Physics of X-ray and photoelectric effect The first works of Louis de Broglie (early 1920s) were performed in the laboratory of his
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
photoelectron spectra, and gave a systematic classification of X-ray spectra. 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. 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" (, presented at a meeting of the Paris Academy of Sciences on September 10, 1923), which marked the beginning of the creation of wave mechanics. In this paper and his subsequent PhD thesis, The
de Broglie wavelength is the
Planck constant divided by
momentum : \lambda = \frac{h}{p}. This theory set the basis of wave mechanics. It was supported by Albert Einstein, confirmed by the
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.
Conjecture of an internal clock of the electron 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. Subsequently,
David Hestenes has proposed a link to the
zitterbewegung that was suggested by Schrödinger. While attempts at verifying the internal clock hypothesis and measuring clock frequency are so far not conclusive, recent experimental data is at least compatible with de Broglie's conjecture.
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 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 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
laws of nature. His last work made a single system of laws from the two large systems of thermodynamics and of mechanics: 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. 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: : m c^2 = h \nu
Neutrino theory of light The
neutrino theory of light, which dates from 1934, introduces the idea that the photon is equivalent to the fusion of two
Dirac neutrinos. In 1938, the concept was challenged as not rotationally invariant and work on the concept was largely discontinued.
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. In this work,
action becomes a sort of opposite to
entropy, through an equation that relates the only two universal dimensions of the form: : {\text{action}\over h} = -{\text{entropy}\over k} 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. == Recognition ==