In the spring of 1912 two research assistants in Munich directed an x-ray beam through a crystal and found that the beam was reformed into a well-defined interference pattern. The property most characteristic of periodic waves – their ability to interfere – is shared by the x-rays. Max Laue, the man chiefly responsible for the discovery, thought he had found proof that characteristic secondary x-rays from the crystal are periodic waves. But H. A. Lorentz quickly pointed out that impulses should interfere too. He showed, in a tour de force argument, that the accepted square pulse is an impossible representation of x-rays. William Henry Bragg and his son concluded that the interference maxima could, indeed, be due to irregular x-ray pulses. But, as such, x-ray impulses were not different from ordinary white light. They supported this claim with a new technique of crystal analysis fully analogous to ordinary optical spectroscopy.

Crystal diffraction provided a new tool for the analysis of x-rays. Pushed furthest by Henry Moseley and Charles Darwin, the technique soon showed that some x-rays comprise periodic wave trains of great length. The extremely sharp angular resolution of observed x-ray interference maxima indicated beyond doubt that x-rays are no different, except in frequency, from ordinary light. Rutherford soon extended the technique to the y-rays. Not only could one isolate characteristic γ-rays, he believed, one could show, with some effort, that they interfere too.

The successful integration of the new spectroscopy with the Bohr atom came, as had x-ray diffraction, from Sommerfeld's Munich.

The same x-ray spectroscopic techniques that led to the identification of the atomic origin of x-ray spectra also offered means to test the localization of energy in the radiation. In the second decade of this century, x-ray spectrometers used as monochromatizers provided more purely defined x-rays than had been available from natural characteristic radiation. This, coupled with techniques to determine the kinetic energy of secondary electrons, provided opportunities for precise testing of the quantum transformation relation, E = hv. These experiments form the subject of this chapter.

We are primarily concerned here with the absorption of radiation, not with its emission. To be sure, the quantum regulation of the emission of radiant energy has no classical explanation; yet there is no electromechanical inconsistency implied in the creation of a spherical wave containing a definite amount of energy. It is the inverse case that causes real difficulty. How can that quantum of spherically radiating energy concentrate its full power on a single electron? For this reason, verification of the quantum relationship for emitted radiation lies outside our direct concerns. The Franck-Hertz experiments beginning in 1912, for example, demonstrated the quantum nature of energy transfer, but they did little to encourage acceptance or even consideration of the lightquantum. On the other hand, the experiments detailed here that verified the quantum nature of the absorption of light and x-rays gave substance to the lightquantum hypothesis because they verified the particlelike transfer of radiant energy to matter.

Between 1898 and 1912, a majority of physicists thought that x-rays were impulses propagating through the electromagnetic field. Only the extremely large number of pulses gave the x-ray beam its seeming continuity. Although this hypothesis was compatible with the wave theory of light, it was a special case of that theory. Impulses are not ordinary waves. Although they propagate spherically outward from their source, pulses are not periodic oscillations. The energy in an impulse is temporally but not spatially localized. It is contained within an ever-expanding shell, but the shell's radial thickness remains constant and small. Along the circumference, energy is distributed uniformly. But radially, from front to back so to speak, electromagnetic energy rises quickly from zero and drops back just as rapidly. When it passes a point in space, an impulse exerts only a single push or a single push – pull. A pulse collides, rather than resonates, with an atom.

In their temporal discontinuity, impulses differ decisively from their periodic-wave cousins. Light has an intrinsic oscillatory character that allows it to interfere; the superposition of two beams of coherent monochromatic light produces alternate regions of constructive and destructive interaction, the well-known interference fringes. A pulse has no oscillatory structure. Its interference properties are qualitatively different from those of light. A truly monochromatic light wave must extend infinitely in time; if it does not, an intrinsic ambiguity arises in the definition of its frequency. A pulse is restricted in temporal extent, and the very concept of frequency cannot readily be applied.

When x-rays or γ-rays strike atoms, electrons and secondary x-rays are emitted. Experiments to sort out the differing properties of the two secondary components produced new and perplexing observations in the first decade of this century. The most perplexing problems concerned the effect of the rays in producing secondary electrons. First, x-rays and γ-rays ionize only a small fraction of the total number of gas molecules through which they pass. Spherically expanding pulses should affect all molecules equally; manifestly, they do not. Second, the velocity that x-rays impart to electrons is many orders of magnitude higher than one would expect to come from a spreading wave. The energy in the new radiations seemed to be bound up in spatially localized packages, available to an electron in toto.

British physicists responded to these paradoxes with attempts to revise, rather than replace, classical electromechanics. J. J. Thomson suggested that old ideas about the microscopic structure of the aether might have to be reformulated. William Henry Bragg concluded that x-rays and γ-rays are not impulses at all but rather neutral material particles. Bragg and Thomson tried at first to find explanations using models based on human experience with machines. Each sought a resolution within the context of classical mechanics; each ultimately failed.

Between 1909 and 1912, many influential physicists first realized that the problems preventing a consistent understanding of x-rays applied as well to ordinary light. But unlike the relatively new impulse theory of x-rays, the wave theory of light was exceedingly well founded. It rested on a century's accumulation of experimental evidence. Spatial concentration in the energy of light could not be attributed to a temporal discontinuity, as it could for x-ray impulses. Light was known to be a repeating periodic wave. It was not fully realized at first that hypotheses about the nature of ordinary light required modification. For a decade after 1910, the significance of the growing empirical evidence favoring spatial localization of luminous energy went largely unrecognized. This occurred because the data ran counter to the orthodox view of visible light, the spectral region wherein the periodic properties of radiation were most easily demonstrated and most firmly established.

H. A. Lorentz attacked the problem in much the same spirit, but with quite the opposite intent, as had Einstein. He showed in 1909 that the lightquantum hypothesis is incompatible with the quantum transformation relation itself, let alone with classical ideas about radiation. In so doing, he laid the foundation for a restatement of a major difficulty with any classical explanation of the photoelectric effect: It takes an extraordinarily long time for the observed quantity of energy to build up from periodic waves incident on an electron.

It is not entirely surprising that the earliest reaffirmation of the dualism inherent in radiation came neither from Britain nor Germany. There the issues had been recognized, discussed, and dismissed over the preceding twenty years. And American research traditions were largely derivative of German and British models; Duane and Millikan had both studied under Planck, and Richardson did research with Thomson in Cambridge. It took an outsider to these traditions to raise the issues in a way that began to convince others.

That process began in France. Maurice and Louis de Broglie were, by any standards, unusual physicists. Amateurs in an age of professionals, possessing a confidence born of noble status, working on experiments that had only the meagerest precedent in their homeland, they were not as firmly bound by the predispositions that prevented physicists of other nations from directly assessing the spatially localized lightquantum.

Their conversion was real. Maurice had once been convinced that x-rays and γ-rays fit neatly into the electromagnetic spectrum. In his discussion, La nature des rayons de Röntgen in 1915, there was no thought that x-rays might be anything other than periodic waves. As late as May 1920, he spoke freely of x-ray “wavelengths” and discussed the optical fluorescence that results from degradation of x-ray “frequency.” But late in 1920 he reviewed the new evidence accumulated at high x-ray frequencies. There he hinted at unspecified difficulties in the orthodox wave interpretation of x-rays.

The discussions between Bragg and Barkla in Britain, and between Stark and Sommerfeld in Germany, encouraged attempts to determine how much spatial concentration of radiant energy was demanded by ionization, and how much was compatible with classical electromagnetic theory. Mirroring the different perceptions of and approach to the problems of x-ray absorption in Britain and in Germany, there were two parallel responses. J. J. Thomson recognized that the paradoxes applied equally to all forms of radiation. He influenced important experimental tests of energy localization, and concluded that the classical ideal of symmetry of the electric field around an electron would have to be abandoned. Arnold Sommerfeld took no refuge in the alteration of the physical interpretation of Maxwell's theory. He pressed formal electrodynamics to its extreme to show that the energy of y-rays might be localized to an extent compatible with recent experiments.

But neither Thomson's nor Sommerfeld's treatment addressed the most compelling problem raised by Bragg and Stark. The energy transferred from a wave to an electron does not seem to change when the distance from the source changes. No matter how severely limited in angular extent the energy of x-rays and γ-rays might be according to Thomson or Sommerfeld, that energy is still diluted in strength as the rays traverse space. Neither of them therefore confronted the issues in quite the same way as did Bragg, who had never intended his neutral-pair hypothesis to apply to ordinary light.

The first three decades of the twentieth century embraced two great changes in physical theory: relativity, both general and special, and quantum theory, both the old and the new. Among the innovations that constituted these theories, none was more difficult to accept and assimilate than Einstein's suggestion that light displays particulate properties, especially at high frequencies. Together with the related recognition of the wavelike properties of material particles, Einstein's light-particle theory has proved a fundamental constituent of modern physics, perhaps the single feature that most sharply distinguishes it from the generally Newtonian physics of the preceding three hundred years. But for nearly twenty years after Einstein's proposal in 1905, the concept of light-particles was almost everywhere rejected. Even R. A. Millikan, who in 1914–16 provided the first unequivocal evidence for Einstein's surprising law of photoelectric emission, continued, equally unequivocally, to disdain the light-particle hypothesis from which that law had been derived. Only after 1923, when Compton and Debye independently used the light-particle hypothesis to explain the shift in frequency of scattered x-rays, did more than a very few isolated physicists begin to take seriously the idea that electromagnetic radiation often behaves like particles.

That, in outline, is the way that historians of physics have recently been telling the story of the light-particle hypothesis, and with respect to Einstein it remains very nearly the way the story should be told. But, as Bruce R. Wheaton amply demonstrates in the pages that follow, Einstein's was only one approach to conceiving radiation as particulate.

The discovery of x-rays reduced much natural reluctance on the part of physicists to report other discoveries. The most significant new claim, one recognized within weeks of Röntgen's announcement, was the discovery of radioactivity by Henri Becquerel. Certain minerals were found to emit rays spontaneously. Not even the electrical potential difference necessary for the production of cathode rays and x-rays was required. No human artifice or intervention was needed to produce the Becquerel rays; this was always their most significant and unique property. For this reason, it was soon widely believed that the rays were the residue of spontaneously disintegrating atoms.

However distinct the physical origin of Becquerel rays was from that of x-rays, telling similarities between the two new emanations were quickly recognized. Both could penetrate opaque paper to expose a photographic plate. Like x-rays, Becquerel rays were first discovered in this way. They seemed to be another invisible radiation, rendered perceivable only through the superhuman sensitivity of photographic plates. It was soon shown that x-rays and Becquerel rays both induce electrical conductivity in gases through which they pass. In fact, as we have seen, Becquerel's rays were first thought to fill the gap that separated x-rays from ordinary light. Becquerel claimed that they could be refracted and polarized; although soon disproven, these claims served to solidify the view that Becquerel rays resembled light more closely than did x-rays. For these reasons, Becquerel rays were early on identified as a form of radiation in the aether.

The first years of this century witnessed the final rejection of determinism in physical theory; there is no more compelling example of this than the synthesis forged in the early 1920s between theories of matter and theories of light. The insight of Louis de Broglie that led to the most complete formulation of wave–particle dualism was the last act in a series of preliminary attempts by physicists to resolve paradoxes that had arisen in theories of radiation following the discovery of x-rays. Historians have not directed sufficient attention either to radiation theory or to experimental studies of recent physics. In the case at hand, significant empirical data were recognized to challenge classical radiation theory long before the theory was successfully modified to agree with them. The gradual recognition, based on these experimental results, that internal consistency is unattainable by electromechanical interpretations of radiation forms the subject of this book.

This study grew out of concerns first raised while I was a student of physics. The inadequacy of most textbook discussions of historical and epistemological issues led me back to the original papers and then to the literature on history of science. I was fortunate to be introduced to the latter by John Heilbron, whose critical approach and demand for clarity in expression showed how insight can be won in historical analysis of scientific thought.