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The central question in de Broglie's life was whether the statistical nature of atomic physics reflects an ignorance of the underlying theory or whether statistics is all that can be known. For most of his life he believed the former although as a young researcher he had at first believed that the statistics hide our ignorance. Perhaps surprisingly, he returned to this view late in his life stating that:-

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p = ℏ k E = ℏ ω {\displaystyle {\begin{aligned}&\mathbf {p} =\hbar \mathbf {k} \\&E=\hbar \omega \\\end{aligned}}}

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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.