THESIS Minkowski, Abraham and the photon momentum One might expect that the he proposed an early theory of the counter-propagating light beams and momentum of a photon, under electron, and worked hard to fi nd a detected the interference of the two almost any conditions, would consistent mathematical description component recoiling condensates. no longer be a matter of dispute. of the reaction force due to radiation Second, although the index of Most textbooks certainly give emitted by an accelerating charged refraction for a dilute atomic gas is that impression. Yet, in fact, a particle. Abraham argued that the close to one, larger deviations can be fundamental uncertainty, recognized photon inside the medium would obtained for a condensed gas. Th e a century ago, still lingers. Suppose have a lower velocity and lower interference fringes measured agreed that a photon, having momentum momentum, the medium itself closely with Minkowski’s formula. ħk in vacuum, enters a transparent absorbing the diff erence. In classical One recent Even so, Ulf Leonhardt of the medium with index of refraction terms, Abraham’s momentum University of St. Andrews points n > 1. What is the photon’s new is ∫ d 3x E × H, or in quantum experiment out that Abraham’s ideas may still momentum? Remarkably, there is terms p = ħk/n. backs up have life (Nature 444, 823–824; still no defi nitive answer. Nearly 100 years later there is 2006). Starting from the perspective In 1908, the German still no clear answer as to which Minkowski’s of general relativity, other theorists (although Russian-born) physicist of these formulae is correct. It’s answer — but have shown that both Abraham’s Hermann Minkowski derived one possible, of course, that both could and Minkowski’s formulae can possible, yet surprising, answer. be, yet refer to subtly diff erent still may not be derived, and may apply under In classical terms, Minkowski situations or interpretations. Th e past prove Abraham diff erent conditions. Still other work found the total momentum of the decade has seen renewed interest wrong. argues that these two formulae electromagnetic fi eld to be equal to in this puzzle, stimulated in part by correspond to essentially diff erent ∫ d 3x D × B. In quantum terms, this the increasing precision of quantum quantities — one (Abraham) to the suggests that the photon momentum optics. One recent experiment backs momentum of the photon itself, should actually increase and take up Minkowski’s answer — but still and the other (Minkowski) to that the value nħk. In eff ect, Minkowski may not prove Abraham wrong. of the photon plus the medium in started from Einstein’s earlier Th e idea was to measure the which it lives. To be certain which suggestion that a photon’s energy is recoil of a Bose–Einstein condensate momentum an experimental set-up given by E = hυ. Assuming a velocity as photons are refl ected from its measures is non-trivial. c/n and p = h/λ, one fi nds that p = nħk. surface (G. M. Campbell et al. So despite what seems like One year later, the German Phys. Rev. Lett. 94, 170403; 2005). conceptual simplicity itself, there physicist Max Abraham proposed a Such a set-up off ers two advantages. is actually very little that is simple. diff erent answer. Abraham’s entire First, extreme accuracy can And the debate over this matter career focused on the classical be achieved through atom shows no sign of ending soon. theory of electromagnetism. In 1902, interferometry. Th e researchers used Mark Buchanan Three steps to fraud

In every case of scientifi c fraud under career pressure (as most By international agreement, new I knew of, I realized that three scientists almost always are) and elements are not offi cial until their factors were present: the scientist both thought they knew the right discovery has been reproduced, was under career pressure; he answer. Th e test of my hypothesis which groups in Germany and thought he knew the answer, and would be the third factor. Japan immediately undertook to didn’t need to go to all the trouble Th e Schön case fi ts like a glove. do — but both failed. of obeying the scientifi c method; He apparently made a breath-taking In 2001, the BGS group and he was working in a fi eld series of discoveries in MOSFETs produced a fourth signature decay where reproducibility was not (metal-oxide semiconductor fi eld- chain. By now, suspicions had been precise. Th e last of these explained eff ect transistors), a fi eld that is The scientists aroused. A series of investigations why fraud was almost always in notoriously sample-dependent: the ensued, in which it was found that biomedicine, where the truth is fact that nobody could reproduce were under the data for all four decay chains generally more statistical and less his results could just have meant career pressure, had been fabricated, and that directly causal. that they had bad samples. Ninov was the only person in a Th en, in 2002, two cases Victor Ninov was a leader and thought position to have done it. of scientifi c misconduct by of the group at LBNL using the they knew the Th us he had turned my third physicists came to light, one Berkeley Gas-fi lled Separator right answer. factor on its head. Ninov had involving Jan Hendrick Schön at (BGS) to sort through the debris assumed that his result would Bell Laboratories, and the other of nuclear collisions. In 1999, the be reproduced — and that Victor Ninov at Lawrence Berkeley group announced the observation he would get the credit for National Laboratory (LBNL). In of three instances of decay chains discovering it fi rst. both cases, the scientists were characteristic of the element 118. David Goodstein

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