Editing Louis de Broglie (section)

== Scientific activity ==
{{more citations needed section|date=June 2015}}

=== Physics of X-ray and photoelectric effect ===
The first works of Louis de Broglie (early 1920s) were performed in the laboratory of his [[Maurice de Broglie|older brother Maurice]] and dealt with the features of the [[photoelectric effect]] and the properties of [[x-rays]]. These publications examined the absorption of X-rays and described this phenomenon using the [[Bohr theory]], applied quantum principles to the interpretation of [[Photoemission spectroscopy|photoelectron spectra]], and gave a systematic classification of X-ray spectra.<ref name="Abragam" /> The studies of X-ray spectra were important for elucidating the structure of the internal electron shells of atoms (optical spectra are determined by the outer shells). Thus, the results of experiments conducted together with Alexandre Dauvillier, revealed the shortcomings of the existing schemes for the distribution of electrons in atoms; these difficulties were eliminated by [[Edmund Stoner]].<ref>''The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective''. New York: Wiley-Interscience, 1974. {{ISBN|0-471-43958-4}}</ref> Another result was the elucidation of the insufficiency of the Sommerfeld formula for determining the position of lines in X-ray spectra; this discrepancy was eliminated after the discovery of the electron spin. In 1925 and 1926, Leningrad physicist [[Orest Khvolson]] nominated the de Broglie brothers for the Nobel Prize for their work in the field of X-rays.<ref name="Nye" />

=== Matter and wave–particle duality ===
{{Main|De Broglie hypothesis}}
Studying the nature of X-ray radiation and discussing its properties with his brother Maurice, who considered these rays to be some kind of combination of waves and particles, contributed to Louis de Broglie's awareness of the need to build a theory linking particle and wave representations. In addition, he was familiar with the works (1919–1922) of [[Marcel Brillouin]], which proposed a hydrodynamic model of an atom and attempted to relate it to the results of Bohr's theory. The starting point in the work of Louis de Broglie was the idea of Einstein about the [[Photon|quanta of light]]. In his first article on this subject, published in 1922, the French scientist considered blackbody radiation as a gas of light quanta and, using classical statistical mechanics, derived the [[Wien approximation|Wien radiation law]] in the framework of such a representation. In his next publication, he tried to reconcile the concept of light quanta with the phenomena of interference and diffraction and came to the conclusion that it was necessary to associate a certain periodicity with quanta. In this case, light quanta were interpreted by him as relativistic particles of very small mass.<ref name="Mehra">{{cite book |author = J. Mehra. |editor= J. Mehra. |title= The Golden Age of Theoretical Physics| chapter=Louis de Broglie and the phase waves associated with matter |edition=  |year= 2001 |publisher= World Scientific |pages = 546–570 }}</ref>

It remained to extend the wave considerations to any massive particles, and in the summer of 1923 a decisive breakthrough occurred. De Broglie outlined his ideas in a short note "Waves and quanta" ({{langx|fr|Ondes et quanta}}, presented at a meeting of the Paris Academy of Sciences on September 10, 1923),<ref>{{Cite web |date=1923 |title=Membres de l'Académie des sciences depuis sa création: Louis de Broglie Ondes et quanta |language=fr |url=https://www.academie-sciences.fr/pdf/dossiers/Broglie/Broglie_pdf/CR1923_p507.pdf |website=academie-sciences.fr}}</ref> which marked the beginning of the creation of wave mechanics. In this paper and his subsequent PhD thesis,<ref name="De_Broglie_PhD_English"></ref> the scientist suggested that a moving particle with energy ''E'' and velocity '''v''' is characterized by some internal periodic process with a frequency <math>E/h</math> (later known as [[Compton frequency]]), where <math>h</math> is the [[Planck constant]]. To reconcile these considerations, based on the quantum principle, with the ideas of special relativity, de Broglie associated wave he called a "phase wave" with a moving body, which propagates with the [[phase velocity]] <math>c^2/v</math>. Such a wave, which later received the name [[matter wave]], or [[de Broglie wave]], in the process of body movement remains in phase with the internal periodic process. Having then examined the motion of an electron in a closed orbit, the scientist showed that the requirement for phase matching directly leads to the quantum [[Bohr-Sommerfeld quantization|Bohr-Sommerfeld condition]], that is, to quantize the angular momentum. In the next two notes (reported at the meetings on September 24 and October 8, respectively), de Broglie came to the conclusion that the particle velocity is equal to the [[group velocity]] of phase waves, and the particle moves along the normal to surfaces of equal phase. In the general case, the trajectory of a particle can be determined using [[Fermat's principle]] (for waves) or the [[principle of least action]] (for particles), which indicates a connection between geometric optics and classical mechanics.<ref>[[Max Jammer]] ''The Conceptual Development of Quantum Mechanics''. New York: McGraw-Hill, 1966 2nd ed: New York: American Institute of Physics, 1989. {{ISBN|0-88318-617-9}}. Olivier Darrigol, "Strangeness and soundness in Louis de Broglie's early works", ''Physis'',  30 (1993): 303–372.</ref> The ''de Broglie wavelength'' {{math|''λ''}} is the [[Planck constant]] {{math|''h''}} divided by  [[momentum]] {{math|''p''}}:
<math display="block"> \lambda = \frac{h}{p}.</math>

This theory set the basis of wave mechanics. It was supported by Einstein, confirmed by the [[Davisson–Germer experiment|electron diffraction experiments]] of [[George Paget Thomson]] in the United Kingdom and [[Clinton Davisson]] and [[Lester Germer]] in the United States, and generalized by the work of Erwin Schrödinger.

Originally, de Broglie thought that real wave (i.e., having a direct physical interpretation) was associated with particles. However, when the wave aspect of matter was formalized by a [[wavefunction]] defined by the [[Schrödinger equation]], it came out as a pure mathematical entity having a probabilistic interpretation, without the support of physical elements. This wavefunction gives wave behavior to matter but it is only observed through individual quantum samples. However, in 1956 de Broglie again attempted a theory of a direct and physical interpretation of matter-waves, following the work of [[David Bohm]] and suggestions of [[Jean-Pierre Vigier]].<ref name=Bridgman-1960>{{Cite journal |last=Bridgman |first=P. W. |last2=de Broglie |first2=Louis |last3=Knodel |first3=Arthur J. |last4=Miller |first4=Jack C. |date=1960 |title=Review of Non-Linear Wave Mechanics: A Causal Interpretation, de BroglieLouis, KnodelArthur J., MillerJack C. |url=https://www.jstor.org/stable/24940668 |journal=Scientific American |volume=203 |issue=4 |pages=201–206 |issn=0036-8733}}</ref>

=== Conjecture of an internal clock of the electron <span class="anchor" id="de Broglie internal clock"></span> ===
[[File:Solvay conference 1927 (group photograph) with frame.jpg|thumb|de Broglie presented at the Solvay conference 1927 (third from right in middle row).]]

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.<ref>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, ([http://leopard.physics.ucdavis.edu/rts/p298/pilotwavetheory.pdf PDF] {{webarchive|url=https://web.archive.org/web/20110819234038/http://leopard.physics.ucdavis.edu/rts/p298/pilotwavetheory.pdf |date=19 August 2011 }})</ref> Subsequently, [[David Hestenes]] has proposed a link to the [[zitterbewegung]] that was suggested by Schrödinger.<ref>D. Hestenes, October 1990, The Zitterbewegung interpretation of quantum mechanics, Foundations of Physics, vol.&nbsp;20, no.&nbsp;10, pp.&nbsp;1213–1232</ref>

While attempts at verifying the internal clock hypothesis and measuring clock frequency are so far not conclusive,<ref>See for example G.R. Osche, ''Electron channeling resonance and de Broglie's internal clock'', Annales de la Fondation Louis de Broglie, vol.&nbsp;36, 2001, pp.&nbsp;61–71 ([http://aflb.ensmp.fr/AFLB-361/aflb361m718.pdf full text])</ref> recent experimental data is at least compatible with de Broglie's conjecture.<ref>Catillon, Foundations of Physics, July 2001, vol.&nbsp;38, no.&nbsp;7, pp.&nbsp;659–664</ref>

=== Non-nullity and variability of mass ===
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 ===
{{ Also| Hamilton's optico-mechanical analogy}}
In the second part of his 1924 thesis, de Broglie used the equivalence of the mechanical principle of least action with [[Fermat's principle|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 latter equivalence had been pointed out by [[William Rowan Hamilton]] a century earlier, and published by him around 1830, for the case of light.

=== Duality of the laws of nature ===
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 [[Natural law|laws of nature.]]

His last work made a single system of laws from the two large systems of thermodynamics and of mechanics:{{cn|date=December 2023}}
{{blockquote|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 [[Gottfried Wilhelm Leibniz]], who posited the necessity of "architectonic principles" to complete the system of mechanical laws.{{cn|date=December 2023}}

However, according to him, there is less duality, in the sense of opposition, than synthesis (one is the limit of the other){{cn|date=December 2023}} 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:
: <math> m c^2 = h \nu </math>

=== Neutrino theory of light ===
{{main|Neutrino theory of light}}
This theory, which dates from 1934, introduces the idea that the photon is equivalent to the fusion of two [[Dirac fermion|Dirac neutrino]]s.<ref>{{Cite journal |last1=Pryce |first1=Maurice Henry Lecorney |last2=null |first2=null |last3=Dirac |first3=Paul Adrien Maurice |last4=null |first4=null |date=1997 |title=On the neutrino theory of light |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1938.0058 |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |volume=165 |issue=921 |pages=247–271 |doi=10.1098/rspa.1938.0058}}</ref> In 1938, the concept was challenged as not rotationally invariant and work on the concept was largely discontinued.<ref>{{Cite journal |last=Perkins |first=W. A. |date=1965 |title=Neutrino Theory of Photons |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.137.B1291 |journal=Physical Review |volume=137 |issue=5B |pages=B1291–B1301 |doi=10.1103/PhysRev.137.B1291|bibcode=1965PhRv..137.1291P }}</ref>

=== Hidden thermodynamics ===
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's theorem (thermodynamics)|Carnot]].

In this work, [[Action (physics)|action]] becomes a sort of opposite to [[entropy]], through an equation that relates the only two universal dimensions of the form:
: <math>{\text{action}\over h} = -{\text{entropy}\over k}</math>
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''.