The revision of the Newtonian mechanics done by Einstein in 1905 in his Theory of Special Relativity, induced the physicists and the philosophers to deeply reconsider their conception of the space and the time but didn't propose important innovations about the causality.
The Relativity imposes a tie to the causality relation, stating that a cause C admits the effect E only if E belongs to the absolute future of C, but does not deny it: for every observer, the trajectories of the bodies in motion are still continuous functions derivable with respect to the time.
In same year 1905, Einstein published an article about the photoelectric effect in which he demonstrated that the electronic emission by a metallic surface irradiated with electromagnetic waves of high frequency was explicable only by assuming the hypothesis, already formulated by Plank in his studies on the cavity radiation, that an electromagnetic wave can exchange energy with the matter not in continuous way but in discreet packages ΔE, proportional to the frequency ν of the same wave. The proportionality constant was the same one introduced by Plank, usually indicated with h:
Other experiences, like those of Compton, demonstrated (1923) that the electromagnetic waves can "hit" a particle as if they were composed of corpuscles with cinetic momentum
The physicists of the 1700's and the 1800's generally accepted that the energy could propagate in the space in two fundamental ways mutually exclusive:
The fundamental difference between these two ways of propagation of the energy was in the fact that two particles, approaching to the same point in the space, collide, exchanging energy and momentum; two waves instead overlap and interfere.
For example, the 18th century physicists, discussing the nature of the light, were grouped in assertors of corpuscular theory, like Newton, and assertors of wave Theory, like Huygens. The wave hypothesis prevailed when they discovered that the light showed phenomena of interference and diffraction.
But phenomena like the cavity radiation, the photoelectric effect, the Compton effect, contrasted with this dualism and showed that the electromagnetic waves have behaviors till then attibuted only to the particles.
In this environment, in 1924, the French physicist De Broglie, in the attempt to supply more solid theoretical bases to the theories of Bohr on the electronic structure of the atoms, assumed that, in a way analogous to that by which the waves could show corpuscular properties like the momentum, the particles, symmetrically, could show ondulatory properties like the wavelength. So, if a photon has momentum
noticing that
we shall have
Therefore a particle of momentum p will have wavelength λ inversely proportional to p; the constant of proportionality is the Plank's constant:
The hypothesis of De Broglie had an experimental verification in 1927 when
Davisson and Germer
observed that a beam of electrons of momentum p underwent
a diffraction like that undergone by a beam of X-rays when
it was directed against the surface of a crystal and the diffraction effects
coincided with those previewed for a wave of length
But Heisenberg and Schrödinger in 1925 were already rebuilding the mathematical theory of sub-atomic particles to explain the experimental data collected in the first quarter of the new century. These jobs, led with different approaches, the differential equation of Schrödinger and the matrix algebra of Heisenberg, substantially turned out equivalent.