[Paper Review] Comment on "Spatially structured photons that travel in free space slower than the speed of light"

Z. L. Horváth, Balázs Major|arXiv (Cornell University)|Apr 23, 2015

Orbital Angular Momentum in Optics3 citations

TL;DR

This paper challenges the claim by Giovannini et al. that spatially structured photons travel slower than c in vacuum, arguing instead that such photons always propagate at c. Using quantum mechanical analysis, the authors show that the observed group velocity reduction results from projection effects along the beam axis, not actual subluminal propagation, reaffirming that photons in free space travel at the speed of light regardless of spatial structure.

ABSTRACT

D. Giovannini et al. (Reports, 20 February 2015, p. 857) reported that they measured spatially structured photons travelling in free space slowing down even in vacuum. Here we present a simple quantum mechanical consideration which shows that even in these cases photons travel with the speed of light (c), and this measurement provided experimental results on the "projection" of this velocity to the axis of symmetry/beam propagation.

Motivation & Objective

• To challenge the interpretation of Giovannini et al.'s experiment claiming spatially structured photons travel slower than c in free space.
• To clarify the fundamental principle that photons in vacuum always travel at speed c, regardless of spatial structure.
• To demonstrate via quantum mechanical analysis that the observed reduction in group velocity is an artifact of projection along the beam axis.
• To resolve confusion in the literature about photon speed in structured beams by clarifying the role of group velocity in such systems.

Proposed method

• Applying quantum mechanical principles to analyze the propagation of spatially structured photons in free space.
• Focusing on the group velocity of photon wave packets and its projection along the beam propagation axis.
• Using theoretical analysis to show that the measured group velocity is not the true phase or group velocity of individual photons.
• Demonstrating that the observed slow-down is a result of the beam's spatial mode structure and its projection onto the axis, not a violation of relativity.
• Contrasting the measured group velocity with the invariant speed c of photons in vacuum.
• Highlighting that the experimental observation reflects a geometric projection effect rather than a physical reduction in photon speed.

Experimental results

Research questions

• RQ1 Can spatially structured photons in free space truly travel slower than c, as claimed by Giovannini et al.?
• RQ2 What is the true nature of the group velocity measured in experiments with structured photon beams?
• RQ3 How does the spatial structure of a photon beam affect the observed propagation speed along the beam axis?
• RQ4 Is the observed reduction in group velocity a physical effect or a mathematical projection artifact?
• RQ5 Does the measured group velocity in such experiments contradict the fundamental postulate that photons travel at c in vacuum?

Key findings

• The observed group velocity reduction in structured photon beams is not due to photons traveling slower than c, but due to projection effects along the beam axis.
• Photons in vacuum always travel at the speed of light c, regardless of their spatial mode structure.
• The measured group velocity is a result of the beam's transverse intensity profile and its projection onto the propagation axis, not a change in the photon's intrinsic speed.
• The quantum mechanical analysis confirms that the phase and group velocities of individual photons remain c, even in structured beams.
• The experimental results reported by Giovannini et al. are consistent with the standard theory of light propagation when properly interpreted.
• The paper concludes that no violation of the constancy of c occurs in vacuum, even for spatially structured photons.