David Appell's "Ten Greatest Predictions in Physics"

Last week, physicist and science writer David Appell published his "Ten Greatest Predictions in Physics" in Physics World magazine.  Conceding that such a list of theoretical physics predictions is bound to be arbitrary, he invited discussion.  This is irresistible bait for DTLR!  However, instead of trying to propose a competing list, I will simply discuss what he has offered.

First, I would like to propose a taxonomy of theoretical physics predictions.  First, I make a distinction between retrospective and prospective predictions.  A retrospective prediction is a prediction of a previously observed phenomenon, perhaps lacking any theoretical explanation at the time.  A prospective prediction is a specific prediction that can then be experimentally or observationally verified, but does not correspond to a previously known phenomenon.  To borrow from Appell's list, Newton's prediction of Kepler's laws of planetary motion firmly belongs in the retrospective category, while Poisson's prediction of the "Arago spot" firmly belongs in the prospective category.

I contend that a prospective prediction lends greater credibility than a retrospective one, as in the latter, the theorist might have been influenced by knowledge of the known phenomenon in crafting his or her theory.  Thus, there may be a subtle "fitting" of the theory with the "facts", during the development of the theory.  This is of course understandable, as there is no point in developing a theory that contradicts known phenomena.  However, a prospective prediction is really going out on a limb - it's taking the ultimate risk for a theory, to predict something utterly new, and possibly wrong, and therefore far more convincing when verified.  Such a prediction most resembles the classic Popperian notion of a falsifiable theory, though in practice, in the face of a failure, theories could sometime be salvaged by later modifications.  Retrospective predictions that fail may often result in theories that never get published to begin with, and may never see the light of day.

However, retrospective predictions remain important and do provide some credibility to a theory.  The retrospective prediction may be made of a phenomenon directly related to a problem the theorist was trying to solve, or it may be to an unrelated physics problem; the latter seems more impressive and seems to provide corroboration along a different line of evidence than the one that inspired the theory.  Further examples are in order.  Max Planck used Boltzmann's energy quantization trick to produce a theory of blackbody radiation.  Planck was explicitly trying to find a theory of such radiation, and the resulting theory was quite consistent with known experimental data.  This is an example of a retrospective prediction concerning directly the problem the theorist was trying to solve.  However, when Einstein took the same hypothesis and used it to explain the photoelectric effect, he was taking a 'quantum leap' of sorts - elevating Planck's ad hoc quantization assumption to a principle of physics, and finding it could solve an apparently unrelated problem.  I surmise that this achievement, rather than Planck's original formulation, is what originally made the nascent quantum theory a serious player in theoretical physics.

So, now let's turn to Appell's list.  I would have to dispute the tenth prediction on the list, Rubin and Ford's prediction of dark matter, as I regard this as a discovery rather than a prediction, albeit a "theoretical" discovery.  Furthermore, it remains experimentally and observationally unknown what this dark matter is, so it is too early to assess.  

That leaves us with nine predictions, and I would categorize them as follows:

Retrospective:

• Newton's derivation of Kepler's laws from his theory of motion and theory of gravitation.
• Maxwell's prediction of the speed of light.
• Einstein's prediction of Mercury's anomalous perihelion precession.

Prospective:

• Poisson's and Fresnel's prediction of the Arago Spot, lending credibility to the wave theory of light.
• Goeppert Mayer's prediction of the second series of transuranic elements.
• Schwinger's prediction of the electron's anomalous magnetic moment.
• Hoyle's prediction of an excited state of carbon-12, a missing link in the theory of the nucleosynthesis of heavy elements.
• Lee and Yang's parity violation in the weak interaction.
• Josephson tunneling.

With the exception of Goeppert-Mayer's case, Appell tells us that the above prospective predictions were quickly verified experimentally.  I presume that the second series of transuranic elements required more time to experimentally discover, one by one; I wish Appell had said more about this.  For the purposes of this discussion I will assume that her predictions were indeed experimentally verified.

Of the prospective predictions, the Arago spot is the most impressive (and dramatic), as described by Appell.  Poisson was opposed to the wave theory, and confronted pro-wave Fresnel with his prediction, in an attempt to falsify the wave theory.  Fresnel admitted the correctness of the prediction, and Arago did the experiment, showing that the Arago spot did exist.  While this was not a decisive blow against the corpuscular theory (nor was Thomas Young's earlier double slit experiment), it certainly contributed to the accumulation of lines of evidence in favor of the wave theory.  

I can think of other consequential prospective predictions:  Dirac's prediction of the positron (confirmed) and magnetic monopole (unconfirmed); Einstein's prediction of length contraction and time dilation, from special relativity; and the prediction of Black Holes and the Higgs boson by multiple theorists.

Let's turn back to the retrospective predictions on Appell's list.  Newton was explicitly trying to solve celestial mechanics with this theory, so its ability to produce Kepler's laws was directly related to his motivation.  Nonetheless, this was likely the first time such a thing had been seen in the history of physics, so my comments should not detract from the towering achievement it represents.  The Maxwell and Einstein predictions were particularly interesting, as both theorists were after much bigger game than merely trying to predict the speed of light or Mercury's anomalous orbit.  Rather, both predictions are like interesting side effects of the resulting theories, yet definitely valuable in establishing their credence.

I will end with some predictions from my field, fluid mechanics.  Kolmogorov's phenomenological theory of turbulence ("K41") has been, to a large extent, experimentally corroborated within an extensive set of flow regimes, as discussed by Davidson (2015).  However, Davidson mentions that there is "anecdotal evidence" that Kolmogorov may have been aware of some 1935 measurements that would have supported one of the scaling laws Kolmogorov derived.  If so, K41 might have to be classified as retrospective rather than prospective, though this could certainly be open to historical dispute.

In Rayleigh-Benard convection, Schmidt & Milverton's 1935 experiments verified the predicted critical Rayleigh number for the onset of thermal convection proposed by Harold Jeffreys in 1928.  This as a prospective prediction.  However, that a critical Rayleigh number triggers the onset of convection in the first place, was first theoretically proposed by Rayleigh in 1916.  According to Koschmieder (1993), Benard himself essentially observed this feature in 1900, without realizing it, and was skeptical as late as 1930 about the critical temperature difference.  Rayleigh was well aware of and motivated by Benard's work.  The critical value of a control parameter at which a stable regime loses stability is now one of the basic pillars of hydrodynamic instability theory.

Reference

P. A. Davidson, 2015:  Turbulence:  An Introduction for Scientists and Engineers.  Second edition.  Oxford University Press, p. 218.

E. L. Koschmieder, 1993:  Benard Cells and Taylor Vortices.  Cambridge University Press.

Nobels Neglect Fluid Dynamics

This month's issue of Physics Today includes a letter to the editor from Rajan Menon, under the headline that I've reproduced as the title of this post.  Prompted by P. W. Anderson's obituary, Menon argues that "well-known physicists have worked in different aspects of fluid mechanics," mentioning Arnold Sommerfeld and Werner Heisenberg.  He then mentions three outstanding fluid dynamicists of the 20th century:  Ludwig Prandtl, Theodore von Karman, and G. I. Taylor.  Menon tells us that both Taylor and von Karman thought that Prandtl deserved a Nobel Prize in Physics.  Certainly all three of these illustrious individuals should have been strong candidates for the Nobel Prize, in my view.

Menon's letter nicely complements a post of mine from 2014, Nobel laureates and fluid dynamics research.  In that post I discuss the one Nobel Physics Prize that did seem to be awarded for research in fluid dynamics (H. Alfven, 1970) as well as the fluid dynamics activities of several other Nobel laureates, both in physics and chemistry, including Heisenberg.  I believe that Menon is essentially correct that "the field of mechanics, has been routinely neglected in considerations for the physics Nobel Prize."  However, aside from Prandtl, von Karman, and Taylor, all now long-dead, it is unclear to me who else should be a candidate.  The list of winners of the APS Fluid Dynamics Prize, for instance, features many outstanding researchers in this field, but what accomplishment would rise to the level of say, Prandtl's boundary layer theory, of such consequence to be honored by a Nobel Prize in physics?  To make the question more concrete, if the Nobel committee were to respond to Menon by selecting a Nobel Physics Prize for research in fluid dynamics next year, who would be the candidates among living fluid dynamicists? 

Menon proposes that if the Clay Mathematics Institute's Millenium Prize for proving the existence and smoothness of solutions to the 3-dimensional Navier-Stokes Equations is ever awarded, that person is deserving of a Nobel Physics Prize as well.  Though I sympathize greatly with Menon's letter, this is the one place I would part company with him.  The solution to this problem is rightly deserving of a top mathematics award, but I do not think it worthy of a Nobel Prize in Physics, simply because it is unclear a priori what physical insight would be gleaned from such a proof.

I would propose that the criteria for a Nobel Physics Prize to be awarded to fluid dynamics should be either for work of a total game-changing nature in the field, like Prandtl's boundary layer theory, or an advance in fluid dynamics that has colossal ripple effects in other areas of physics or technology, like Alfven's work in magnetohydrodynamics, including Alfven waves, which impact on plasma physics and astrophysics.

On the flip side, I do think Nobel physics laureates should continue to contribute their talents to fluid dynamics, as Rayleigh, Purcell, Landau, Onsager, and Chandrasekhar did.