### 2.6 Systematic vs. non-systematic violations

Most tests of Lorentz violation deal with systematic Lorentz violation, where the deviation is constant in
time/space. For example, consider the modified dispersion relation for a photon
where is some fixed coefficient. There is no position dependence, so the Lorentz violating term is a
constant as the particle propagates. However, various models [99, 255, 231] suggest that particle
energy/momentum may not be constant but instead vary randomly by a small amount. Some
authors have combined these two ideas about quantum gravity, Lorentz violation and stochastic
fluctuations, and considered a stochastic violation of Lorentz invariance characterized by a fluctuating
coefficient [12, 232, 24, 108, 115]. We will discuss non-systematic models in greater detail in
Section 3.5.