Vavilov–Cherenkov radiation when cosmic rays pass through the relic photon gas and when fast charged particles traverse an optical laser beam

Using a new [9, 10] quantum theory of Vavilov–Cherenkov radiation (VCR) based on Abraham's theory, we show that a threshold VCR effect can be excited by the relic photon gas when relativistic charged cosmic-ray particles with γ ≥ γ_th ≈ 1.9 × 10¹⁰ (where γ^–2 = 1–v²/c², v is the particle speed, and c is the speed of light in a vacuum) pass through it. This is compatible with the well-known GZK cutoff [7, 8] at γ ≈ 10¹¹. We have obtained the condition γ > γ_th ≈ 2.1 × 10² for the appearance of VCR when a sufficiently fast charged particle (an electron, a proton, or a nucleus) passes through intense laser radiation. This condition ensures that VCR can be observed experimentally (e.g., on the Large Hadron Collider) without invoking any additional conditions required from the currently existing estimate of γth > 8.8 × 10⁴ [13] based on the now universally accepted quantum theory of VCR, which follows from Minkowski's theory (and which gives an estimate of γ > 10²¹ when excited by the relic photon gas).