TL;DR
This paper investigates the probability of a photon exceeding light speed under Einstein dynamics with a singular dispersion relation, demonstrating it diminishes over time through advanced propagation estimates.
Contribution
It introduces novel multi-scale propagation estimates to analyze photon velocity probabilities in Einstein dynamics with singular dispersion relations.
Findings
Probability of superluminal photon movement approaches zero over time
Established minimal velocity bounds for photons under Einstein dynamics
Developed new analytical techniques for controlling low-frequency contributions
Abstract
We estimate the probability of a photon to move faster than light, under the Einstein dynamics which, unlike the wave equation or Maxwell wave dynamics, has singular dispersion relation at zero momentum. We show that this probability goes to zero with time, using propagation estimates suitably multi-scaled to control the contribution of low frequencies. We then prove minimal velocity bounds
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