Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [79]
Figure 10: Standing electron waves in the quantum atom
If viewed as a standing wave around the nucleus instead of a particle in orbit, an electron would experience no acceleration and therefore no continual loss of radiation sending it crashing into the nucleus as the atom collapsed. What Bohr had introduced simply to save his quantum atom, found its justification in de Broglie's wave-particle duality. When he did the calculations, de Broglie found that Bohr's principal quantum number, n, labelled only those orbits in which electron standing waves could exist around the nucleus of the hydrogen atom. It was the reason why all other electron orbits were forbidden in the Bohr model.
When de Broglie outlined why all particles should be viewed as having a dual wave-particle character in three short papers in the autumn of 1923, it was not immediately clear what was the nature of the relationship between the billiard ball-like particles and the 'fictitious associated wave'. Was de Broglie suggesting that it was akin to a surfer riding a wave? It was later established that such an interpretation would not work and that electrons, and all other particles, behaved exactly like photons: they are both wave and particle.
De Broglie wrote up his ideas in an expanded form and presented them as his PhD thesis in the spring of 1924. The necessary formalities of acceptance and its reading by the examiners meant that de Broglie did not defend his doctoral dissertation until 25 November. Three of the four examiners were professors at the Sorbonne: Jean Perrin, who had been instrumental in testing Einstein's theory of Brownian motion; Charles Mauguin, a distinguished physicist working on the properties of crystals; and Elie Cartan, a renowned mathematician. The last member of the quartet was the external examiner, Paul Langevin. He alone was well versed in quantum physics and relativity. Before officially submitting his dissertation, de Broglie approached Langevin and asked him to look at his conclusions. Langevin agreed and afterwards told a colleague: 'I am taking with me the little brother's thesis. Looks far-fetched to me.'13
Louis de Broglie's ideas may have been fanciful, but Langevin did not quickly dismiss them. He needed to consult another. Langevin knew that Einstein had publicly stated in 1909 that future research into radiation would reveal a kind of fusion of the particle and wave. Compton's experiments had convinced almost everyone that Einstein had been right about light. It did after all appear to be a particle in collisions with electrons. Now, de Broglie was suggesting the same kind of fusion, wave-particle duality, for all of matter. He even had a formula that linked the wavelength of the 'particle' to its momentum p, =h/p where h is Planck's constant. Langevin asked the physicist prince for a second copy of the dissertation and sent it to Einstein. 'He has lifted a corner of the great veil', Einstein wrote back to Langevin.14
The judgement of Einstein was enough for Langevin and the other examiners. They congratulated de Broglie for 'having pursued with a remarkable mastery an effort that had to be attempted in order to overcome the difficulties in the midst of which the physicists found themselves'.15 Mauguin later admitted that he 'did not believe at the time in the physical reality of the waves associated with grains of matter'.16 All Perrin knew for sure was that de Broglie was 'very intelligent'.17 As for the rest he had no idea. With Einstein's support, aged 32, he was no longer just Prince Louis Victor Pierre Raymond de Broglie, but had earned the right to call himself plain Dr Louis de Broglie.
Having an idea was one thing, but could it be tested? De Broglie had quickly realised in September 1923 that if matter has wave properties, then a beam of electrons should spread out like a beam of light – they should be diffracted. In one of his short papers written that year, de Broglie had predicted that a 'group of electrons that passes through a small aperture should show diffraction effects'.18 He tried,