[Paper Review] Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo

Giovanni Amelino-Camelia, John Ellis+3 more|Dec 7, 1997

Gamma-ray bursts and supernovaePhysics and Astronomy16 references615 citations

TL;DR

This paper proposes that gamma-ray burst (GRB) observations can probe quantum-gravity-induced dispersion in vacuum, where photon group velocity depends on energy via $\delta v \sim E/E_{\text{QG}}$. With millisecond time structure and cosmological distances, GRBs offer sensitivity to $E_{\text{QG}}$ scales near the Planck energy ($\sim10^{19}$ GeV), enabling tests of quantum-gravity models through energy-dependent time delays in high-energy photons.

ABSTRACT

The recent confirmation that at least some gamma-ray bursters (GRBs) are indeed at cosmological distances raises the possibility that observations of these could provide interesting constraints on the fundamental laws of physics. Here we demonstrate that the fine-scale time structure and hard spectra of GRB emissions are very sensitive to the possible dispersion of electromagnetic waves in vacuo with velocity differences $δv \sim E/E_{\QG}$, as suggested in some approaches to quantum gravity. A simple estimate shows that GRB measurements might be sensitive to a dispersion scale $E_{QG}$ comparable to the Planck energy scale $E_{P} \sim 10^{19}$ GeV, sufficient to test some of these theories, and we outline aspects of an observational programme that could address this goal.

Motivation & Objective

• To investigate whether gamma-ray bursts (GRBs) at cosmological distances can serve as probes for quantum-gravity effects via vacuum dispersion of electromagnetic waves.
• To assess the sensitivity of GRB observations to energy-dependent photon propagation, specifically time delays proportional to $E/E_{\text{QG}}$.
• To compare GRB sensitivity with other astrophysical sources (e.g., pulsars, supernovae, CMB) in detecting quantum-gravity effects.
• To outline an observational strategy for detecting such effects using fine time-resolution data from high-energy GRB emissions.

Proposed method

• Model vacuum dispersion using a deformed photon dispersion relation: $c^2 \mathbf{p}^2 = E^2 \left[1 + \xi E/E_{\text{QG}} + \mathcal{O}(E^2/E_{\text{QG}}^2) \right]$, leading to energy-dependent group velocity.
• Derive the time delay for photons of energy $E$ traveling distance $L$: $\Delta t \sim \xi E L / (c E_{\text{QG}})$, with $E_{\text{QG}} \sim E_{\text{P}} \sim 10^{19}$ GeV.
• Estimate the sensitivity factor $\eta = |\Delta t^*| / \delta t$, where $\delta t$ is the observed time structure, to compare GRBs with other astrophysical sources.
• Use known cosmological redshifts (e.g., $z = 0.835$ for GRB 970508) to infer path lengths $L \sim 10^{10}$ light years for distance calibration.
• Propose using lensed GRBs as a clean probe: achromatic gravitational lensing produces multiple paths with time delays, allowing energy-dependent shifts to be isolated.
• Distinguish quantum-gravity effects from source or medium effects by their energy dependence: quantum-gravity shifts increase with energy, unlike source-induced or plasma-like medium effects.

Experimental results

Research questions

• RQ1 Can gamma-ray burst observations detect energy-dependent time delays in photon propagation due to quantum-gravity-induced vacuum dispersion?
• RQ2 What is the sensitivity of GRBs to the quantum-gravity scale $E_{\text{QG}}$, particularly when $E_{\text{QG}} \sim E_{\text{P}} \sim 10^{19}$ GeV?
• RQ3 How does the sensitivity of GRBs compare to other astrophysical sources like pulsars, supernovae, and the cosmic microwave background in probing vacuum dispersion?
• RQ4 Can lensed GRBs provide a clean, achromatic baseline to isolate energy-dependent time delays from quantum-gravity effects?
• RQ5 How can observational features such as fine time structure and energy-dependent arrival times be used to disentangle quantum-gravity effects from conventional astrophysical effects?

Key findings

• GRBs with millisecond time structure and energies around 20 MeV, traveling over cosmological distances ($\sim10^{10}$ light years), yield a sensitivity factor $\eta \sim 1$ to quantum-gravity effects at the Planck scale.
• For GRBs with 1-second time structure and 100 MeV photons, or 1-hour structure and 1 TeV photons, the sensitivity remains high, indicating broad applicability across energy and timescale ranges.
• The sensitivity factor $\eta \sim 10^{-6}$ can be achieved in lensed GRB events with TeV emission, if detected by air Cerenkov telescopes like HEGRA or Whipple.
• Pulsars and X-ray sources offer much lower sensitivity ($\eta \sim 10^{-10}$ to $10^{-8}$) due to shorter distances and lower photon energies.
• Supernova neutrinos provide $\eta \sim 10^{-4}$ sensitivity, still significantly less than GRBs, due to limited distance and time resolution.
• The cosmic microwave background offers negligible sensitivity ($\Delta I/I \sim 10^{-32}$) due to the extremely small spectral distortion from velocity dispersion.