[Paper Review] The Vavilov-Cherenkov radiation by relict photon gas

S. G. Chefranov|arXiv (Cornell University)|Sep 3, 2010

Crystallography and Radiation Phenomena2 references3 citations

TL;DR

This paper proposes that Vavilov-Cherenkov radiation (VCR) can occur in the modern universe due to relativistic cosmic rays interacting with the relic photon gas, using a new quantum VCR theory that redefines the threshold condition. Unlike standard theory, this approach accounts for energy and momentum balance involving the medium's effective photon mass, yielding a significantly lower threshold velocity. The key result is that for Lorentz factors ≥ 2×10¹⁰, Cherenkov photon emission becomes detectable, resolving a long-standing contradiction with the GZK cutoff.

ABSTRACT

Based on the new quantum Vavilov-Cherenkov,s radiation(VCR) theory (PRL,2004),it is stated the possibility of threshold realization in the modern epoch of the novel VCR effect by the relict photon gas, when it is traversed by relativistic particles of the cosmic rays with γ\geq γ_th \cong 2 \cdot 10^10, where γ^2 = 1 - \frac{V^2}{C^2}, v is the speed of particles, and c is the speed of the light in vacuum.

Motivation & Objective

• To re-evaluate the possibility of Vavilov-Cherenkov radiation (VCR) by the relic photon gas in the modern universe.
• To resolve the contradiction between standard VCR theory—predicting an unphysically high threshold—and observational constraints like the GZK cutoff.
• To demonstrate that a revised quantum VCR theory, incorporating energy and momentum balance with the medium, allows for a feasible threshold condition.

Proposed method

• Derives a new threshold condition for VCR using energy and momentum conservation, where the medium's effective photon mass is explicitly included in the energy balance.
• Applies the Abraham representation of photon momentum in a medium, leading to a finite and real effective photon mass, in contrast to the Minkowski representation used in standard theory.
• Uses the refractive index of the relic photon gas, derived from nonlinear quantum electrodynamics, with δ ≈ 3×10⁻⁴², to compute the modified threshold velocity.
• Replaces the standard threshold condition v_th = c/n with v_th = c/n*, where n* = (n² - 1 + n)/n, significantly reducing the required particle speed.
• Estimates the number of radiated Cherenkov photons using the new threshold, comparing results under standard and new VCR theories.
• Analyzes the implications for detecting VCR in cosmic ray showers and cosmic microwave background anisotropy.

Experimental results

Research questions

• RQ1 Can Vavilov-Cherenkov radiation be realized in the modern universe by relativistic cosmic rays traversing the relic photon gas, despite the extremely small refractive index of the medium?
• RQ2 How does the new quantum VCR theory, which includes the medium's role in energy balance, alter the threshold condition compared to standard VCR theory?
• RQ3 What is the estimated number of Cherenkov photons radiated under the new threshold condition, and is it sufficient for detectability?
• RQ4 Does the new threshold condition resolve the conflict with the GZK cutoff, which forbids cosmic ray particles with γ > 10¹¹?
• RQ5 Can the VCR mechanism, as described by the new theory, explain observed anisotropies in wide atmospheric showers and the cosmic microwave background?

Key findings

• The new quantum VCR theory predicts a threshold Lorentz factor of γ_th ≈ 2×10¹⁰ for Cherenkov radiation in the relic photon gas, which is compatible with the GZK cutoff.
• The modified threshold velocity v_th = c/n* is significantly lower than the standard v_th = c/n, due to the effective refractive index n* = (n² - 1 + n)/n.
• For δ ≈ 3×10⁻⁴², the value of n* - 1 is many orders of magnitude larger than n - 1, drastically reducing the required particle speed.
• The number of radiated Cherenkov photons is estimated at ~3×10¹⁹ for a 1 Mpc path length under the new theory, which is feasible for detection, unlike the ~3×10⁵ predicted by standard theory.
• The new theory allows for transverse electromagnetic wave emission even when n < 1, removing a fundamental restriction in standard VCR theory.
• The results suggest that VCR should be considered as a potential mechanism in interpreting cosmic ray anisotropies and cosmic microwave background fluctuations.