This page is a nontechnical version of my article Are atoms waves or particles? Even for the nontechnical reader, the figures, especially Figs. 1 and 4, of that article will help in understanding the nature of the Kapitza-Dirac effect.
I have been classified as a stubbornly nineteenth-century physicist, and that is a label I happily accept. During that century the wave theory of light triumphed over the corpuscular theory of Newton, which was the forerunner of today's fashionable theory of photons . I think that today's supporters of the photon theory, known as Quantum Optics, are as misguided as the disciples of Newton's Opticks in the eighteenth century. The first quantum optician was Albert Einstein. He wrote the first article on photons in 1905, the same year as his first article on Relativity. I think his photon article, for which he was awarded the Nobel prize in 1921, was misguided.
The other great theory of the nineteenth century was the Kinetic Theory of Heat, which established that matter is made up of atoms with diameters rather less than 1 nanometer. Its establishment entailed another immense ideological struggle. Indeed the kinetic theory became the dominant one only at the beginning of the twentieth century. You can read the history of the struggle in the book The Kind of Motion We Call Heat by Stephen Brush. There was a succession of famous, and also some undeservedly obscure, scientists involved, but the decisive contributions were those of Ludwig Boltzmann and Albert Einstein. The latter showed that the Brownian motion of small dust particles is caused by the bombardment of the even smaller atoms of the surrounding gas or liquid. That article of Einstein, together with his justly celebrated Relativity article, was published in 1905. So he published only one misguided article during that year!
Although Einstein took something of a false turn in his treatment of the light field, he rejected the wave description of atoms in the new Quantum Mechanics of Erwin Schroedinger, Werner Heisenberg and Paul Dirac. The latter, together with Peter Kapitza, designed a particularly striking demonstration of wavelike behaviour, originally for electrons but later extended to atoms. A uniform beam was predicted to give, when scattered by a laser wave, a pattern not unlike that when a uniform beam of light is scattered from a diffraction grating. The observation of the Kapitza-Dirac effect in recent times has been widely accepted as evidence that such "atomic waves" really exist. But how can that be, since Boltzmann showed, and every chemist now knows, that atoms have a diameter less than 1 nanometer, whereas the spacing of the laser "grating" is about 600 nanometers?
My answer is one which Boltzmann and Einstein would have readily accepted. A scattering pattern quite similar to that predicted on the atomic-wave model may be obtained from a pointlike model of the atom. The latter, being rather heavy compared with an electron, suffers almost no actual deflection in its passage across the laser, but it does acquire a small transverse momentum. Furthermore, this momentum change depends on the part of the laser wave the atom passes through. A crucial part of the model, which makes the scattering pattern resemble very closely the "diffraction pattern" of the wave theory, is that it is stochastic. At any given moment in its passage through the laser the atom may receive an impulse sending it in either an "up" or a "down" direction with respect to the laser (Fig.4 from my technical article will help here).
This kind of capricious behaviour has been widely believed as unique to quantum systems. Einstein once wrote, in a letter to Max Born, that God does not play dice, and Born replied that classical God does not, but quantum God does. The fact is that Einstein wrote that letter to Born on one of his off-days, since Einstein himself had written the article in 1905 on Brownian motion that I referred to above. The capricious bombardment of the dust particles which Einstein demonstrated was not God's fault at all, but simply the submicroscopic environment of the fluid's molecules. It is a simple feature of Nature, discovered by the thermodynamicists of the nineteenth century (Kelvin, Maxwell, Clausius, and above all Boltzmann) that every physical system must be considered to be embedded in a heat bath, which means that no description of the system by a set of internal dynamical variables is complete; we neglect the environment at our peril.
We are not quite in the same position with respect to the capricious impulses suffered by the atom as that of Einstein in analyzing the bombardment of the dust particle. But we do now know that, as well as experiencing the organized field of the laser, the atom is subject to a random or stochastic electromagnetic field, whose properties have been quite extensively studied for more than 50 years. This field, known as the "vacuum" or "zeropoint" field, was actually first proposed by Max Planck in 1911, because Planck was unable to accept Einstein's photons. There is a modern discipline, known as Stochastic Electrodynamics, which continues to develop this very simple, though unfashionable, concept of Planck. We believe we are using the least well known of Einstein's three 1905 articles, in order to repair the damage caused by the one for which he is most revered, and for which he was awarded, misguidedly, the Nobel prize.