Eistein on the Photoelectric Effect

Light and other electromagnetic radiation, such as radio waves, are obviously waves—or so everyone thought. Maxwell and Lorentz had firmly established the wave nature of electromagnetic radiation in electromagnetic theory. Numerous experiments on the interference, diffraction, and scattering of light had confirmed it. We can well appreciate the shock and disbelief when Einstein argued in 1905 that under certain circumstances light behaves not as continuous waves but as discontinuous, individual particles. These particles, or "light quanta," each carried a "quantum," or fixed amount, of energy, much as automobiles produced by an assembly plant arrive only as individual, identical cars—never as fractions of a car. The total energy of the light beam (or the total output of an assembly plant) is the sum total of the individual energies of these discrete "light quanta" (or automobiles), what are called today "photons." Theories of matter and electromagnetic radiation in which the total energy is treated as "quantized" are known as quantum theories. Although Einstein was not the first to break the energy of light into packets, he was the first to take this seriously and to realize the full implications of doing so.

Like the special theory of relativity, Einstein's quantum hypothesis arose from an experimental puzzle and an asymmetry or duality in physical theories. The duality consisted of the well-known distinction between material atoms and continuous ether, or, as Einstein wrote in the opening sentence of his light quantum paper, "between the theoretical conceptions that physicists have formed about gases and other ponderable bodies and the Maxwell theory of electromagnetic processes in so-called empty space." As noted earlier, Boltzmann and others conceived of gases as consisting of myriads of individual atoms, while Maxwell and Lorentz envisioned electromagnetic processes as consisting of continuous waves. Einstein sought a unification of these two viewpoints by removing the asymmetry in favor of a discontinuous, "atomic," or quantum, theory of light. Resolution of an experimental puzzle encouraged this approach.

The puzzle concerned so-called blackbody radiation, that is, the electro-magnetic radiation given off by a hot, glowing coal in a fireplace, or the radiation emerging from a small hole in a perfectly black box containing electromagnetic radiation at a high temperature. Scientists at the German bureau of standards in Berlin, who were interested in setting standards for the emerging electric lighting industry in Germany, had measured the distribution of the total electromagnetic energy in a black box—which would also apply to a glowing light bulb—among the different wavelengths of the light. But no one until Max Planck, at the turn of the century, was able to give a single mathematical formula for the observed distribution of the energy among the emitted wavelengths. Starting with the Maxwell-Lorentz theory of radiation and some natural assumptions about energy, Planck hoped to derive this formula from the second law of thermodynamics. Planck failed to attain the observed formula on these assumptions. Even Lorentz had to admit that his own electron theory could not account for blackbody radiation.

Only by reluctantly introducing a radical new assumption into his mathematics could Planck attain the correct formula. The assumption was that the energy of the radiation does not act continuously, as one would expect for waves, but exerts itself in equal discontinuous parcels, or "quanta," of energy. In essence Planck had discovered the quantum structure of electromagnetic radiation. But Planck himself did not see it that way; he saw the new assumption merely as a mathematical trick to obtain the right answer. Its significance remained for him a mystery. Thomas Kuhn has argued that it is not to Planck in 1900 but to Einstein in 1905 that we owe the origins of quantum theory.

Encouraged by his brief but successful application of statistical mechanics to radiation in 1904, in 1905 Einstein attempted to resolve the duality of atoms and waves by demonstrating that part of Planck's formula can arise only from the hypothesis that electromagnetic radiation behaves as if it actually consists of individual "quanta" of energy. The continuous waves of Maxwell's equations, which had been confirmed experimentally, could be considered only averages over myriads of tiny light quanta, essentially "atoms" of light.

With his light quantum hypothesis Einstein could not only derive part of Planck's formula but also account directly for certain hitherto inexplicable phenomena. Foremost among them was the photoelectric effect: the ejection of electrons from a metal when irradiated by light. The wave theory of light could not yield a satisfactory account of this, since the energy of a wave is spread over its entire surface. Light quanta, on the other hand, acting like little particles, could easily eject electrons, since the electron absorbs the entire quantum of energy on impact.

At first Einstein believed that the light-quantum hypothesis was merely "heuristic": light behaved only as if it consisted of discontinuous quanta. But in a brilliant series of subsequent papers in 1906 and 1907, Einstein used his statistical mechanics to demonstrate that when light interacts with matter, Planck's entire formula can arise only from the existence of light quanta—not from waves. Einstein considered that light quanta, together with the equivalence of mass and energy, might result in a reduction of electrodynamics to an atom-based mechanics. But in 1907 he
discovered that atoms in matter are also subject to a quantum effect.

Here he made use of another galling experimental problem. Experimentalists had found that when solid bodies were cooled, the amount of heat they lost failed to fit a simple formula that followed from Newtonian mechanics. Einstein showed that the experiments could be explained only on the assumption that the oscillating atoms of the solid lattice can have only certain, specific energies, and nothing in between. In other words, even the motions of atoms—which are continuous in Newtonian mechanics—exhibit a quantum structure. Mechanics and electrodynamics both required radical revision, Einstein now concluded: neither could yet account for the existence of electrons or energy quanta.