De Broglie tried to interpret this duality as phase matching between a particle embedded in a wave, the pilot wave. There should be phase matching between both: "les photons incidents possèdent une fréquence d’oscillation interne égale à celle de l’onde (my translation: the incident photons have an internal oscillation frequency equal to that of the wave)". He saw photons, as well as electrons, as little clock-watches embedded in their wave. I am sure this intuition will lead to new physics in the future, because this aspect of duality has hardly been investigated, see Couder's bouncing droplets in pilot wave. Personally I am working with this pilot wave idea in order to explain some properties of quantum dots.
As Louis de Broglie lived his last years in a little town, Louveciennes, that is close to where I live, I had a walk there today. Maybe I could find some place related to him. Unfortunately, I didn't find the exact location of his residence (please drop a comment if you know). But surely the scenery of the pictures below near to the royal residence of the Manoir du Coeur Volant must have been very familiar to him.
|Manoir du Coeur Volant|
|Abreuvoir of Marly-le-Roi|
|Royal Domain of Marly-le-Roi|
|Commemoration plaque of the Manoir du Coeur-Volant|