100 years ago, a prince turned physicist sketched quantum physics ⚛️

By François Vannucci – Professor emeritus, researcher in particle physics, specialist in neutrinos, Paris Cité University

The story of Louis de Broglie is that of a prince who became a physicist, whose work on the nature of the electron marked history and contributed to the development of quantum mechanics.

100 years ago, on November 25, 1924, Prince Louis Victor de Broglie (1892-1987), aged 32, defended his doctoral thesis in physics before a jury including Paul Langevin and Jean Perrin. There he presented his theory of wave-particle duality applied to electrons.

Five years later, at just 37 years old, he received 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, then in 1944 at 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 corpuscle

The world of the infinitely small, that of elementary particles, brings into play laws very far from those which apply to the ordinary world, first and foremost the strictly deterministic law of gravitation. The behavior of particles is governed by so-called “quantum” mechanics, which has the particularity of only predicting the probabilities of a phenomenon occurring. We know how to precisely calculate the trajectory of the falling stone, this is no longer true for a particle.

The nature of light had been debated since the 17th^e century between the granular vision of Newton and the undulatory vision of Huyghens. In the 19th century^e century, with the Maxwell's equationsthe mass seemed said and the undulatory nature of the light proven.

But 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 composed of a flow of elementary objects that he called photons: the effect was interpreted as a collision between the electrons of the metal and the photons of the incident light. A minimum energy is necessary to remove the electrons from the plate, which is enabled by blue photons, which are more energetic than red photons.

This was in line with the idea put forward by Planck in 1900, who, to explain the radiation of the black body, that is to say a heated cavity filled with gas, put forward the hypothesis that energy exchanges take place in small quantities. well-determined which he calls “quanta” (that is to say elementary grains), whose energy verifies the so-called Planck formula E = hf where E designates the energy and f the frequency and therefore the color (h is a tiny physical parameter called Planck's constant).

Based on this speculation by Max Planck, Niels Bohr designed the planetary model of the atom, where the electrons revolve around the nucleus in fixed energy orbits, like the planets around the sun.

With Einstein's interpretation of the photoelectric effect, the “quantization of light” (that is, that light is composed of “elementary grains”, particles) returned with force.

So, is light a wave or a stream of particles? Both, is the surprising answer. This is the famous wave-particle duality which admits two facets of reality: light interacts in the form of photons (particles), but it propagates in the form of waves.

This leads to consequences that can shock common sense, calling into question determinism. In particular, Werner Heisenberg wrote his uncertainty relations which teach us that it is impossible to know precisely both the position and the speed of a particle.

The electron plays string

De Broglie's contribution is to have demonstrated that electrons can also behave like a wave. He therefore extended the idea of ​​wave-particle duality beyond the photon, proposing symmetry between all particles. This symmetry was not obvious because there is a big difference between a photon of zero mass and an electron of well-defined mass.

The zero mass of the photon forces it to always move at the speed c = 300,000 kilometers per second. For the photon, the Planck quantization relation is written E = hf. De Broglie generalizes to the case of a massive particle and proposes that the wavelength λ of a particle of 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 (i.e. thirty-three 0s then a 1 after the decimal point)! But for an electron accelerated by a voltage of 100 V, the wavelength becomes 10^-10 meters, it is the spacing between atoms in a crystal and it is therefore by sending a beam of electrons through a crystal that we can hope to detect an “electron wave” effect.

Davisson and Germer carried out the corresponding experiment and observed in 1927 images of interference and diffractions from electrons, as observed with X-rays, thus validating de Broglie's hypothesis.

The planetary model of the atom according to de Broglie

The electrons of the atom revolve around the nucleus in “quantized” orbits, that is to say with 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 the nucleus of the atom in standing waves.

When the string of a violin is attacked by the bow, numerous waves are generated, but only those with knots at the ends remain, these are the “resonant modes” which give the musical notes. By analogy, de Broglie imagines the electrons moving in circles around the nucleus, the orbits must then correspond to circular standing waves which close on themselves, like the violin string whose ends touch each other.

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, n being an integer taking values ​​1,2,3. .. according to the different orbits. With λ = h/mv, we obtain the condition of a stable orbit: mvR = nh/2π. This is what Bohr postulated. Wave-particle duality therefore explains the planetary structure of the atom. In practice, the model is well verified for an atom having one electron, that is to say the case of hydrogen, but it is deficient for a more complicated case.

It will be necessary to imagine a completely new theory, quantum mechanics, developed forcefully in particular in Copenhagen by Niels Bohr and his students to understand the atomic structure, and then the vision of reality becomes much more complex: the orbits are no longer circles. defined but clouds of electrons whose probability of presence at each point in space is given by a “wave function” which verifies Schrödinger's evolution equation.

Wave mechanics vs quantum mechanics

Today, de Broglie's wave theory seems to be a beginning alongside quantum mechanics, which marks a real revolution in thought. De Broglie remained within the old framework (what could be more classic than a rope?). He did not really participate in quantum developments.

Already at the Solvay Congress, organized 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 tenors 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, are present — all or almost all already or soon Nobel Prize winners.

Quantum mechanics revealed very surprising aspects of reality: antimatter exists, reality is no longer deterministic but probabilistic, the state of a system is no longer described by positions and velocities but by function functions. wave, chance is an intrinsic property of matter… Like Einstein, who spent the last years of his life in his Princeton lair, refused the new concept of reality given by quantum mechanics and searched in vain for the Holy Grail of a “theory of the unified field” hoping to link electrodynamics to gravitation, de Broglie tried to extend his ideas of wave mechanics into a “hidden thermodynamics of particles” (Comptes reports de l'Académie des sciences, 1963) which led to nothing concrete . His last years were unhappy. Losing his memory, he lived totally dependent and died forgotten by the public and his colleagues.

When you have a glorious heraldic pedigree like Louis de Broglie, it is difficult to step out of the ranks and assert yourself personally, a duke is just an almost anonymous number in a series of successions. We must become, like the electron, a dual being and free ourselves from our environment to stand out individually.

Proust, who knew the world of the aristocracy well, makes an allusion in his masterpiece to a prince who transcends his original environment by becoming a doctor of physics (or famous politician). I can't help but think that he had in mind the prince and physicist Louis de Broglie, whose family he must have known, unless it was brother Maurice, also a physicist.

Thus the formula λ=h/mv probably brought our prince into the casting of In search of lost timewhich, for some, is as notorious a recognition as that coming from the Nobel committee.