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Quantum Foundations

Subluminal and superluminal velocities of free-space photons

arXiv

Authors: Konstantin Y. Bliokh

Year

2026

Paper ID

1182

Status

Preprint

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~2 min

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Abstract

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 c². 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'.

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We consider rectilinear free-space propagation of electromagnetic wavepackets using electromagnetic field theory, scalar wavepacket propagation, and quantum-mechanical formalism.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2602.17576 [2] arXiv https://arxiv.org/abs/2602.17576 [3] Publisher https://arxiv.org/abs/2602.17576

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External citation index: OpenAlex citation signal • updated 2026-06-12 12:35:23

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