A farewell to waves

The wave nature of particles is a notoriously unintuitive feature of quantum theories. However, it is often deemed essential, due to material particles exhibiting diffraction and interference. Troublingly, Land\'e and L\'evy-Leblond have shown that de Broglie wavelengths are not relativistically covariant, making any such wave properties physically inconsistent. In this work we explore whether modern experiments vindicate an alternative view: that apparent waviness in diffraction and interference scenarios emerges as a consequence of quantised interactions between particles. Such a view has historically received very little attention, despite being the exact modern explanation of both the Kapitza-Dirac effect and ultrafast electron diffraction. We study a photon orbital angular momentum realisation of the double slit to prove this explanation capable of unifying quantum interference phenomena. Finally, we demonstrate that the quantum formalism demands that particle momentum is determined at the point of scattering, contravening wave accounts of quantum interference.