Taking quantisation seriously: a farewell to waves

The dual wave-particle nature of quantum objects is a notoriously unintuitive feature of quantum theories. However, it is often deemed essential, due to quantum objects exhibiting diffraction and interference. We extend the work of Land\'{e} and L\'{e}vy-Leblond to demonstrate that de Broglie wavelengths are not relativistically covariant as simultaneous spatial structures, making wave properties an unviable explanation of apparent interference. We then 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 then study a photon orbital angular momentum realisation of the double slit to show that quantised exchanges can mimic interference. Finally, we demonstrate that the quantum formalism demands that particle momentum is determined at the point of scattering, contravening wave-based explanations of quantum interference.