Testing Planck-Scale Gravity with Accelerators

Quantum or torsion gravity models predict unusual properties of space-time at very short distances. In particular, near the Planck length, around ${10}^{-35}\mathrm{m}$, empty space may behave as a crystal, singly or doubly refractive. However, this hypothesis remains uncheckable for any direct measurement, since the smallest distance accessible in experiment is about ${10}^{-19}\mathrm{m}$ at the LHC. Here I propose a laboratory test to measure the space refractivity and birefringence induced by gravity. A sensitivity from ${10}^{-31}\mathrm{m}$ down to the Planck length could be reached at existent GeV and future TeV energy lepton accelerators using laser Compton scattering. There are already experimental hints for gravity signature at distances approaching the Planck length by 5–7 orders of magnitude, derived from SLC and HERA data.

Figure 1

Polarization of the Compton scattered photon on a 6 or 250 GeV electron as a function of the photon energy. The solid and dotted lines correspond to the initial laser light helicity: $+1$ solid, $-1$ dotted.

Figure 2

Experimental reach of the accelerators for vacuum birefringence and refractivity. Birefringence at the scale $\xi$ will produce a Compton edge asymmetry (lower scale), while the refractivity produces absolute energy shifts (upper scale). The Planck length $l_P$ is shown by an arrow.