Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness

Abstract

Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a phenomenological model of massive particles propagating in a Minkowski spacetime which arises from an underlying causal set. The particles undergo a Lorentz invariant diffusion in phase space, and we speculate on whether this could have any bearing on the origin of high energy cosmic rays.

Causal sets and conservation laws in tests of Lorentz symmetry

“…This result, on its face, is incompatible with another hypothesized effect of causal sets, a violation of translation invariance due to the so-called "swerve" effect [19]. The swerve effect, which we discuss in more detail in the next section, manifests itself at low energies via a Lorentz invariant diffusion equation in momentum space.…”

“…A change in velocity is equivalent to the particle moving to a different point on its mass shell, which is assumed to be unchanged since causal sets are Lorentz invariant. The net result of swerving is that a collection of particles initially with an energy-momentum distribution ρ(p) will diffuse in momentum space along their mass shell according to the unique Lorentz invariant diffusion equation [19,26],…”

“…The essence of our argument is that swerves, a hypothetical effect on particle propagation in causal set theory [19], can mimic a signal of LV in time of flight or threshold astrophysics experiments where the expected flux of incoming high energy particles is very low. This may seem strange, as causal sets are supposed to not give any LV signal.…”

Causal sets: Quantum gravity from a fundamentally discrete spacetime

“…There are several models considered [20,21], that in all of those, when taking the continuum approximation, the particle follows approximately timelike geodesic, but deviating (swerving) slightly. In other words it is like having some drift, and all models result in a diffusion equation depending on a single parameter the diffusion strength k. Let us here briefly describe the first model ( [20]). The particles trajectory is a chain {e 1 , e 2 , · · ·} in the causal set.…”

Spectral line broadening and angular blurring due to spacetime geometry fluctuations

“…One approach to the study of fluctuating spacetimes is stochastic gravity [1]. More generally, there has been considerable activity in recent years in the area of quantum gravity phenomenology, which seeks to find observational signatures of the quantum nature of spacetime [2,3,4,5,6,7,8,9,10,11,12]. There has also been considerable attention given to the effects of classical stochastic gravitational fields [13,14,15,16,17] and to scattering of probe particles by gravitons in an S-matrix approach [18,19].…”