Louis de Broglie's story is that of a prince who became a physicist, whose work on the nature of the electron has left a mark on history and contributed to the development of quantum mechanics.
Louis Victor de Broglie vuonna 1929.
Encyclopedia Britannica
One hundred years ago, on November 25, 1924, Prince Louis Victor de Broglie (1892-1987), at the age of 32, defended his doctoral thesis in physics before a jury that included Paul Langevin and Jean Perrin. In it, he presented his theory of wave-particle duality applied to electrons.
Five years later, at just 37 years old, he would receive the Nobel Prize in Physics for his "discovery of the wave nature of the electron".
He was elected a member of the Academy of Sciences in 1933, and then in 1944 to the French Academy, where he was welcomed by his own brother Maurice. In 1960, Louis inherited the title of duke upon the death of this older brother. What a fascinating journey!
The photon between wave and particle
The world of the infinitely small, that of elementary particles, operates under laws that are very different from those that apply to the ordinary world, primarily the strictly deterministic law of gravitation. The behavior of particles is governed by a so-called "quantum" mechanics, which uniquely predicts only the probabilities of a phenomenon occurring. We can precisely calculate the trajectory of a falling stone, but this is no longer true for a particle.The nature of light had been debated since the 17th century between Newton's granular view and Huyghens' wave view. In the 19th century, with Maxwell's equations, the matter seemed settled, and the wave nature of light was established.
However, in 1905, Einstein changed the game by interpreting the "photoelectric effect", in which an illuminated metal plate can produce electricity only if the light it receives has a sufficient frequency. To explain this phenomenon, Einstein imagined light as a flow of elementary objects he called photons: the effect was interpreted as a collision between the metal's electrons and the incident light's photons. A minimum energy is required to free the electrons from the plate, which is provided by blue photons, which are more energetic than red photons.
This aligned with the idea put forth by Planck in 1900, who, to explain black body radiation, that is, a heated cavity filled with gas, hypothesized that energy exchanges occur in small, well-defined quantities he called "quanta" (i.e., elementary grains), whose energy satisfies the so-called Planck formula E = hf where E represents energy and f frequency, and thus color (h is a tiny physical parameter known as Planck's constant).
From this speculation by Max Planck, Niels Bohr conceived the planetary model of the atom, where electrons orbit around the nucleus on fixed energy orbits, like planets around the sun.
With Einstein's interpretation of the photoelectric effect, the "quantization of light" (that is, light is composed of "elementary grains", particles) returned with force.
So, is light a wave or a flow of particles? The surprising answer is both. This is the famous wave-particle duality that acknowledges two facets of reality: light interacts in the form of photons (particles), but it propagates in the form of a wave.
This leads to consequences that may shock common sense, challenging determinism. In particular, Werner Heisenberg wrote his uncertainty relations, which teach us that it is impossible to know both the position and the speed of a particle precisely.
The electron plays the string
Broglie's contribution was to demonstrate that electrons can also behave like a wave. He thus extended the idea of wave-particle duality beyond the photon, proposing a symmetry among all particles. This symmetry was not obvious because there is a significant difference between a massless photon and an electron with a well-defined mass.The massless nature of the photon forces it to always move at the speed c = 300,000 kilometers per second. For the photon, Planck's quantization relation is written as E = hf. De Broglie generalizes to the case of a massive particle and proposes that the wavelength λ of a particle with mass m traveling at speed v is given by the formula: λ = h/mv.
Note that this wavelength is infinitesimal for a macroscopic object: a 200-gram ball moving at a speed of 15 meters per second corresponds to a wavelength of 2 × 10^-34 meters (that is, thirty-three 0s followed by a 1 after the decimal)! But for an electron accelerated by a voltage of 100 V, the wavelength becomes 10^-10 meters, which is the spacing between atoms in a crystal, and thus by sending a beam of electrons through a crystal, one can hope to detect an "electron wave" effect.
Davisson and Germer conducted the corresponding experiment and observed in 1927 interference and diffraction patterns from electrons, similar to those observed with X-rays, thus validating Broglie's hypothesis.
The planetary model of the atom according to de Broglie
The electrons of the atom orbit around the nucleus in "quantized" orbits, meaning fixed energies, and in his thesis, de Broglie explained this property based on the wave nature of the electron. A simple geometric reasoning was developed: electrons orbit around the nucleus of the atom in stationary waves.When the string of a violin is struck by the bow, many waves are generated, but only those with nodes at the ends remain; these are the "resonant modes" that produce musical notes. By analogy, de Broglie imagines electrons moving in circles around the nucleus; the orbits must then correspond to circular stationary waves that close in on themselves, like the violin string whose ends would touch.
Thus, for an orbit of radius R, the circumference must be a multiple of the wavelength associated with the electron, which gives the relation: 2πR = nλ, where n is an integer taking values 1, 2, 3... according to the different orbits.
With λ = h/mv, we obtain the condition for a stable orbit: mvR = nh/2π. This is what Bohr had postulated. The wave-particle duality thus explains the planetary structure of the atom. In practice, the model is well verified for an atom with one electron, that is, the case of hydrogen, but it is deficient for a more complicated case.
A completely new theory will need to be imagined, quantum mechanics, forcefully developed particularly in Copenhagen by Niels Bohr and his students to understand atomic structure, and then the vision of reality became much more complex: orbits are no longer defined circles but clouds of electrons whose probability of presence at each point in space is given by a "wave function" that satisfies Schrödinger's evolution equation.
Wave mechanics vs quantum mechanics
Today, de Broglie's wave theory seems like a draft compared to quantum mechanics, which marks a true revolution in thought. De Broglie remained within the old framework (what could be more classical than a string?). He did not really participate in quantum developments.Already at the Solvay Conference, held in October 1927 on the theme "Electrons and Photons" at the Solvay Institute of Physics in the Léopold Park in Brussels, de Broglie found himself among the titans of quantum mechanics who had come in force around their pope, Niels Bohr. Ehrenfest, Schrödinger, Pauli, Heisenberg, Debye, Bragg, Kramers, Dirac, Compton, Born, Planck, Lorentz were present—all or almost all already or soon to be Nobel Prize winners.
Quantum mechanics revealed aspects of reality that are very surprising: antimatter exists, reality is no longer deterministic but probabilistic, the state of a system is no longer described by positions and speeds but by wave functions, chance is an intrinsic property of matter...
Like Einstein, who spent the last years of his life in his lair in Princeton, rejecting the new concept of reality given by quantum mechanics and vainly seeking the Grail of a "unified field theory" hoping to link electrodynamics to gravitation, de Broglie attempted to extend his ideas of wave mechanics into a "hidden thermodynamics of particles" (Proceedings of the Academy of Sciences, 1963) that led to nothing concrete. His last years were unfortunate. Losing his memory, he lived totally dependent and died forgotten by the public and his colleagues.
When one has a glorious heraldic pedigree like Louis de Broglie, it is difficult to stand out and assert oneself personally; a duke is just an almost anonymous number in a series of successions. One must become, like the electron, a dual being and free oneself from one's milieu to shine individually.
Proust, who knew the world of aristocracy well, makes in his masterwork an allusion to a prince who transcends his original milieu by becoming a doctor in physics (or a famous politician). I cannot help but think that he had in mind the prince and physicist Louis de Broglie, whose family he must have known, unless it was his brother Maurice, also a physicist.
Thus, the formula λ=h/mv has probably brought our prince into the cast of In Search of Lost Time, which, for some, is as notable a recognition as that coming from the Nobel committee.