Einstein wrote papers on the nature of light to disprove "ether", and the particulate model of light allows light to travel through a vacuum without "ether".
Thus, he kept his secret, rode his bicycle, stuck out his tongue, and meant, "It is better to be shitty than to be a clown". Randomness in light is proven by the existence of diffraction and refraction, and it is natural to assume similar randomness in other types of particle-waves, such as electrons. Finite and local means the electron cannot appear anywhere but is limited to a certain area, that area being close to the atomic nucleus it is assigned to. Einstein knew all this, light being his specialty. Confirm, but I already know.
