempffer merely gives a pædagogical proof of the startling theorem, discovered by Valentine Bargmann in 1954, that Galilean symmetry forbids the existence of superposed quantum-states involving particles with different masses (and thus that any theory of the elementary-particle mass-spectrum must be relativistic). The connexion to Galileo, beyond invocation of his invariance principle, seems too tenuous to call this an example of cenochronic history.

The physicist Henriette von Aigentler with her "sweet, fat, darling Ludwig". Engagement picture, 1875.

This objection does not apply to Elliott H. Lieb's similarly-titled 2006 paper "What if Boltzmann had known about quantum mechanics?" [in G. Gallavotti et al., Boltzmann's Legacy, Zurich: European Mathematical Society (2008), pp. 27-36]. Here we have a very subtle and profound investigation, not actually of what the historical Ludwig Boltzmann would have thought in a counterfactual environment, but rather of what his ability to find the laws of thermodynamics without knowing quantum mechanics tells us about the world: a true cenochronic conversation across time. Lieb writes:

"Much remains to be done if a derivation of the laws of thermodynamics is to be found that is free of physical assumptions and uncontrolled mathematical approximations ...

"I will not have much to say about the third question, but it is worth asking and it is not completely disconnected from the first question. To a physicist a question like this is a waste of mental energy because we do know that atoms exist, so why bother with alternatives. The point is that the deduction of the second law from a certain mechanical picture may not be as impressive as thought at first. If the second law follows from other (wrong, but not 'unphysical') assumptions then the implication is that we need not consider the second law to be astonishing, but rather that it is hard to avoid.

"The following quotation from L. Kadanoff illustrates the content of the third question: 'Boltzmann was right about atoms but utterly wrong in believing that atoms provide a necessary basis for thermodynamics. The second law does not require atoms. Thermodynamics would be equally correct if the basic constituents of the world were atoms, or quantum fields, or even strings.' While this may not be completely fair to Boltzmann, it is true that ... [t]he macroscopic laws of thermodynamics, by themselves, do not reveal properties of atoms, for otherwise the argument in Boltzmann's time about the existence of atoms would not have taken so long to resolve ... If atoms are not necessary for the second law of thermodynamics, what is necessary?"

To find out Lieb's answer, the reader is urged to read his remarkable cenochronic enquiry in full. Our present concern is with his general philosophical approach. He is interested in whether the Second Law can be discovered without making either Nineteenth-Century classical-atomist assumptions like the historical Boltzmann or Twentieth-Century quantum-mechanical assumptions of the sort commonly found in modern "derivations". How model-independent are the "laws of Nature"?

Euclidean & Non-Euclidean
Modification of the Parallel Postulate. Image by Søren Peo Pedersen

This is not a purely abstract metaphysical question without practical significance for the working scientist. If a "law of nature" reappears independently in quite different theoretical models, it must have a deep "fundamental" character, and is likely to survive Kuhnian paradigm-shifts. If, on the other hand, a "law", however predictively powerful and well-supported by evidence, can only be derived by following one particular sequence of arguments, one cannot help doubting its ultimate truth -- unless, of course, the chain of necessary steps has some non-obvious fundamental significance of its own. Either way, the issue of model dependence hints at a profound level of truth or falsity going beyond current fashion.

Whenever a "law of nature" shows signs of being dependent on a specific model, one is surely entitled to consider it dispensible, and to develop a new theory not including it. In pure mathematics, this is the standard way of proceeding. Want to discover a new kind of geometry? Go back to Euclid and drop the Parallel Postulate, so much weaker and more specialised than the other four. A new kind of logic? Go back to Aristotle and drop the Law of the Excluded Middle. New set-theory? Drop the Axiom of Choice. And so on.

In physics, however, this attitude is almost always considered suspect. "We know there are atoms, so we can't just pretend there aren't any!" There is a fallacy here. It lies in its assumption that there is a single uniform level of truth assignable to all propositions and discoveries.

Sketch of Saturn by Galileo in 1610
Galileo's view of Saturn, 1610.

Sketch of Saturn by Huygens in 1655
Huyghens's view of Saturn, 1655.

Cassini's Sketch of Saturn in 1676 Showing the Gap in the Rings
Cassini's view of Saturn, 1676.

What is a "fact"? Certainly, at least to a scientist, direct observation gives one access to "facts" about a situation. It is a "fact" that Saturn has rings; not only can one see them plainly through a small telescope, but in the Twenty-First Century spacecraft have flown through them. To doubt the Rings of Saturn would be akin to the solipsism of thinking all sensory data unreliable and the world a dream.

Nevertheless, although we have just agreed that "one can see the Rings plainly through a small telescope", early observers, including some of history's most renowned astronomers, were unable to do so. This was not because of inadequate optics; reconstructed Seventeenth-Century telescopes are demonstrably up to the task. It was these great observers' eyes, or rather brains, which were unable to resolve the Rings. Even today -- as I can attest from experience, having worked with the public at observatory star-parties -- many people who do not quite know what to expect will look at Saturn and see a strange, non-circular object ... but not the famous Rings.

Thus the Rings of Saturn, an observational fact, were for much of the 1600s a construct -- "those lights near Saturn are a great hoop encircling the planet!" -- which some people could reasonably deny in favour of other constructs -- "no, they're moons, or they're a hoop behind the planet, or they're just some kind of distortion". Over time, the ring interpretation of the observations became more and more difficult to deny, although someone with the perverse ingenuity of a clever flat-earther might continue to do so even now.

Atoms, which were finally imaged to most people's satisfaction in the late 1900s, were likewise only theoretical constructs for much of scientific history, and the details of their inner structure remain so today. As physics enters realms in which direct observation is ever more difficult, it becomes much harder to obtain unambiguous data which admit only one plausible interpretation; nevertheless, one interpretation of the data almost always comes to the fore. Sometimes this is because of its simplicity or its connexion to other accepted hypotheses; sometimes it is by sociological accident.

Perhaps, as in the case of atoms, technological advances may eventually provide strong support for the reigning theory, or for one of its competitors. Until then, however, one needs some additional assurance that a particular interpretation is correct. Model independence -- the spontaneous emergence of the same interpretation from rival paradigms -- is one instance of such assurance.

An Attractor. Image: Adam Majewski

Certain scientific concepts, then, are so firmly established that we may consider them "facts". Atoms may be one of these; the Rings of Saturn, the roundness of the earth, and the circulation of the blood are even better examples. Such facts, if facts they are, will inevitably emerge from any valid theoretical approach. They are attractors in theory space. A line of speculation which does not eventually lead to factual conclusions is useless. However, there is no need for a particular line of argument to predict every fact in order to be interesting.

To consider a more concrete example, one might choose to reject, say, quantum electrodynamics, in spite of the fact that it is contradicted by no experiment, and that its prediction of the Lamb shift is the greatest triumph of all theoretical physics in terms of numerical accuracy. These strengths notwithstanding, QED is a construct, an elaborate chain of argument. It does not (yet) "jump out" from the data, even though it explains them and is compatible with them. It could be wrong; the discovery of an error in QED would be far less astonishing than the discovery that Saturn has never had rings!

Thus, I say, it is reasonable to "reject" QED, not in the sense of proclaiming it false but in the sense of seeking an alternative. It might turn out that all reasonable attempts like this will fail to explain the data, or to explain them as well as QED; that would constitute a traditional form of verification, although obviously one can never be sure that every alternative has been considered.

More interestingly, it might turn out that any viable alternative to QED really is QED in disguise, as in fact happened in the early history of the field when Dyson showed that the (moderately) different approaches of Schwinger, Tomonaga, and Feynman were all in fact equivalent. This would point to QED being an attractor on which diverse theories must converge; the model independence would be indicative of its (possible) truth.

Finally, one might discover a new theory of microscopic electrodynamics: consistent, verifiable, elegant. This theory might or might not explain every datum explained by QED, and thus might or might not constitute a viable replacement for it, but this is unimportant. What would matter would be if the new theory could explain new facts or predict new phenomena beyond the scope of QED. If so, it would have earned its place in the scientific pantheon.

This example suggests an "alternate history" approach to doing research might be as fruitful in science as in pure mathematics. It would also restore an experimental aspect to theoretical physics and unite history of science with scientific practice.

Clio, Muse of History [Old Senate Chamber, US Capitol]

We now arrive at the end of this seven-part blog-entry. I have pointed out that when most "ordinary" people, outside of the academic-history establishment, think about the past, they do so anachronically, that is, in terms of a normative present. The ancients were "just like us", and "we" are the continuation if not culmination of their story. When anachronic thinkers address the question "What if ...", they are willing to entertain very different presents as outcomes of historical development. Nevertheless, they usually assume that modern scientific knowledege (in our timestream) accurately describes the physical universe, and therefore that, while the rate and sequence of scientific discovery might vary in an alternate world, all histories of science converge on the same theory of everything.

By contrast, academic historians are trained to think diachronically, and to treat the past as a world unto itself. They carefully avoid going beyond the evidence, thus making the ancients seem not at all "just like us", but inscrutable if not alien in motivation. They reject the "What if ... " question as undecidable, and therefore meaningless. Even though many academic historians would describe themselves as post-modernist and sceptical of science, there is paradoxically an underlying scientism in their devotion to what can be proven.

I have advocated a third approach, which I call "cenochronic". I propose that history, or at least the history of ideas, should be seen as an ongoing conversation between participants from different eras and therefore different cultures who nevertheless share a common humanity. The task of the historian is neither to judge whether past ideas were "significant contributions" to present understanding (the anachronic position) nor to isolate them as productions of a lost and separate world (the diachronic position). Rather, they should be debated as perpetually new, the latest thought from a foreign country which happens to be located not to the east, west, north, or south, but along the fourth dimension.

With this understanding, the "What if ..." question becomes central to historical research, at least in the field of intellectual history. By "going back" to the point in history where an idea was first proposed and considering what might have happened if the reception of the idea had been otherwise than the historical record indicates, one re-opens the idea as a living option. It becomes the basis for a vital field of enquiry which does not ignore the subsequent conclusions actually arrived at "in our timestream", but is not slavishly bound to accept them.

This approach can be applied to experimental science: the cenochronic historian recreates old experiments to see what new understanding emerges from them. It can also be applied to pure theory: the cenochronic historian re-thinks old ideas as if they were new.

This seems an appropriate place to end this essay on the experimental history of science. Nevertheless, I will next week append an epilogue discussing a subculture -- "steampunk" -- which has taken a cenochronic approach to recreating certain aspects of Nineteenth-Century technology and society, with mixed but largely encouraging results.

One of the steampunk movement's more impressive creations: the steam-powered vehicle Neverwas Haul in the Nevada desert, 2010.
Film © The Civilized Explorer. [34 sec]

Next: Epilogue