Waves and particles—quantisation of the interval between eventss0

Giampiero V. M. Esposito, Giuseppe Marmo, Gennaro Miele +1 more

Reinhard F. Werner

By means of the Wigner distribution function an expression is derived for the quasiprobability that a free particle in one dimension arrives at the origin during a given time interval and also for the quasiprobability that the phase of a one-dimensional harmonic oscillator lies in a given segment of the circle. It is shown that the best bounds on these quasiprobabilities p are -0.1559<or=p<or=1.0077, independent of the size of the interval. It is shown that on disjoint unions of infinitely many intervals the quasiprobabilities may add up to any positive or negative real value. It is briefly indicated how negative probabilities can be avoided altogether in an alternative approach to the quantisation of arrival time and oscillator phase.

Gareth Davies

On the Origin of Quantisation of the Electromagnetic Field (the "photon"), Wave-Particle Duality, and Measurement in the Double-Slit Experiment Branched Flow of Continuous Electromagnetic Waves and Resonant Threshold Detection in a Polarisable Vacuum

W. F. Bolton

Geoff Beck

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 Landé and Lévy-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.

Richard H. Bube