With the war over, de Broglie started work on his physics Ph.D., attracted he says, “by the strange concept of the quantum.” Three years into his studies, he read the recent work of the American physicist Arthur Compton. An idea clicked in his head. It led to a short doctoral thesis and eventually to a Nobel Prize.
Compton had, in 1923, almost two decades after Einstein proposed the photon, discovered, to his surprise, that when light bounced off electrons its frequency changed. This is not wave behavior. When a wave reflects from an object, each incident crest produces one other wave crest. The frequency of the wave therefore does not change in reflection from a stationary object. On the other hand, if Compton assumed that light was a stream of particles, each with the energy of an Einstein photon, he got a perfect fit to his data.
The “Compton effect” did it. Physicists now accepted photons. Sure, in certain experiments light displayed its spread-out wave properties and in others its compact particle properties. As long as one knew under what conditions each property would be seen, the photon idea seemed less troublesome than finding another explanation for the Compton effect. Einstein, however, still “a man apart,” insisted a mystery remained, once saying “Every Tom, Dick, and Harry thinks they know what the photon is, but they’re wrong.”
Graduate student de Broglie shared Einstein’s feeling that there was a deep meaning to light’s duality, being either extended wave or compact particle. He wondered whether there might be symmetry in Nature. If light was either wave or particle, perhaps matter was also either particle or wave. He wrote a simple expression for the wavelength of a particle of matter This formula for the “de Broglie wavelength” of a particle is something every beginning quantum mechanics student quickly learns.
The first test of that formula came from a puzzle that stimulated de Broglie’s wave idea. If an electron in a hydrogen atom were a compact particle, how could it possibly “know” the size of an orbit in order to follow only those orbits allowed by Bohr’s by-now-famous formula?
The length of violin string required to produce a given pitch are determined by the whole number of half-wavelengths of vibrations that fit along the length of the string. Similarly, if the electron was a wave, the allowed orbits might be determined by a whole number of electron wavelengths that fit around the orbit’s circumference. Applying this idea, de Broglie was able to derive Bohr’s ad hoc quantum rule.
(In the violin, it’s the material of the string that vibrates. What vibrates in the case of an electron “wave” was a mystery. It’s become an even deeper one.)
It’s not clear how seriously de Broglie took his conjecture. He certainly did not recognize it as advancing a revolutionary view of the world. In his own later words:
[H]e who puts forward the fundamental ideas of a new doctrine often fails to realize at the outset all the consequences; guided by his personal intuitions, constrained by the internal force of mathematical analogies, he is carried away, almost in spite of himself, into a path of whose final destination he himself is ignorant.
De Broglie took his speculation to his thesis adviser, Paul Langevin, famous for his work on magnetism. Langevin was not impressed. He noted that in deriving Bohr’s formula de Broglie merely replaced one ad hoc assumption with another. And de Broglie’s assumption, that electrons could be waves, seemed ridiculous.
Were de Broglie an ordinary graduate student, Langevin might have summarily dismissed his idea. But he was Prince Louis de Broglie. Aristocracy was meaningful, even in the French republic. So no doubt to cover himself, Langevin asked for a comment on de Broglie’s idea from the world’s most eminent physicist. Einstein replied that this young man has “lifted a corner of the veil that shrouds the Old One.”
Meanwhile, there was a minor accident in the laboratories of the telephone company in New York. Clinton Davisson was experimenting with the scattering of electrons from metal surfaces. While Davisson’s interests were largely scientific, the phone company was developing vacuum tube amplifiers for telephone transmissions, and for that the behavior of electrons striking metal was important.
Electrons usually bounced off a rough metal surface in all directions. But after the accident, in which a leak allowed air into his vacuum system and oxidized a nickel surface, Davisson heated the metal to drive off the oxygen. The nickel crystallized, essentially forming an array of slits. Electrons now bounced off in only a few well-defined directions. The discovery confirmed de Broglie’s speculations that material objects could also be waves.
I began these recent “Histories” with the first hint of quantum in 1900. It was a hint largely ignored. We now reach the state of physics in 1923 where scientists finally are forced to accept a wave-particle duality and the concept of quantum. A photon, an electron, an atom, a molecule — in principle any object — can be either compact or widely spread-out. You can choose which of these two contradictory features to demonstrate. The physical reality of an object depends on how you choose to look at it.
So we go from the strange concept of quantum energy in physics to the even weirder view that energy waves can be particles and solid objects can be waves. This duality of Nature is not the strangest thing in Quantum Mechanics. It’s strange and weird, that’s for sure, but there’s more to come — even stranger and weirder.
Since I really consider this series in my blog a “rough draft” of some ideas that need polish and editing, I still have time to go back and correct an oversight in Chapter One. The ancient Greeks recognized that the music from their stringed instruments was most pleasing when the various notes in a melody came from whole number fractions of the basic (or tonic) string. Out of that came modern music with octaves (when the string length is one-half), thirds, fourths, fifths, etc. This was reflected in their mathematics and what we call “rational numbers.”
The Greeks thought that all numbers were made up of fractions of whole numbers just like the pleasing music of the whole number fractions on stringed instruments.
A story is told that when the first mathematician realized that the square root of two was not a number made from a fraction, that he was thrown overboard (literally) as some kind of heretic.
It has always been my hypothesis that it was this recognition of the connection between simple fractional string lengths and the pleasing esthetics of the musical result that demonstrated to the Greeks that concepts of Nature could be represented as simple formulas. That idea was the beginning of scientific thought.
So isn’t it interesting that the concept of string lengths and half-wavelength explanation that impressed the Greeks appears again a couple of thousand of years later in the most sophisticated science we know of.
That fact has always been a significant point to me. I probably won’t win the Nobel Prize for describing it. But it is something to think about — isn’t it? Who knew that science would be so advanced by “music.”