Subluminal and superluminal velocities of free-space photons

We consider rectilinear free-space propagation of electromagnetic wavepackets using electromagnetic field theory, scalar wavepacket propagation, and quantum-mechanical formalism. We demonstrate that spatially localized wavepackets are inherently characterized by a subluminal group velocity and a superluminal phase velocity, whose product equals $c^2$. These velocities are also known as the 'energy' and 'momentum' velocities, introduced by K. Milton and J. Schwinger. We illustrate general conclusions by explicit calculations for Gaussian beams and wavepackets, and also highlight subtleties of the quantum-mechanical description based on the 'photon wavefunction'.

Source: arXiv:2602.17576v1 - http://arxiv.org/abs/2602.17576v1 PDF: https://arxiv.org/pdf/2602.17576v1 Original Link: http://arxiv.org/abs/2602.17576v1