## Louis Broglie Dissertation

"de Broglie" redirects here. For other members of the family, see House of Broglie.

**Louis-Victor-Pierre-Raymond de Broglie** (; French: [dəbʁɔj]^{[2]}^{[3]} or [dəbʁœj] ( listen); 15 August 1892 – 19 March 1987) was a French physicist who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave–particle duality, and forms a central part of the theory of quantum mechanics.

De Broglie won the Nobel Prize for Physics in 1929, after the wave-like behaviour of matter was first experimentally demonstrated in 1927.

The 1925 pilot-wave model,^{[4]} and the wave-like behaviour of particles discovered by de Broglie was used by Erwin Schrödinger in his formulation of wave mechanics.^{[5]} The pilot-wave model and interpretation was then abandoned, in favor of the quantum formalism, until 1952 when it was rediscovered and enhanced by David Bohm.^{[6]}

Louis de Broglie was the sixteenth member elected to occupy seat 1 of the Académie française in 1944, and served as Perpetual Secretary of the French Academy of Sciences.^{[7]}^{[8]} De Broglie became the first high-level scientist to call for establishment of a multi-national laboratory, a proposal that led to the establishment of the European Organization for Nuclear Research (CERN).^{[9]}

## Biography[edit]

Louis de Broglie was born to a noble family in Dieppe, Seine-Maritime, younger son of Victor, 5th duc de Broglie. He became the 7th duc de Broglie in 1960 upon the death without heir of his older brother, Maurice, 6th duc de Broglie, also a physicist. He never married. When he died in Louveciennes,^{[1]} he was succeeded as duke by a distant cousin, Victor-François, 8th duc de Broglie.

De Broglie had intended a career in humanities, and received his first degree in history. Afterwards, though, he turned his attention toward mathematics and physics and received a degree in physics. With the outbreak of the First World War in 1914, he offered his services to the army in the development of radio communications.

His 1924 thesis *Recherches sur la théorie des quanta* (Research on the Theory of the Quanta) introduced his theory of electron waves. This included the wave–particle duality theory of matter, based on the work of Max Planck and Albert Einstein on light. This research culminated in the de Broglie hypothesis stating that *any moving particle or object had an associated wave*. De Broglie thus created a new field in physics, the *mécanique ondulatoire,* or wave mechanics, uniting the physics of energy (wave) and matter (particle). For this he won the Nobel Prize in Physics in 1929.

In his later career, de Broglie worked to develop a causal explanation of wave mechanics, in opposition to the wholly probabilistic models which dominate quantum mechanical theory; it was refined by David Bohm in the 1950s. The theory has since been known as the De Broglie–Bohm theory.

In addition to strictly scientific work, de Broglie thought and wrote about the philosophy of science, including the value of modern scientific discoveries.

De Broglie became a member of the Académie des sciences in 1933, and was the academy's perpetual secretary from 1942. He was asked to join *Le Conseil de l'Union Catholique des Scientifiques Francais*, but declined because he was non-religious and an atheist.^{[10]}^{[11]} On 12 October 1944, he was elected to the Académie française, replacing mathematician Émile Picard. Because of the deaths and imprisonments of Académie members during the occupation and other effects of the war, the Académie was unable to meet the quorum of twenty members for his election; due to the exceptional circumstances, however, his unanimous election by the seventeen members present was accepted. In an event unique in the history of the Académie, he was received as a member by his own brother Maurice, who had been elected in 1934. UNESCO awarded him the first Kalinga Prize in 1952 for his work in popularizing scientific knowledge, and he was elected a Foreign Member of the Royal Society on 23 April 1953.^{[12]}

In 1961 he received the title of Knight of the Grand Cross in the Légion d'honneur. De Broglie was awarded a post as counselor to the French High Commission of Atomic Energy in 1945 for his efforts to bring industry and science closer together. He established a center for applied mechanics at the Henri Poincaré Institute, where research into optics, cybernetics, and atomic energy were carried out. He inspired the formation of the International Academy of Quantum Molecular Science and was an early member.

## Important theories[edit]

### Matter and wave–particle duality[edit]

Main article: De Broglie hypothesis

"The fundamental idea of [my 1924 thesis] was the following: The fact that, following Einstein's introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated... My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons." "With every particle of matter with mass **m** and velocity **v** a real wave must be 'associated'", related to the momentum by the equation:

where is the wavelength, is the Planck constant, is the momentum, is the rest mass, is the velocity and is the speed of light in a vacuum."

This theory set the basis of wave mechanics. It was supported by Einstein, confirmed by the electron diffraction experiments of G P Thomson and Davisson and Germer, and generalized by the work of Schrödinger.

However, this generalization was statistical and was not approved of by de Broglie, who said "that the particle must be the seat of an internal periodic movement and that it must move in a wave in order to remain in phase with it was ignored by the actual physicists [who are] wrong to consider a wave propagation without localization of the particle, which was quite contrary to my original ideas."

From a philosophical viewpoint, this theory of matter-waves has contributed greatly to the ruin of the atomism of the past. Originally, de Broglie thought that real wave (i.e., having a direct physical interpretation) was associated with particles. In fact, the wave aspect of matter was formalized by a wavefunction defined by the Schrödinger equation, which is a pure mathematical entity having a probabilistic interpretation, without the support of real physical elements. This wavefunction gives an appearance of wave behavior to matter, without making real physical waves appear. However, until the end of his life de Broglie returned to a direct and real physical interpretation of matter-waves, following the work of David Bohm. The de Broglie–Bohm theory is today the only interpretation giving real status to matter-waves and representing the predictions of quantum theory.

### Conjecture of an internal clock of the electron[edit]

In his 1924 thesis, de Broglie conjectured that the electron has an internal clock that constitutes part of the mechanism by which a pilot wave guides a particle.^{[13]} Subsequently David Hestenes has proposed a link to the Zitterbewegung that was suggested by Erwin Schrödinger.^{[14]}

While attempts at verifying the internal clock hypothesis and measuring clock frequency are so far not conclusive,^{[15]} recent experimental data is at least compatible with de Broglie's conjecture.^{[16]}

### Non-nullity and variability of mass[edit]

According to de Broglie, the neutrino and the photon have rest masses that are non-zero, though very low. That a photon is not quite massless is imposed by the coherence of his theory. Incidentally, this rejection of the hypothesis of a massless photon enabled him to doubt the hypothesis of the expansion of the universe.

In addition, he believed that the true mass of particles is not constant, but variable, and that each particle can be represented as a thermodynamic machine equivalent to a cyclic integral of action.

### Generalization of the principle of least action[edit]

In the second part of his 1924 thesis, de Broglie used the equivalence of the mechanical principle of least action with Fermat's optical principle: "Fermat's principle applied to phase waves is identical to Maupertuis' principle applied to the moving body; the possible dynamic trajectories of the moving body are identical to the possible rays of the wave." This equivalence had been pointed out by Hamilton a century earlier, and published by him around 1830, in an era where no experience gave proof of the fundamental principles of physics being involved in the description of atomic phenomena.

Up to his final work, he appeared to be the physicist who most sought that dimension of action which Max Planck, at the beginning of the 20th century, had shown to be the only universal unity (with his dimension of entropy).

### Duality of the laws of nature[edit]

Far from claiming to make "the contradiction disappear" which Max Born thought could be achieved with a statistical approach, de Broglie extended wave–particle duality to all particles (and to crystals which revealed the effects of diffraction) and extended the principle of duality to the laws of nature.

His last work made a single system of laws from the two large systems of thermodynamics and of mechanics:

When Boltzmann and his continuators developed their statistical interpretation of Thermodynamics, one could have considered Thermodynamics to be a complicated branch of Dynamics. But, with my actual ideas, it's Dynamics that appear to be a simplified branch of Thermodynamics. I think that, of all the ideas that I've introduced in quantum theory in these past years, it's that idea that is, by far, the most important and the most profound.

That idea seems to match the continuous–discontinuous duality, since its dynamics could be the limit of its thermodynamics when transitions to continuous limits are postulated. It is also close to that of Leibniz, who posited the necessity of "architectonic principles" to complete the system of mechanical laws.

However, according to him, there is less duality, in the sense of opposition, than synthesis (one is the limit of the other) and the effort of synthesis is constant according to him, like in his first formula, in which the first member pertains to mechanics and the second to optics:

### Neutrino theory of light[edit]

This theory, which dates from 1934, introduces the idea that the photon is equivalent to the fusion of two Diracneutrinos.

It shows that the movement of the center of gravity of these two particles obeys the Maxwell equations—that implies that the neutrino and the photon both have rest masses that are non-zero, though very low.

### Hidden thermodynamics[edit]

De Broglie's final idea was the hidden thermodynamics of isolated particles. It is an attempt to bring together the three furthest principles of physics: the principles of Fermat, Maupertuis, and Carnot.

In this work, action becomes a sort of opposite to entropy, through an equation that relates the only two universal dimensions of the form:

As a consequence of its great impact, this theory brings back the uncertainty principle to distances around extrema of action, distances corresponding to *reductions in entropy*.

## Honors and awards[edit]

## Publications[edit]

*Recherches sur la théorie des quanta*(*Researches on the quantum theory*), Thesis, Paris, 1924, Ann. de Physique (10)**3**, 22 (1925).*Introduction à la physique des rayons X et gamma*(*Introduction to physics of X-rays and Gamma-rays*), with Maurice de Broglie, Gauthier-Villars, 1928.*Ondes et mouvements*(*Waves and Motions*), Paris: Gauthier-Villars, 1926.*Rapport au 5ème Conseil de Physique Solvay*(*Report for the 5th Solvay Physics Congress*), Brussels, 1927.*La mécanique ondulatoire*(*Wave Mechanics*), Paris: Gauthier-Villars, 1928.*Matière et lumière*(*Matter and Light*), Paris: Albin Michel, 1937.*La Physique nouvelle et les quanta*(*New Physics and Quanta*), Flammarion, 1937.*Continu et discontinu en physique moderne*(*Continuous and discontinuous in Modern Physics*), Paris: Albin Michel, 1941.*Ondes, corpuscules, mécanique ondulatoire*(*Waves, Corpuscles, Wave Mechanics*), Paris: Albin Michel, 1945.*Physique et microphysique*(*Physics and Microphysics*), Albin Michel, 1947.*Vie et œuvre de Paul Langevin*(*The life and works of Paul Langevin*), French Academy of Sciences, 1947.*Optique électronique et corpusculaire*(*Electronic and Corpuscular Optics*), Herman, 1950.*Savants et découvertes*(*Scientists and discoveries*), Paris, Albin Michel, 1951.*Une tentative d'interprétation causale et non linéaire de la mécanique ondulatoire: la théorie de la double solution.*Paris: Gauthier-Villars, 1956.- English translation:
*Non-linear Wave Mechanics: A Causal Interpretation.*Amsterdam: Elsevier, 1960.

- English translation:
*Nouvelles perspectives en microphysique*(*New prospects in Microphysics*), Albin Michel, 1956.*Sur les sentiers de la science*(*On the Paths of Science*), Paris: Albin Michel, 1960.*Introduction à la nouvelle théorie des particules de M. Jean-Pierre Vigier et de ses collaborateurs*, Paris: Gauthier-Villars, 1961. Paris: Albin Michel, 1960.- English translation:
*Introduction to the Vigier Theory of elementary particles*, Amsterdam: Elsevier, 1963.

- English translation:
*Étude critique des bases de l'interprétation actuelle de la mécanique ondulatoire*, Paris: Gauthier-Villars, 1963.- English translation:
*The Current Interpretation of Wave Mechanics: A Critical Study*, Amsterdam, Elsevier, 1964.

- English translation:
*Certitudes et incertitudes de la science*(*Certitudes and Incertitudes of Science*). Paris: Albin Michel, 1966.- with Louis Armand, Pierre Henri Simon and others.
*Einstein.*Paris: Hachette, 1966.- English translation:
*Einstein.*Peebles Press, 1979.^{[17]}

- English translation:
*Recherches d'un demi-siècle*(*Research of a half-century*), Albin Michel, 1976.*Les incertitudes d'Heisenberg et l'interprétation probabiliste de la mécanique ondulatoire*(*Heisenberg uncertainty and wave mechanics probabilistic interpretation*), Gauthier-Villars, 1982.

## References[edit]

## External links[edit]

- ^
^{a}^{b}Leroy, Francis (2003).*A Century of Nobel Prize Recipients: Chemistry, Physics, and Medicine*(illustrated ed.). CRC Press. p. 141. ISBN 0-8247-0876-8. Extract of page 141 **^**Léon Warnant (1987).*Dictionnaire de la prononciation française dans sa norme actuelle*(in French) (3rd ed.). Gembloux: J. Duculot, S. A. ISBN 978-2-8011-0581-8.**^**Jean-Marie Pierret (1994).*Phonétique historique du français et notions de phonétique générale*(in French). Louvain-la-Neuve: Peeters. p. 102. ISBN 978-9-0683-1608-7.**^**The final pilot-wave model was presented in Solvay Conferences and later published, in "*Ondes et mouvements*" of 1926.**^**Antony Valentini:*On the Pilot-Wave Theory of Classical, Quantum and Subquantum Physics*, Ph.D. Thesis, ISAS, Trieste 1992**^**"de Broglie vs Bohm". Excerpts from 1960 book published by Elsevier Pub.Co. Retrieved 30 June 2015.**^**O'Connor, John J.; Robertson, Edmund F., "Louis de Broglie",*MacTutor History of Mathematics archive*, University of St Andrews .**^**"History of International Academy of Quantum Molecular Science". IAQMS. Retrieved 2010-03-08.**^**"Louis de Broglie". Soylent Communications. Retrieved 12 June 2015.**^**Evans, James; Thorndike, Alan S. (2007).*Quantum Mechanics at the Crossroads: New Perspectives From History, Philosophy And Physics*. Springer. p. 71. ISBN 9783540326632.**^**Kimball, John (2015). Physics Curiosities, Oddities, and Novelties. CRC Press. p. 323. ISBN 978-1-4665-7636-0.- ^
^{a}^{b}Abragam, A. (1988). "Louis Victor Pierre Raymond de Broglie. 15 August 1892-19 March 1987".*Biographical Memoirs of Fellows of the Royal Society*.**34**: 22–26. doi:10.1098/rsbm.1988.0002. JSTOR 770045. **^**See for example the description of de Broglie's view in: David Bohm, Basil Hiley:*The de Broglie pilot wave theory and the further development and new insights arising out of it*, Foundations of Physics, volume 12, number 10, 1982, Appendix: On the background of the papers on trajectories interpretation, by D. Bohm, (PDFArchived 19 August 2011 at the Wayback Machine.)**^**D. Hestenes, October 1990, The Zitterbewegung interpretation of quantum mechanics, Foundations of Physics, vol. 20, no. 10, pp. 1213–1232**^**See for example G.R. Osche, Electron channeling resonance and de Broglie's internal clock*, Annales de la Fondation Louis de Broglie, vol. 36, 2001, pp. 61–71 (full text)***^**Catillon, Foundations of Physics, July 2001, vol. 38, no. 7, pp. 659–664**^**"Review of*Einstein*by Louis de Broglie and others".*Bulletin of the Atomic Scientists*.**36**(3): 50. March 1980.

**15.1 Compton scattering**

German-Swiss-American physicist Albert Einstein’s theory of special relativity was first published in 1905^{[1]} (discussed in Book I). This suggested that light has a momentum - which is classically equal to an object’s mass multiplied by its velocity - even if photons have no mass.

Special relativity shows that energy is related to mass via *E*^{2}=*p*^{2}*c*^{2}+*m*^{2}*c*^{4}, where *E* refers to energy, *p* to momentum, *c* to the speed of light, and *m* to an object’s mass. An object with no mass, like a photon, will have an energy of *E*^{2}=*p*^{2}*c*^{2}, or *E*=*pc*.

American physicist Arthur Compton proved that photons do have the momentum Einstein predicted in 1922.^{[2]} Compton did this by firing X-rays at aluminium foil. When the X-rays hit the electrons in the outermost shell of the aluminium atoms, they transferred some of their angular momentum. The electrons gained enough energy to leave the atom, and the X-ray photon lost the same amount of energy. This process is now known as Compton scattering.

When a photon collides with an electron and gains energy, the process is known as inverse Compton scattering. Compton scattering is now utilised in radiobiology,^{[3]} and both Compton scattering and inverse Compton scattering are important in X-ray astronomy^{[4]}.

**15.2 Electron waves**

In 1924, French physicist Louis de Broglie used Einstein’s equations to show that electrons can act like waves, just as photons can act like particles.^{[5]}

**15.2.1 The wavelength of photons**

The wavelength of a photon is calculated by combining Einstein’s equation for determining a photon’s energy with the Planck relation.^{[6]} Using *E* = *pc* (which is the energy of photons according to special relativity) and *E* = *hν* (which is the energy of photons according to the Planck relation):

*c*=

*λν*

**15.2.2 The wavelength of particles**

De Broglie proposed that particles also have a wavelength, and that this can be calculated using the same equation, except here the particle’s momentum is equal to *mv*, where *m* is the particles’ mass, and *v* is its velocity:

De Broglie realised that electrons must orbit the nucleus like a standing wave - a wave that is constrained at each end. This means that only a whole number of wavelengths fit exactly around each orbit:

λ = 2πr/n | (15.4) |

Here, the orbit is assumed to be circular. 2*πr* is the circumference of a circle of radius *r*, and *n* is the shell number. This means that the angular momentum of each electron is quantised, in agreement with Danish physicist Niels Bohr’s theory of the atom^{[7]} (discussed in Chapter 10).

Bohr had previously shown that the angular momentum of each electron (*L*) is equal to the shell number multiplied by a constant:

h/mv = 2πr/n | (15.5) |

nh/2π = rmv | |

nh/2π = rp = L |

Figure 15.2 | Allowed (left) and forbidden (right) standing waves. |

If an electron drops to a lower energy level, its orbit has a smaller radius. This means that fewer full wavelengths can fit, and so the frequency and energy are lower. The difference in energy between shells is always a quantised number, because *E* = *hν*. The lowest minimum energy is always more than zero because a full number of wavelengths must fit in each shell.

**What is the wavelength of a person?**

De Broglie’s theory can be extended to show that all matter exhibits the same wave-particle duality as light. This means that everything in the universe can act like a wave.^{[8]}

*λ* = *h*/*mv*, and *h*=6.626×10^{-34} m^{2}kg s^{-1}.

This shows that an object’s wavelength gets smaller the more massive it is, and the faster it’s moving.

If a person has a mass of 75 kg, and is jogging at 8 km/h (which is about 2.2 m/s), then

*λ* = 6.626×10^{-34}/7.5 × 2.2 = 4.016×10^{-36} m.

This is about 700 billion, billion times smaller than the classical electron radius, which is about 2.8×10^{-15} m.

Diffraction works best if the slit is about the same size as the wavelength, and so this explains why we do not notice wave-like behaviour in people.

De Broglie’s theory was greatly extended by German physicist Werner Heisenberg^{[9]} (discussed in Chapter 16) and Austrian physicist Erwin Schrödinger^{[10]} (discussed in Chapter 17) in 1925-1926. American physicists Clinton Davisson and Lester Germer proved that electrons have wave-like properties in 1927.^{[11]} Davisson and Germer measured the wavelength of electrons by firing a beam of electrons at a nickel crystal, which acts like a diffraction grating, and then measuring the angles they were deflected by.

The wave-like nature of electrons meant that electron microscopes could be built in the 1930s.^{[12]} The fact that electrons are more massive than photons means they have a smaller wavelength, and this is why electron microscopes have a better resolution than microscopes that use light.

In 1961, German physicist Claus Jönsson performed British natural philosopher Thomas Young’s double-slit experiment with electrons, and found that they behave the same way as photons.^{[13]} This experiment has since been conducted on larger particles and molecules. In 2012, Thomas Juffmann and physicists from University of Vienna in Austria conducted the experiment on molecules containing over 100 atoms.^{[14]}

By 1993, electron microscopes could be used to create images of individual atoms on metallic surfaces, known as quantum corrals^{[15]} (discussed in Chapter 16). Electron waves could be seen in these images, and look like ripples on the metal’s surface.

Figure 15.4 | A sculpture showing a quantum corral made from iron atoms (the raised points) on copper, the ripples on the surface are electron waves. |

↑ Einstein, A. in *The principle of relativity; original papers*, The University of Calcutta, **1920** (1905).

↑ Compton, A. H., *Physical Review***1923**, *21*, 483–502.

↑ Saha, G. B., *Physics and Radiobiology of Nuclear Medicine*, Springer Science & Business Media, **2013**.

↑ Frank, J., King, A., Raine, D., *Accretion Power in Astrophysics*, Cambridge University Press, **2002**.

↑ De Broglie, L., *PhD thesis*, University of Paris, **1924**.

↑ Planck, M., *Annalen der Physik***1901**, *4*, 90–100.

↑ Bohr, N., *The London Edinburgh and Dublin Philosophical Magazine and Journal of Science***1913**, *26*, 1–25.

↑ Katz, D. M., *Physics for Scientists and Engineers: Foundations and Connections, Extended Version with Modern*, Cengage Learning, **2016**.

↑ Heisenberg, W., *Zeitschrift für Physik***1925**, *33*, 879–893.

↑ Schrödinger, E., *Physical Review***1926**, *28*, 1049–1070.

↑ Davisson, C., Germer, L. H., *Physical Review***1927**, *30*, 705–741.

↑ Palucka, T., *Overview of Electron Microscopy*, Caltech, **2002**.

↑ Jönsson, C., *Zeitschrift für Physik***1961**, *161*, 454–474.

↑ Juffmann, T., Milic, A., Müllneritsch, M., Asenbaum, P., Tsukernik, A., Tüxen, J., Mayor, M., Cheshnovsky, O., Arndt, M., *Nature nanotechnology***2012**, *7*, 297–300.

↑ Crommie, M. F., Lutz, C. P., Eigler, D. M., *Science***1993**, *262*, 218–220.

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